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A NN A R B O R . Ml 4 8 1 0 6 18 B E D F O R D ROW. L O N D O N W C1R 4 E J . E N G L A N D 8106408 MACHADO DA SILVA, CLOVIS LUIZ. ORGANIZATIONAL EFFECTIVENESS: IN MICHIGAN A STUDY OF SCHOOL DISTRICTS Michigan State University University Microfilms International 300 N. Zeeb Road, Ann Arbor, MI 48106 PH.D. 1980 ORGANIZATIONAL EFFECTIVENESS: A STUDY OF SCHOOL DISTRICTS IN MICHIGAN By Clovis Luiz Machado da Silva A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Administration and Higher Education 1980 ABSTRACT ORGANIZATIONAL EFFECTIVENESS: A STUDY OF SCHOOL DISTRICTS IN MICHIGAN By Clovis Luiz Machado da Silva The purpose of this investigation was to analyze school district effects on aggregate levels of student aca­ demic achievement from an organizational effectiveness per­ spective. Employing the comparative method of organizational analysis with an individual school district defined as a case, the researcher tested a causal recursive model of the academic production process of school district organiza­ tions that included four environmental input factors (school district size, school district fiscal resources, average income of the families in the school district, and student racial characteristic), four school district organizational attributes (student-facuity ratio, faculty qualifications, faculty distribution, and administrative differentiation), and the selected operative goal of schooling, aggregate student academic achievement. The statistical technique used to test the model was path analysis. The study popu­ lation was Michigan K-12 school district organizations, and the data were obtained from official documents and records. Clovis Luiz Machado da Silva The posited model of the academic production pro­ cess of school district organizations basically was sup­ ported by the data. This suggests the adequacy of the framework of analysis used in the study. The findings and conclusions of the study included the following: 1. Contrary to the frequently held position that schooling makes no difference in students' academic achieve ment, it was found that at the school district level of analysis, organizational attributes do affect aggregate student academic achievement; yet, this influence is small. 2. School district size has a relevant influence on the structure of school districts in Michigan; its effect is particularly strong on the functional division of managerial and administrative labor of school district organizations. Size also shows indirect effects on aggre­ gate student academic achievement through student-faculty ratio, faculty qualifications, and administrative differ­ entiation; the opposing direction of these indirect effects suggests the difficulties to be faced by policy makers and practicing administrators in regard to the issue of optimal school district size. 3. The amount of fiscal resources available for school districts to operate affects aggregate student academic achievement through its influence on the struc­ ture of school districts. The evidence from this study Clovis Luiz Machado da Silva supports past and continuous efforts to equalize the revenues of school districts with the objective of increas­ ing educational parity. 4. As in input-output studies, the indicator of socioeconomic status (family average income) is the great­ est contributor to the explanatory power of the model in regard to aggregate student academic achievement. 5. Finally, the findings from this investigation seem to provide support to (a) the proposition that attri­ butes of school district organizations do mediate, to some degree, the relationships between environmental input factors and aggregate student academic achievement; (b) the conception of educational organizations as being loosely coupled in terms of instructional activities and tightly controlled in terms of ritual classifications and cate­ gories; and (c) the commonly accepted position that the technology of instruction is labor intensive, requiring persisting interaction between each individual teacher and his students; this suggests the centrality of the role of teachers to effective school district performance. To Heloisa, Luciana, and Angela with love. ACKNOWLEDGMENTS A number of persons and institutions contributed to the completion of my graduate program of study and to this dissertation. To them, I wish to express my appreciation and gratitude: To Dr. Frederick R. Ignatovich, academic advisor and committee chairman, who was always ready to contribute time, expertise, and encouragement. His support throughout the program of study was invaluable. To Dr. Samuel A. Moore II, Dr. Philip M. Marcus, and Dr. Ted W. Ward, who were valued members of the commit­ tee and whose interest over a long period of time was most helpful. To several members of tion and Higher Education who the Department ofAdministra­ provided support, in one way or another, during my graduate education, especially to Dr. Philip A. Cusick, Dr. Walter F. Johnson, Dr. James H. Nelson, and Dr. Stanley E. Hecker. To Dr. John M. Graves, my fellow doctoral student, who deserves special mention for his friendship and for his intellectual openness. friendship. Also to Mrs. Geneva Speas for her To Dr. Robert H. Richardson, who generously provided access to the data used in this research. Without his coop­ eration, this study would not have been possible. To the Brazilian Ministry of Education and Culture and to the Coordination for Training Higher Education Per­ sonnel, for their financial support during my graduate edu­ cation. Also to the Committee on Grants to Doctoral Students from the Sage Foundation Fund, chaired by Dr. Walter F. Johnson, for the financial support of this research. To Mrs. Susan Cooley, who edited and typed this dis­ sertation; her cooperation exceeded a simple professional duty. To my parents for all they have provided. To my brothers and sisters, especially to Dr. Moacir A. Machado da Silva for his constant support throughout the years of my graduate studies. Most of all, to my wife, Heloisa, and my daughters, Luciana and Angela, for their indispensable understanding. iv TABLE OF CONTENTS Page LIST OF T A B L E S ....................................... viii LIST OF F I G U R E S ..................................... ix Chapter I. INTRODUCTION ................................. Background ................................ Statement of the Problem ................. Theoretical Framework ................... Perspectives in the Study of Organizations ........................ Strategies Within the Organizational Perspective .......................... Approaches to the Study of Organizational Effectiveness ......... Organizational Effectiveness in E d u c a t i o n ............................ Characteristics of Educational Organizations ........................ Task-Facilitating and Task-Inhibiting A t t r i b u t e s ............................ Summary of the Theoretical Framework . . Limitations and Considerations of the S t u d y .................................. Contributions of the S t u d y ............... Overview of the S t u d y ................... II. REVIEW OF RELATED L I T E R A T U R E ............... Introduction .............................. Input-Output Studies ..................... Students' Background Factors ........... Students' Racial Characteristic . . . . Students' A b i l i t y ..................... School and School District Size . . . . Fiscal Resources ........................ Teachers' Characteristics ........... . Organizational-Effectiveness Studies . . . Conclusions From the R e v i e w ............. v 1 1 4 5 5 8 10 17 19 22 24 25 27 28 30 30 30 39 40 41 42 44 47 53 60 Page III. A MODEL OF SCHOOL DISTRICT EFFECTIVENESS . . O v e r v i e w .................................. A Causal Recursive Model of School District Effectiveness ................. The Postulated Relationships: Explanation and Discussion ........... Method of A n a l y s i s ........................ Population and Data C o l l e c t i o n ........... V a r i a b l e s ................................ Summary ............................ IV. EVALUATION OF THE BASIC M O D E L ............. Introduction .............................. The Explanation of Student-Faculty Ratio . The Explanation of Faculty Qualifications. The Explanation of Faculty Distribution . The Explanation of Administrative Differentiation ....................... The Explanation of Aggregate Student Academic Achievement: Direct Effects . . The Basic Model Revised ................. The Explanation of Aggregate Student Academic Achievement: Indirect Effects . Concluding Remarks ....................... V. SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS 63 63 63 68 89 96 100 103 104 104 106 110 113 119 124 133 136 144 . 147 O v e r v i e w .................................. Summary and Discussion ............... Conclusions and Recommendations ........ Conclusions: Summary ..................... 147 149 158 171 A P P E N D I C E S ........................................... 173 A. OPERATIONAL DEFINITION OF VARIABLES B. MEAN AND STANDARD DEVIATION OF VARIABLES . . 177 C. DATA S O U R C E S ................................. 179 D. TABLES FOR FIGURES 3 THROUGH 10 PRESENTED IN CHAPTER I V ............................ 181 MATRIX OF SIMPLE C O R R E L A T I O N S ............. 191 E. . . . . 174 Page F. CRITERION FOR THE INTERPRETATION OF THE MAGNITUDE OF THE PATH COEFFICIENTS . . . . 193 CRITERION FOR THE INTERPRETATION OF THE MAGNITUDE OF THE COEFFICIENT OF D E T E R M I N A T I O N ............................ 195 BIBLIOGRAPHY ......................................... 197 G. vii LIST OP TABLES Table 1. 2. 3. Page Mean and Standard Deviation of Variables Indicated in the M o d e l ................... 98 Decomposition of Indirect Causal Effects of Environmental Input Factors on Aggregate Student Academic Achievement Through Intervening Organizational A t t r i b u t e s ................................ 137 Decomposition of the Total Effect of Environmental Input Factors on Organi­ zational Attributes and of Environmental Input Factors and Organizational Attributes on Aggregate Student Academic A c h i e v e m e n t .................................. viii 145 LIST OF FIGURES Figure 1. 2. 3. Page A Causal Recursive Model of School District Effectiveness ................................ 65 The Basic Model of School District Effectiveness ................................ 92 Path Coefficients Between Environmental Input Factors and Student-Faculty Ratio ........... 107 4. Significant Path Coefficients Between Envi­ ronmental Input Factors and Student-Faculty R a t i o ........................................... 108 5. Significant Path Coefficients Between Envi­ ronmental Input Factors and Faculty Qualifications .............................. Ill Path Coefficients Between Environmental Input Factors and Faculty Distribution ........... 114 Significant Path Coefficients Between Envi­ ronmental Input Factors and Faculty Distribution ................................ 118 6. 7. 8. 9. Path Coefficients Between Environmental Input Factors and Administrative Differentiation . 120 Significant Path Coefficients Between Envi­ ronmental Input Factors and Administrative D i f f e r e n t i a t i o n .......... 121 10. Significant Path Coefficients Between Envi­ ronmental Input Factors/Organizational Attributes and Aggregate Student Academic A c h i e v e m e n t ................................ 128 11. The Revised Model of School District Effectiveness ................................ 135 Illustration of Indirect Effects of School District Fiscal Resources on Aggregate Student Academic Achievement Through Intervening Organizational Attributes . . . . 139 12. ix Figure 13. 14. Page Illustration of Indirect Effects of School District Size on Aggregate Student Academic Achievement Through Intervening Organizational Attributes ................. 141 Illustration of Indirect Effects of Average Income of the Families in the School District on Aggregate Student Academic Achievement Through Intervening Organiza­ tional A t t r i b u t e s ......................... 143 x CHAPTER I INTRODUCTION Background The Equality of Educational Opportunity survey (EEO) carried out by Coleman et al. (1966) was not the first major study of relationships between school characteristics and school outcomes, but since this work the issue of school effects has become a growing concern among researchers and policy makers (Erickson, 1977). However, the EEO as well as other studies that have been undertaken to determine input-output (the production-function approach) relation­ ships in education was not conducted from an organizational­ effectiveness perspective^- (Bidwell & Kasarda, 1975; Wagenaar, 1978). Researchers have analyzed relation­ ships between input and output in education without taking into consideration the organizational attributes of schools and school districts. Even though the call for inquiry into the deter­ minants of school effects from the standpoint of organiza­ tional effectiveness can be traced back at least to Halpin (1957), "only in the past ten years have school analysts iThis term is defined and discussed in a later sec­ tion of this chapter. 2 diligently applied the organizational approach to school issues" (Wagenaar, 1978, p. 609). According to Erickson (1977), four major explana­ tions can be given for the lack of research concerning school effects from the standpoint of organizational effec­ tiveness: (1) the difficulty in obtaining clear evidence of organizational effects in view of the powerful influence of genetic and environmental factors, (2) the constant pre­ occupation of most scholars with disciplinary concerns; (3) the interdisciplinary effort of some scholars to under­ stand organizations in the abstract, with little regard for specific settings such as education; and (4) the notion, in some universities, that research designed to arrive at implications for policy decisions is inferior. The development of more sophisticated research methodology and statistical tools, on the one hand, and a change in the perspective of scholars, on the other, have resulted in a growing concern with organizational effec­ tiveness (Steers, 1977). paradigmatic shift: Erickson (1977) attested to this "A deep-seated fixation on organiza­ tional process and structure in their own right may be giving way to systematic work on causal models that link structure and process to organizational outcomes, including outcomes that virtually all educational leaders must strive to achieve" (p. x ) . 3 As a consequence of this, several investigators have acknowledged the need to carry out research that deals with the issue of school effects from the standpoint of organizational effectiveness (see, for example, Bidwell & Kasarda, 1975; Erickson, 1977; Wagenaar, 1978). There is a growing concern with the use of causal models for study­ ing the effectiveness of educational organizations. This was observed by Erickson (1977), who stated that "we need intense work on causal models linking process and struc­ ture to student behavior and long-term accomplishment. We must produce theories of educational organization and edu­ cational product" (p. 4). In line with the preceding argument, Bidwell and Kasarda (1975) pointed out the need for causal analytic "school effects" studies in which an attempt is made to determine whether and, if so, how organi­ zational attributes mediate the relationships between envi­ ronmental input factors and organizational outputs. Bidwell and Kasarda further observed that the need for causal models of organizational effectiveness is not restricted to educational-type organizations but is applicable to all types of organizations. In their words, "We badly need empirical studies, conducted in a variety of organizational settings, that use well defined models of the links between input and output" (p. 55). 4 Statement of the Problem In this study the problem of school district effects on aggregate levels of student academic achievement from an organizational-effectiveness perspective was addressed. Employing the comparative method of organiza­ tional analysis with an individual school district defined as a case, the researcher attempted to examine hypotheses concerning the links (school district organizational attri­ butes) between inputs (environmental factors) and output (students' academic achievement aggregated at the school district level) using a framework of analysis for studying organizational effectiveness proposed by Bidwell and Kasarda (1975), Steers (1977), and Zey-Ferrell (1979). Given the posited research problem, the researcher tested a causal recursive model^ of school district effec­ tiveness that encompassed the following three sets of variables: 1. Concerning school district environmental input factors: 2 a. school district fiscal resources, b. school district size, c. average income of families in the school district, and d. students' racial characteristic; ^The proposed causal model is discussed in detail in Chapter III. 2 This variable is treated in the singular throughout the dissertation since it constitutes a collective noun. 5 2. Concerning school district organizational attributes: 3. a. student-faculty ratio, b. faculty qualifications, c. faculty distribution, and d. administrative differentiation; and Concerning school district output: aggregate student academic achievement. The study population of interest consisted of 508 Michigan K-12 school district organizations out of 530 public K-12 school districts in Michigan during the 1975-76 school year. Theoretical Framework Perspectives in the Study of Organizations Three basic perspectives for studying organizations can be identified in the organizational theory and research literature: the individual perspective, the group perspec­ tive, and the organizational perspective {Blau, 1965; Blau & Meyer, 1971). The individual perspective is focused on "the char­ acteristics and behavior of individuals in their roles as members of organizations" (Blau & Meyer, 1971, p. 81). In a more recent treatment of the matter, Roberts, Hulin, and Rousseau (1978) summarized this perspective as being con­ cerned with individual-level phenomena such as the 6 relationship between employees' satisfaction and their performance, absenteeism, and turnover. Given that the unit of analysis is the individual, advocates of this per­ spective assume characteristics of the organization as a whole to be constant. The group perspective is concerned with "the struc­ ture of social relations among individuals in the various groups within the organization" Roberts, Hulin, and Rousseau (Blau, 1965, p. 325). (1978) underscored Blau's characterization, observing that this perspective focuses on the nature of social interactions among group members, examining processes through which group members influence one another's attitudes, perceptions, and behavior. As in the individual perspective, organizational attributes are givens when the group is the unit of analysis. The organizational perspective1 entails "the system of interrelated elements that characterizes the organization as a whole" (Blau, 1965, p. 325). These elements are organizational attributes such as division of labor, hier­ archy of authority, centralization, and standardization. This perspective, which reflects the structural view of organizations (Perrow, 1970), may focus on the interrela­ tions between the organizational attributes; the relationship 1The terms "organizational perspective," "organiza­ tional approach," "organizational dimension of analysis," and "organizational analysis" have been used interchangeably in the organizational theory and research literature. 7 between organizational attributes and organizational envi­ ronment; the relationship between organizational attributes and organizational performance; and the relationship between organizational environment, organizational attri­ butes, and organizational performance {Roberts, Hulin, & Rousseau, 1978; Steers, 1977; Zey-Ferrell, 1979). The unit of analysis is the organization as a whole; therefore, indi­ vidual behavior and group processes are taken for granted. Under each of these three perspectives, the atten­ tion of the researcher is directed to particular aspects of the organization. As Blau and Meyer (1971) observed, these three perspectives "focus attention upon different phenomena in the study of organizational life" (p. 82). The obvious disadvantage of studying an organization from a particular perspective is that any systematic analysis from one perspective excludes aspects of the organization that might be considered from other perspectives. In addition, each perspective leads to different methodologi­ cal problems 1979). (Blau, 1965; Richardson, 1978; Zey-Ferrell, The organizational perspective,1 for example, requires the use of the comparative method of analysis since theoretical explanations of why organizations have certain characteristics and how these characteristics relate to each other depend on comparisons of many organizations (Blau, 1965). 1For a critique of this perspective, see Argyris (1972). 8 Strategies Within the Organizational Perspective Within the organizational perspective, two funda­ mental theoretical strategies can be identified: closed-system and the open-system strategy.^" the These two strategies differ basically in terms of the factors that are regarded as functioning as explanatory variables. Under the closed-system strategy, components within the organization are considered as explanatory variables (e.g., structure, technology). With the open-system strategy, on the other hand, environmental factors are regarded as explanatory variables (e.g., resources) since organizations are viewed as adjusting or adapting to their environment (see Hall, 1977? Thompson, 1967? Zey-Ferrell, 1979). Closed-system strategy.— As described by Hall (1977), Thompson (1967), and Zey-Ferrell (1979), in closed- system strategy a rational view of organizations is taken. Assuming rationality, organizational goals and performance are expected to result from technological, structural, and process factors zation. (explanatory variables) within the organi­ It is assumed that if the organization is well ^•The terms "closed-" and "open-systerns strategies" (approaches, perspectives, models) have been used inter­ changeably in the organizational literature. Closed-system and open-system strategies are not used only within the organizational perspective. However, since this researcher adopted the organizational perspective, these strategies are discussed only in this context. 9 structured it will function as a well-integrated system with a high level of performance. Using this strategy greatly facilitates the work of the researcher since it is not concerned with the dynamics between the organization and its environment; "however, the resulting knowledge is incomplete and often inaccurate" (Zey-Ferrell, 1979, p. 36). On the other hand, Rice and Bishoprick (1971) pointed out that there never was, and probably never will be, a com­ pletely closed system because components are always influenced by forces not being considered— that is, by forces outside the system itself. But closed system analysis as a way of thinking about the inter­ action of components is extremely useful (p. 165). Open-system strategy.— Hall (1977), Thompson (1967), and Zey-Ferrell (1979) pointed out that in the open-system strategy organizations are considered to be dependent on factors from the external environment (explana­ tory variables), and the constant interchange between the external systems and the internal system is recognized. The organization's continual effort to maintain its rela­ tionships with the external environment is reflected in the organization's process, technology, structure, and per­ formance. The organization is viewed not as trying to attain goals but rather as meeting its needs for adapta­ tion and survival, Zey-Ferrell (1979) noted that although the open-system strategy offers a relatively comprehensive conceptual framework, it imposes difficulties on the work 10 of the researcher in view of the abstractness and breadth of the concepts of adaptation and survival as criteria for the assessment of organizational performance. Combined strategy.— In the past few years, several organizational analysts have attempted to combine the best attributes of both the closed- and the open-system strate­ gies (Zey-Ferrell, 1979). In the combined strategy, the organization is viewed as a goal-seeking entity that is open and constantly adjusting to its environment. The organization is placed in a position of constantly defin­ ing, evaluating, and dealing with environmental uncer­ tainty; but at the same time, it is subject to the need for rationality {goal-seeking behavior), requiring predicta­ bility and certainty in order to survive (Steers, 1977; Thompson, 1967; Zey-Ferrell, 1979). As Zey-Ferrell (1979) stated, "Organizations attempt to be rational, controlling their internal and external environment to the best of their ability" (p. 44). Approaches to the Study of Organizational Effectiveness The present study was concerned with school district organizational effectiveness, i.e., with the issue of "school effects" from the standpoint of the organizational perspective. Approaches to the study of organizational effectiveness vary according to the particular strategy adopted within the organizational perspective: the 11 closed-system strategy, the open-system strategy, or the combined strategy. The closed-system strategy entails what is known as the goal approach for studying organizational effectiveness; the open-system strategy entails what is known as the system-resource approach for studying organizational effectiveness; finally, the combined strategy comprises more recent attempts (Steers, 1977; Zey-Ferrell, 1979) to produce a combined approach for studying organizational effectiveness— hereafter termed the combined approach. The traditional approach to the study of organiza­ tional effectiveness that has been widely used by organi­ zational researchers is the goal approach (Georgopoulos & Tannenbaum, 1957; Hall, 1977; Price, 1968; Zey-Ferrell, 1979). In the goal approach, effectiveness is defined "in terms of the degree of goal achievement" p. 3). (Price, 1972, It can be seen that the goal concept is central in this definition of organizational effectiveness. to Etzioni According (1964), "An organizational goal is a desired state of affairs which the organization attempts to realize" (p. 6). Keeley (1978) noted that "the idea of organizations as goal-attainment devices is widely accepted by organiza­ tional theorists" (p. 272). Moreover, the goal concept is crucial not only to the study of effectiveness but for the whole field of organizational theory as well, since it is the defining characteristic of organizations 1956). In the words of Etzioni (Parsons, (1964), "Organizations are 12 social units (or human groupings) deliberately constructed and reconstructed to seek specific goals” (p. 3). Thus, in the goal approach, organizational goals express intents, which are translated into yardsticks for assessing organi­ zational effectiveness. Organizational analysts usually distinguish two types of organizational goals: official and operative. According to Perrow (1961), "Official goals are the general purposes of the organization as put forth in the charter, annual reports, public statements by key executives and other authoritative pronouncements" (p. 855). Operative goals, on the other hand, "designate the ends sought through the actual operating policies of the organization; they tell us what the organization actually is trying to do, regardless of what the official goals say are the aims" (p. 855). Hall (1977) observed that operative goals can either reflect the official goals of the organization, in that they are abstractions made more concrete, or they might not necessarily have any connection with the official goals. Thus, operative goals reflect the derivation of a set of goals from both official and unofficial sources. The goal approach summarized above has been criti­ cized by several organizational analysts, especially Etzioni (1964), Katz and Kahn shore (1967). (1966, 1978), and Yuchtman and Sea­ Official goals have been criticized in view 13 of their nonoperational character; they have been seen to reflect future states that are too vaguely defined to serve as standards for the assessment of organizational effec­ tiveness (Keeley, 1978). On the other hand, two major criticisms are usually made concerning operative goals: (1) organizations usually have multiple and conflicting operative goals that prevent them from being fully effec­ tive, and (2) different constituencies may value different operative goals as criteria for assessing organizational effectiveness (Hall, 1977; Keeley, 1978). Thus, despite the recognized importance of goals in studying organiza­ tions, they remain a problematic issue for assessing organi­ zational effectiveness. The goal approach results from a rationalistic view of organizations. This approach is based on the closed- system strategy for studying organizations (Hall, 1977; Thompson, 1967; Zey-Ferrell, 1979). The most widely known alternative conceptual framework for studying organiza­ tional effectiveness is the system-resource approach, introduced by Yuchtman and Seashore (1967). According to these organizational analysts, the system-resource approach, which is based on the open-system strategy (Hall, 1977; Thompson, 1967; Zey-Ferrell, 1979), eliminates some of the pitfalls of the goal approach because organizational goals are not considered. Accordingly, organizational effective­ ness is defined as the organization's "bargaining position. 14 as reflected in the ability of the organization, in either absolute or relative terms, to exploit its environment in the acquisition of scarce and valued resources” (Yuchtman & Seashore, 1967, p. 898). In the system-resource approach, the contin­ uous processes of exchange and competition over scarce and valued resources among organizations determine any particular organization's "bargaining position" in rela­ tion to resources and in relation to competing organiza­ tions that share all or part of the organization's environ­ ment. It is in the arena of exchange and competition over scarce and valued resources that the performance of organi­ zations can be assessed comparatively. An organization is most effective when it "maximizes" its bargaining position and "optimizes" its resource procurement. The idea of optimization instead of maximization of return to the organi­ zation in its interaction with its environment is emphasized. Yuchtman and Seashore (1967) observed that the con­ cept of "bargaining position" implies the exclusion of any specific goal as the ultimate criterion of organizational effectiveness, which eliminates the pitfalls of dealing with organizational goals. The system-resource approach has been criticized by several organizational analysts (especially by Hall, 1977; Mohr, 1973; Price, 1972; and Steers, 1977). One of the major criticisms of the system-resource approach 15 concerns its exclusion of goals as standards for the assess­ ment of organizational effectiveness. According to Keeley (1978), advocates of the system-resource approach fall short in the analysis of organizational effectiveness because they "sidestep goal disputes by emphasizing the attainment of means to unspecified goals" (p. 275). Mohr (1973) supported this view: Unfortunately, without the concept of organizational goal, resource acquisition fails to satisfy as a cri­ terion of effectiveness. . . . In truth, the determi­ nation of which resources one should count either must be arbitrary or must appeal to the concept of organi­ zational goal. It is possible to find in some manner that the goal of a specific organization is, purely and simply, to acquire certain resources. If that is not the case, then one must identify other goals in order to establish which resources are important for attaining them" (p. 472). Moreover, several organizational analysts (Hall, 1977; Steers, 1977; Zey-Ferrell, 1979) have observed that the advocates of the system-resource approach underestimate the utility of the goal approach because they attach the meaning of "ultimate mission" (official goal) to the goal concept and ignore the notion of operative goals, which is regarded as a very workable one for the assessment of organizational effectiveness. The preceding considerations have led some organi­ zational analysts to regard both approaches as incomplete and unsatisfactory. In fact, the strength of one is the weakness of the other. The strength of the goal approach, defined in terms of operative goals, is its concern for 16 organizational goals. As Keeley (1978) observed, "The goal approach has one obvious advantage. Though goals may vary from organization to organization, resulting in diverse operating criteria of effectiveness, the goal notion itself does provide a theoretical point of reference for reducing this diversity" (p. 272). Or, in Hall's (1977) words, "In a very real sense, if organizational research is to be any­ thing more than simply descriptive, it must be concerned with goals" (p. 73). Yet, since the goal approach employs a closed-system strategy, it has the weakness of not pro­ viding the necessary attention to the relationships between the organization and its environment. Conversely, the system-resource approach, which employs an open-system strategy, has the strength of con­ centrating on the relationships between the organization and its environment; its weakness is underestimating the usefulness of operative goals. It seems that a fruitful strategy would be to combine the strengths of each approach into a single con­ ceptual framework for studying organizational effective­ ness. This was suggested by Steers (1977) and Zey- Ferrell (1979), who recognized the complementary character of both approaches. Steers (1977) attempted to formulate this combined conceptual framework; he defined effective­ ness "in terms of an organization's capacity to acquire and utilize its scarce and valued resources as expeditiously 17 as possible in the pursuit of its operative and operational goals" (p. 5). Such a definition of organizational effec­ tiveness is based on both the open-system strategy and the notion that organizations are purposive social units. Thus, it allows for the recognition that a series of envi­ ronmental constraints as well as the technology and the internal structure of the organization serve to inhibit or facilitate the extent to which goal achievement is opti­ mized. Organizational Effectiveness m Education Besides adopting the combined conceptual framework introduced by Steers (1977), it was assumed in this study that organizations, instead of being typified by the same effectiveness criteria, have different characteristics, goals, and constituencies. Each functional type of organization "requires a unique set of effectiveness cri­ teria" (Cameron, 1978, p. 605). Etzioni (1964) under­ scored this argument, stating that a well-developed organizational theory will include statements on the functional requirements various organizational types must meet. . . . At present, organizational theory is generally constructed on a high level of abstraction, dealing mainly with gen­ eral propositions which apply equally well— but also equally badly— to all organizations (p. 18). Since this research project was concerned with the effectiveness of school districts, which can be classified as a functional type of organization, the operative goal 18 of schooling that was selected as the criterion variable was students' academic achievement aggregated at the school district level. It has been observed (Thompson, 1967; Hauser, 1972) that the goals of school organizations are many and vaguely defined; hence there is a good deal of dis­ agreement among school personnel concerning the identifi­ cation of goals and their degree of importance. However, whatever the goals of schooling and whatever their relative importance, students' academic achievement is one of them. There is consensus among policy makers, school personnel, and investigators that academic achievement is one of the most important goals of school organizations. In the words of Bidwell and Kasarda (1975), "While the goals of schooling are many and vague, the academic attainment of students is clearly among them" (p. 57). This statement was reinforced by Wagenaar (1978), who observed that "consensus exists regarding the salience of basic skills achievement as the major goal school personnel emphasize, especially when the day-to-day operations of school are examined" (p. 610). Given that aggregate student academic achievement was the criterion variable to be used in this study, the following question was set forth: To what extent do school district organizational attributes mediate the relation­ ships between environmental input factors and school dis­ trict aggregate student academic achievement? 19 To answer this question, it is necessary to char­ acterize school district organizations and to discuss why their attributes are regarded here as intervening variables between environmental inputs to schooling and the selected operative goal— aggregate student academic achievement. Characteristics of Educational Organizations Several organizational analysts have conceptualized educational organizations (schools, school districts) as bureaucracies (Anderson, 1968? Bidwell, 1965; Hoy & Miskel, 1978). Bidwell (1965) observed that school systems display in "rudimentary forms" the following bureaucratic characteristics: 1. a functional division of labor (e.g., the alloca­ tion of instructional and coordinative tasks to the school-system roles of teacher and adminis­ trator) ; 2. the definition of staff roles as offices, that is, in terms of recruitment according to merit and competence, legally based tenure, functional specificity of performance, and universalistic, affectively neutral interaction with clients; 3. the hierarchic ordering of offices, providing an authority structure based on the legally defined and circumscribed power of officers, a system of adjudication of staff disputes by reference to superiors, and regularized lines of communication; 4. operation according to rules of procedure, which set limits to the discretionary performance of officers by specifying both the aims and modes of official action (p. 974). Furthermore, following the work of March and Olsen (1976), Meyer and Rowan (1978), Meyer et al. (1978), Pajak (1979), and Weick (1976), educational organizations were 20 viewed in this study as bureaucracies that are loosely coupled in terms of instructional activities and tightly controlled in terms of ritual classifications and cate­ gories. "Loosely coupling is a term which describes the weakness or relative absence of control, influence, coor­ dination, or interaction between events or parts of an organizational system" (Pajak, 1979, pp. 83-84). Con­ versely, "tightly controlled" describes the presence of control, influence, coordination, or interaction between events or parts of an organizational system. Awareness of these characteristics of educational organizations is impor­ tant in understanding the relationship between their organi­ zational structure and their technology, external environ­ ment, and operative goals. Thompson (1967) observed that the nature of the task an organization performs and the environment in which it functions determine in large part its organizational struc­ ture. Concerning educational organizations, however, the influence of the external environment upon structure is greater than the influence of the task since structure and instructional activities are loosely coupled (Weick, 1976). That is, instructional activities take place in the isola­ tion of the classroom, receiving only marginal control. As Meyer et al. (1978) stated, "Instructional work tends to go on beyond the purview of the formal organizational structure of the school and district" (p. 259). 21 Given that educational organizations are loosely coupled in terras of instructional activities, how do they survive and achieve stability, and why do they generally have the same characteristics? The answer suggested by Weick (1976) and further developed in the articles by Meyer and Rowan (1978) and Meyer et al. (1978) is that educational organizations are stable because "they are highly institutionalized, as a structural form, in society" (Meyer et al., 1978, p. 260). That is, the maintenance of tight control over matters of categorization legitimizes and gives meaning to educational organizations' internal processes and at the same time justifies their existence to society. As Pajak (197 9) pointed out, in schools and districts students are categorized according to grade level, age, ethnic background, and residence; teachers are categorized as elementary or secondary and according to subject areas and grade levels; curricular topics are assigned to grade levels and teachers; students, teachers, and topics are organized according to specific rules; and so on. As observed, within this context the environment grows in importance because it is regarded as the major determinant of the structure of school district organiza­ tions. It affects the structure of the school district, which, in turn, constrains and facilitates the instructional 22 activities and, as a consequence, inhibits and facilitates students' academic achievement. Task-Facilitating and TaskInhibiting Attributes The institutionalized structure of school district organizations facilitates aggregate student academic achieve­ ment through certain attributes that enhance the instruc­ tional process. Conversely, it constrains aggregate student academic achievement through certain attributes that inhibit the instructional process. attributes That is, certain organizational (such as student-faculty ratio) are understood to facilitate instructional activities and, as a conse­ quence, may result in higher student academic achievement. This prediction was derived from the commonly accepted position (Bidwell, 1965; Bidwell & Kasarda, 1975; Wagenaar, 1978) that the technology of instruction is labor intensive, requiring "persisting interaction between an individual teacher and his students" (Bidwell, 1965, p. 975), and that the division of labor in schools provides a great amount of discretionary power to teachers working within the boun­ daries of the classroom. As Bidwell and Kasarda (1975) pointed out, "The more students a teacher must handle dur­ ing a class session, the less refined (i.e., the less adaptive to specific performances and characteristics) his response to them is likely to be" (p. 62). 23 On the other hand, certain organizational attri­ butes (such as administrative differentiation) constrain instructional activities and thus may lower students' academic achievement. This prediction was derived from the preceding argument— that in schools and districts, organizational structure is loosely coupled with instruc­ tional activities. Since the organizational structure is derived from the institutionalized rules of the environment and not from the coordinative requirements of instruction, administrative components directed toward exercising con­ trol over matters of categorization are likely to constrain the instructional work of teachers, diverting them from instruction and consequently depressing students' academic achievement. As Weick (1976) observed, "the tasks of edu­ cational organizations do not constrain the form of the organization but rather this constraint is imposed by the ritual of certification and/or the agreements that are made in and by the environment" (pp. 12-13). However, adminis­ trative differentiation does not include only administrative components directed toward exercising control over matters of categorization; it also includes administrative compo­ nents (such as instructional supervision) that are directed toward contributing to the instructional work of teachers, consequently attempting to increase students' academic achievement. However, given the uncertainty and ambiguity that surround the technology of instruction (Weick, 1976; 24 Meyer et al., 1978), which engender a great amount of vague­ ness concerning the link between instructional work (tech­ nical means) and students' academic achievement (operative end), it is likely that administrative components directed toward exercising control over matters of categorization would divert the faculty from instructional work at a rate not overcome by administrative components directed toward contributing to instructional work (see Bidwell & Kasarda, 1975). Thus, overall, it is likely that adminis­ trative differentiation decreases aggregate student academic achievement. The obvious proposition that follows the preceding considerations is that organizational attributes that facili­ tate instructional activities, hereafter referred to as task-facilitating attributes, will increase aggregate stu­ dent academic achievement, and organizational attributes that inhibit instructional activities, hereafter referred to as task-inhibiting attributes, will lower aggregate stu­ dent academic achievement. Summary of the Theoretical Framework The theoretical framework used in this study to assess school district effectiveness comprises three basic components: environmental input factors, school district organizational attributes, and the criterion variable— aggregate student academic achievement. In view of the 25 preceding arguments, school district organizational attributes were regarded as intervening variables between envi­ ronmental input factors and aggregate student academic achievement. It was observed, however, that a school dis­ trict does not relate to its environment as a passive element; rather, the relationship is one of exchange. School districts receive inputs from the environment and produce outputs for the environment. The environment imposes constraints upon school districts, and school dis­ tricts place constraints on the elements in their environ­ ments . The selection of the variables that compose the causal model tested in this study as well as the hypothe­ ses depicted in it was influenced by Bidwell and Kasarda*s (1975) "Model of School District Organization and Student Achievement," the preceding theoretical discussion, find­ ings of empirical research reported in Chapter II, special features of the study population, and anticipated data availability. Limitations and Considerations of the Study A limitation of this research is that the school district output variable, aggregate student academic achievement, was measured only at the elementary-school level. This limitation was a result of the nonexistence of standardized achievement tests for the study population 26 of interest at the secondary-school level. Since the other variables included in the proposed causal model reflected measures of the whole school district, it was necessary to assume proportional relations of these variables concern­ ing elementary- and secondary-school levels across school districts. As a consequence, the results were cautiously interpreted as reflecting school district effectiveness at the elementary-school level. Also, this study was somewhat limited by the absence of a direct measure of student ability since the need to include this factor in any type of study of "school effects" is generally acknowledged in view of its relation­ ship to student achievement (see, for example, Alexander & Griffin, 1976a, 1976b; Hannan, Freeman, & Meyer, 1976; Hanushek, 1970; Hanushek & Kain, 1972; Spady, 1973). Nevertheless, no measure of students' ability is available for all school districts in Michigan. Further­ more, conventional measures such as IQ scores are generally regarded as inadequate (Bidwell & Kasarda, 1976b; Hanushek, 1970; Whimbey & Whimbey, 1975). As a consequence, this researcher used two proxy measures'*’ of aggregate student ability and motivation, which are generally regarded as reasonably sound at the aggregate level to circumvent the most serious problems (see Bidwell & Kasarda, 1976b; Hanushek, 1970). ^These proxy measures are discussed in Chapter III. 27 A particularly important point to be kept in mind throughout this dissertation is that this was a study of the effectiveness of educational organizations at the school district level of analysis.1 As such, it was concerned with the overall "academic production process" of school district organizations and not with a theory of academic achievement of individual students. That is, the fundamental concern was with students' academic achievement aggregated at the school district level of analysis and not with individual students' academic achievement. This concern with aggregate- level research is clearly expressed in the theoretical frame of reference and in the posited research problem. It fol­ lows that the proposed causal model attempted to explain between-district variation in aggregate levels of student academic achievement. Contributions of the Study This study contributes to organizational effec­ tiveness research and theory in general, and to school district effectiveness research and theory in particular, by testing a causal recursive model that depicts how the organization of school districts mediates the relationship 1This position is based on Bidwell and Kasarda's arguments (1975, 1976a, 1976b). For a criticism of this position, see Alexander and Griffin ( 1976a, 1976b) and Hannan, Freeman and Meyer ( 1976). For other considerations, see also Borgatta and Jackson (1979) and Roberts, Hulin, and Rousseau (1978, pp. 81-109). 28 between educational inputs and output. The acknowledgment that this way of thinking about organizational effective­ ness is a fruitful one has been increasing in the pertinent literature in the last few years (see, especially, Bidwell & Kasarda, 1975; Erickson, 1977; Steers, 1977; Zey-Ferrell, 1979). Furthermore, this investigation has the potential to provide important information for practicing adminis­ trators. From the standpoint of policy decisions, several of the tested hypotheses encompass variables that can be manipulated by school administrators with the goal of improving aggregate student academic achievement. Nevertheless, a word of caution is necessary: Because this study follows a new theoretical approach to the study of organizational effectiveness in general and to the study of school district effectiveness in particular, there is the need for repeated research using further elaborated models before any attempt is made to draw con­ clusive policy recommendations. Overview of the Study This study is organized in five chapters. The introductory chapter provided the background, the research problem, the theoretical framework, the limitations, and the anticipated contributions of the investigation. The second chapter is concerned with the review of related 29 literature. In the third chapter, the hypothetical causal model is diagrammatically presented, along with the rationale for each hypothesis and for the network of relations that compose the explanation of school dis­ trict organizational effectiveness. This chapter also includes overall considerations of the statistical method­ ology used for testing the model and a brief description of the study population and data-collection procedures. In the fourth chapter, the findings are analyzed, and the goodness of fit of the hypothesized model is discussed. Finally, the fifth chapter contains a summary of the find­ ings and conclusions of the study, as well as recommenda­ tions for further research. CHAPTER II REVIEW OF RELATED LITERATURE Introduction The review of related literature in this chapter is presented in two parts. In the first part, research findings concerning "school effects" from input-output studies— the educational production-function approach— are reviewed. In the second part of the chapter, research findings concerning "school effects" from organizational­ effectiveness investigations are reported. Input-Output Studies In this section, the findings of a number of empirical investigations of "school effects" that have used the "educational production-function approach" are reviewed. The general formulation of the educational production function that underlies most of the inputoutput studies has been expressed and discussed by several scholars (see, for example, Averch et al., 1972; Hanushek, 1970; Levin, 1976). One such presentation and discussion of the general formulation of the educational production function was pro­ vided by Averch and associates (1972) in their review of 30 31 several substantial input-output studies. In their presentation, it can be observed that in most input-output studies a student's educational outcome is regarded as some function of the following three sets of variables: 1. Student's background factors, which include measures of his/her family and/or community socioeconomic status and the racial composition of the student body and/or the community; 2. Peer group influences, which usually include measures of aspirations, attitudes, motivation, and educa­ tional attainment of the student's classmates; and 3. School resources, which include measures of a variety of school factors such as teachers' qualifications, teachers' experience, pupil-teacher ratio, per pupil expenditures, and number of library books per pupil (pp. 31-36). Averch and associates' preceding formulation of the educational production function is basically in line with the ones provided by Levin (1976) and Hanushek (1970), except it excludes any consideration of students' initial or innate endowments. Averch and associates' exclusion of students' initial or innate endowments in their version of the general formulation of educational production function is understandable since this factor is usually omitted in input-output studies, given the cur­ rent difficulties in obtaining a reliable measure of this 32 concept (Hanushek, 1970; Hanushek & Kain, 1972; Levin, 1970). Nevertheless, it is important to point out that the absence of any measure of initial or innate endow­ ment may be a source of specification biases (Hanushek & Kain, 1972; Levin, 1970, 1976; Spady, 1973). As Hanushek and Kain (1972) observed, If innate ability is independent of the explanatory variables included in the model, it simply will increase the size of the error term— that is, reduce the amount of variance explained by the model. But, if within the sample experience it is correlated positively with any of the explanatory variables, its influences will be represented by these included explanatory variables (p. 129). The basic research problem in the input-output approach is to identify the relationships between inputs and output, i.e., the extent to which output variations can be explained by input variations. Multiple regression is the statistical technique used most often to estimate the relationships between inputs and output (Averch et al., 1972; Campbell, Bridges, & Nystrand, 1977; Cohn & asso­ ciates, 1975). The intended policy implication of input-output studies is that once the relative effectiveness of each school resource is identified, administrators can make opti mum use of those resources to improve students' educational outcomes (Averch et al., 1972; New York State Education Department, 1972). According to Levin (1976), school resources inputs "are of particular interest to economists in their quest for efficiency, for these resources 33 represent the ones that are purchased by the school bud­ get and for which resource allocation decisions can be made" (pp. 292-93). Although most investigators using the input-output approach have acknowledged that schools are multi-purpose organizations, their studies have usually included only output defined in terms of students' cognitive achievement as measured by standardized achievement tests (Averch et al., 1972; New York State Education Department, 1972). The common inclusion of only cognitive output is a result of the present lack of knowledge regarding noncognitive outputs of schooling (Levin, 1976). Several investigators have already discussed the limitations imposed by the use of such a single output measure (see, for example, Averch et al., 1972; Cohn, 1972, 1979; Cohn & associates, 1975; Gintis, 1971; Levin, 1976; Spady, 1973). The best-known input-output study is the Equality of Educational Opportunity survey (EEO) conducted by Coleman et al. (1966). As Erickson (1977) observed, the EEO was not, of course, the first major sophisticated study of relationships between school characteristics and valued school outcomes. . . . But EEO commanded such interest from the academic community (as well as from elsewhere) that it may be regarded as a major catalyst of the current growing research thrust in the area of "school effects” (p. 112). According to Smith (1972), Coleman and his asso­ ciates assumed that the following five sets of variables additively determine a student's achievement: 34 1. 2. 3. 4. 5. His home background experience, The characteristics of his student-body peers, The school's facilities and curriculum, His teacher's characteristics, Other unmeasured factors of his heredity and environment (p. 234). Applying this linear statistical model to the data collected, Coleman et al. (1966) arrived at the following conclusions regarding the relationships between these sets of variables and students' academic achievement: 1. 2. 3. 4. 5. 6. 7. The great importance of family background for achievement; The fact that the relation of family background to achievement does not diminish over the years of school; The relatively small amount of school-to-school variation that is not accounted for by differences in family background, indicating the small inde­ pendent effect of variations in school facilities, curriculum, and staff upon achievement; The small amount of variance in achievement explicitly accounted for by variations in facili­ ties and curriculum; Given the fact that no school factors account for much variation in achievement, teachers' charac­ teristics account for more than any other char­ acteristics of the school; The fact that the social composition of the student body is more highly related to achievement, inde­ pendently of the student's own social background, than is any school factors; The fact that attitudes such as a sense of control of the environment, or a belief in the respon­ siveness of the environment, are extremely highly related to achievement, but appear to be little influenced by variations in school characteristics (p. 325). The overall conclusion in the report was that "schools bring little influence to bear on a child's achievement that is independent of his background and gen­ eral social context. . (Coleman et al., 1966, p. 325). 35 The Report by Coleman and his associates was the object of a number of criticisms by several scholars. Some of the criticism focused on inadequacies of the data, particularly the relatively low response rate, the possibility of nonrandomness in the pattern of responses, and the treatment of nonresponses to particular question­ naire items. Other criticisms concerned the methodology and interpretation of results, the basic argument being that in the measurement of variables and selection of statistical techniques, the EEO survey was biased toward underestimation of the importance of school characteris­ tics in students' academic achievement (see Bowles & Levin, 1968a, 1968b; Cain & Watts, 1970, 1973; Carver, 1975; Erickson, 1977; Hanushek & Kain, 1972; Herriott & Muse, 1973; Jencks, 1972; Spady, 1973). Within the realm of methodology and interpreta­ tion of results, a specific criticism by Bowles and Levin (1968a) is especially important in this investigation's framework: It refers to the probable overestimation of the effect of students' background factors on their aca­ demic achievement; i.e., given that students' background factors and school resources are correlated, Coleman and associates' decision to enter students' background factors into the regression equation before school resources resulted in their attributing entirely to students' back­ ground factors the variance in achievement that both sets 36 share. As a consequence, "the importance of background factors in accounting for differences in achievement is systematically inflated and the role of school resources is consistently underestimated" (Bowles & Lewin, 1968a, p. 16). A reexamination of the EEO survey data undertaken by an interdisciplinary faculty seminar on the Coleman Report at Harvard University addressed, among other things, the aforementioned criticism by Bowles and Lewin. The work of members of this seminar, examining the magni­ tude of the variance accounted for by the resources mea­ sures before controlling for background variables, failed to support the criticism that the fraction of total vari­ ance explained by school resources is seriously understated in the Coleman Report (Smith, 1968). Overall, the reanaly­ sis of the EEO data by members of the seminar upheld the major findings and interpretations presented in the Coleman Report (see Mosteller & Moynihan, 1972). Jencks (1972) raised several technical criticisms of the Coleman Report. However, in his subsequent reanaly­ sis of the data of the EEO, Jencks basically concluded that schools make little difference in students' achievement. Bidwell and Kasarda (1975) addressed a different type of criticism to the EEO survey. They observed that Coleman and his associates did not take into consideration that organizational attributes might mediate or affect the 37 relationships between environmental input factors and students' academic achievement. The Coleman Report did not consider how between-school differences in such organization attributes as the division of labor, formalization of teaching activities, super­ vision of teaching, or the morphology of control might have mediated or otherwise affected relation­ ships between inputs to schools and pupil achieve­ ment (Bidwell & Kasarda, 1975, p. 56). They added that Despite the reanalyses reported in the MostellerMoynihan volume, there are good reasons to suspend judgment about the negative conclusions of EEO. Some of these are technical and center largely on errors of measurement. . . . Others are substantive and have to do with the failure of EEO to take school and school district into account" (p. 56). In addition to the EEO survey, many other inputoutput studies have been carried out by investigators from different disciplinary backgrounds 1972). (Averch et al., Several of these studies have used the EEO data file; others have employed different data sources. Several reviews of input-output studies can be found in the literature (see, for example, Averch et al., 1972; Cohn & associates, 1975; Guthrie, 1970; Guthrie et al., 1971; New York State Education Department, 1972; Spady, 1973). The major drawbacks of the EEO survey are also present in many of the input-output studies reviewed here, although several of them have used improved statistical methodology. Several analysts (Averch et a l ., 1972; Cohn & associates, 1975; Spady, 1973) have discussed the basic 38 difficulties faced by input-output researchers. Three of these difficulties that are especially important within this investigation's framework are listed below: 1. The lack of direct measures of student ability and motivation, which inflates the estimated impact of background factors on students' academic achievement since background factors may act, to some degree, as proxy measures of student ability and motivation; 2. The shared variance in students' achievement because of the high correlation of background factors and school resources, which cannot be exclusively attributed to either one given the simultaneous variations of both factors with students' achievement; and 3. The use of different levels of data aggregation (e.g., individual and school) within individual-level research designs. All of the input-output studies discussed below have used some kind of student cognitive achievement score, usually measured by some type of achievement test, as the indicator of educational output. A few of them also have included some kind of noncognitive output as a criterion variable, but only the findings concerning the relationships between inputs and students' cognitive out­ put are reviewed. Also, given the large number of vari­ ables usually analyzed in input-output studies, this review is restricted to those variables regarded as 39 essential in any educational production-function inves­ tigation and to the variables most frequently used in these studies that are of interest in this dissertation. In terms of level of data aggregation, the unit of analysis most often employed in these investigations was the school and the school with some variables at the individual student level. A few of these studies have used school district, and even fewer have employed the individual student as the unit of analysis. Students1 Background Factors One of the inputs regarded as essential in any educational production-function study is student background (Averch et al., 1972; New York State Education Department, 1972). Measures of student background usually included in input-output studies are indicators of family socio­ economic status (parents' education, average family income, father's occupation) and, less frequently, mea­ sures of community socioeconomic status. Despite the variation in model specification found in the literature, in every study included in previous reviews of research, students' background factors were found to be consistently related to their academic achieve­ ment (Averch et al., 1972; Cohn & associates, 1975; Guthrie et al., 1971; New York State Education Department, 1972). 40 Students1 Racial Characteristic In its review of input-output studies that have examined the relationship between students' race and aca­ demic achievement, the New York State Education Depart­ ment (1972) observed that even though the relationship had been found to be statistically significant in every research analyzed, the association would probably be clarified by analyzing students' race as a proxy measure of other factors such as socioeconomic status. In fact, the relationship between student body racial composition and students' achievement was the object of a great deal of controversy in the input-output studies literature. The basic questions underlying this controversy are: (1) To what extent does racial composition function as a proxy variable picking up variation in students' achieve­ ment due primarily to omitted dimensions of students' background factors and to additional variance, if any, resulting from school social-class composition? and (2) Does racial composition have a unique effect on stu­ dents' achievement after controlling for all dimensions of students' background factors and school social class? The input-output studies reviewed in this research have provided no conclusive answers to the latter question; empirical evidence is contradictory and confusing, at best. Concerning the first question, several investigators have suggested that student body racial composition acts, at 41 least in part, as a proxy measure of omitted dimensions of students' background factors and of additional vari­ ance, if any, due to school social-class composition (Bowles & Levin, 1968a; Cohen, Pettigrew, & Riley, 1972; Mayeske et al., 1969; McPartland, 1969; Smith, 1972). Students' Ability Many input-output studies have not included a direct measure of student ability because of the diffi­ culties involved in dealing with such a concept. Research­ ers who have attempted to account directly for student ability have used student IQ as the indicator. In all these studies, student IQ was found to be significantly related to student academic achievement (see, for example, C a m pbell et a l . , 1968; Gerberich, 1951; Goodman, 1959; Lavin, 1965; New York State Education Department, 1967a, 1967b, 1968; Wohlferd, Armstrong, & Curtis, 1968). The appropriateness of using student IQ as an indicator of student ability is open to discussion (Hanushek, 1970; Hanushek & Kain, 1972). Several scholars have regarded the use of student IQ in input-output studies as problematic (Bidwell & Kasarda, Hanushek, 1970; Hanushek & Kain, 1972). 1976a, 1976b; These indi­ viduals have pointed out the importance of student ability measures in models of "school effects," recognizing, however, the present difficulty in obtaining reliable ./ 42 measures of such a concept. As a consequence, students' background factors have been considered as reflecting to some extent students' ability and motivation (Spady, 1973). Several researchers have pointed out the major drawbacks of using students' background factors as proxy measures in school effects studies (Alexander & Griffin, 1976a, 1976b; Hannan, Freeman, & Meyer, 1976; Hanushek, 1970; Spady, 1973). Yet the use of such proxy measures of student ability is regarded as less problematic in aggregate-level "school effects" research than in individual-level designs (Bidwell & Kasarda, 1976b; Hanushek, 1970). School and School District Size The relationship between school or school district size and students' academic achievement was examined in several of the studies included in this review. The typical variable analyzed was school size because most of these studies focused on the school as the unit of analysis. The few investigators who have examined the rela­ tionship between school district size and academic achieve­ ment are Benson et al. (1965), Cohn (1968), Kiesling (1967, 1969, 1970), and Raymond (1968). School or school district size is most frequently indicated by total number of stu­ dents enrolled or by average daily student attendance. researchers have found no relationship between school or Most 43 school district size and students' academic achievement (Alkin, Benson, & Gustafson, 1968; Cohn, 1968; Kiesling, 1967, 1968, 1969; Mollenkopf & Melville, 1956). Some researchers have found both a negative and no relationship between size and students' academic achievement (Burkhead, Fox, & Holland, 1967; Guthrie et al., 1971; Smith, 1972). Finally, Benson et al. (1965), Katzman (1968), and Summers and Wolfe (1975) found a positive relationship between size and students' academic achievement— Benson within a range of small school districts. These inconsistent and contradictory findings seem to reflect the input-output studies' inadequate approach when testing for the relationship between school or school district size and students' academic achievement. This conclusion is based on previous theoretical and empiri­ cal analyses by organizational researchers (Bidwell & Kasarda, 1975; Price, 1968; Wagenaar, 1978) who have pointed out that size may affect organizational outcomes primarily through its intermediary effects on organiza­ tional attributes. That is, school or school district size may not affect students' academic achievement directly but rather indirectly through intervening organi­ zational attributes that may be related to academic achievement. 44 Fiscal Resources The financial-expenditures variables most often analyzed in input-output studies are expenditures per pupil and teachers' salaries. Other financial-expenditures variables, such as administrators' salaries and expendi­ tures for materials, have been used less frequently. The assessment of the relationship between the financial-expenditures factors and students' academic achievement has been problematic in input-output research, because of the apparent overlap and contradictions among and between these variables and other resource variables expressed in descriptive units such as teachers' qualifi­ cations, teachers' experience, pupil-teacher ratio, and number of special staff per pupil. For example, several input-output studies have examined the relationship between teachers' salaries and students' academic achievement, entering in the same regression equation other variables such as teachers' qualifications and teachers' experience, which are highly correlated with teachers' salaries (Bowles & Levin, 1968a; New York State Education Depart­ ment, 1972; Spady, 1973). Also, these researchers have usually introduced controls on students' background fac­ tors that are correlated with school resources (Bowles & Levin, 1968a, 1968b; Hanushek & Kain, 1972; Spady, 1973). Given the researcher's purpose in this study, the present review was focused on the overall financial variable, 45 expenditures per pupil, because of its inclusiveness and importance as a basic environmental input factor to schooling. Expenditures per pupil is usually indicated by the amount of fiscal resources (local, state, and federal) received by the school district per pupil. The input-output studies that have examined the relationship between expenditures per pupil and students' academic achievement have shown inconsistent and contra­ dictory findings. In several of these studies, a posi­ tive relationship between these two variables was found (Bowles, 1969; Cheal, 1962; Goodman, 1959; Riesling, 1968; New York State Education Department, Ribich, 1968; Thomas, 1962). 1967a, 1967b; On the other hand, Riesling (19 67) found a positive relationship between these two factors in school districts with an enrollment of at least 2,000 students and no relationship in school dis­ tricts with fewer than 2,000 students. Riesling (1969) found a negative relationship between these two variables in urban school districts and no relationship in rural school districts. Finally, several other investigators have found no relationship between expenditures per pupil and students' academic achievement (Alkin, Benson, & Gustafson, 1968; Gerberich, 1951; James, Thomas, & Dyck, 1963; Wohlferd, Armstrong, & Curtis, 1968). Several scholars have attempted to interpret inconsistent and contradictory findings like the ones 46 reported above concerning the relationship between expen­ ditures per pupil (fiscal resources) and the output, students' academic achievement, the most frequently dis­ cussed argument being the inadequate control on students' background factors given their association with school resources (see, especially, Bowles & Levin, 1968a, 1968b; Guthrie et al., 1971; Hanushek & Kain, 1972; Spady, 1973). Although these interpretations provide important insights concerning the relationship between these two factors, in this study the findings reported above are considered likely to be expected by this researcher in view of the inadequate approach used in these investigations. That is, in the reported investigations the researchers attempted to examine the direct relationship between fiscal resources and output. It was observed elsewhere (Bidwell & Kasarda, 1975; New York State Education Department, 1972), though, that the effect of fiscal resources on output is indirect; i.e., fiscal resources may affect output only indirectly through acquiring educational resources that may or may not influence the level of output. might be used to acquire resources Fiscal resources (e.g., better-qualified teachers) that may influence positively the level of output; fiscal resources might also be spent to acquire resources (e.g., transportation) that may be unrelated to students' academic achievement; finally, funds may be used to acquire resources (e.g., greater administrative differentiation) 47 that may influence negatively the level of output. Consequently, a more appropriate approach to examining the relationship between fiscal resources and students' academic achievement would be to identify the important intervening organizational variables, which are referred to in input-output studies as school resources. Teachers1 Characteristics The concern with the relationship between teachers' characteristics and students' academic achievement was present in the input-output studies literature long before Coleman and associates (1966) observed that teachers' characteristics account for more variation in achievement than do any other characteristics of the school. After the Coleman Report, the researchers' attempts to delineate teacher characteristics that can influence students' aca­ demic achievement increased greatly (State of New York, 1974). The two teacher characteristics most frequently analyzed in input-output studies have been teachers' experience and teachers' qualifications. These two vari­ ables have been found to be highly correlated with the financial-expenditures variable, teachers' salaries; i.e., a teacher's salary is typically based on his/her qualifi­ cations and experience (see, for example, Cohn & associates, 1975; New York State Education Department, 1972; Spady, 1973). 48 The evidence from empirical research is important in the context of the present investigation since teachers' salaries constitute a substantial proportion of overall financial expenditure, which is examined here as an important environmental input factor to school district organizations. The analysis of the relationship between teachers' experience and students' academic achievement in inputoutput studies has resulted in contradictory findings. In several investigations, the relationship between these two factors was found to be positive (Boardman, Davis, & Sanday, 1973; Burkhead, Fox, & Holland, 1967; Goodman, 1959; Hanushek, 1968; Katzman, 1968; Levin, 1970; Michelson, 1970; Summers & Wolfe, 1975; Thomas, 1962). investigators have found mixed results: negative relationships Other positive and (Riesling, 1970) and a few positive but mainly no significant relationships (Guthrie et al., 1971). Still others have found the relationship to be negative (New York State Education Department, 1967a, 1967b). Finally, some investigators have found no sig­ nificant relationship between the two factors (Riesling, 1967, 1969; Smith, 1972). Spady (1973) interpreted these dubious findings as the result of assuming a linear relationship between teachers' experience and students' academic achievement; he observed that the relationship is more likely nonlinear 49 than linear: Teacher effectiveness might increase up to a certain number of years of work and "beyond a given point, age and experience will quite likely inhibit capacity to learn and grow on the job" associates (p. 151). Cohn & (1975) underscored Spady's argument to some extent, observing that teacher experience can be regarded as both a positive and a negative school resource because it can reflect better skills to handle the job as well as professional obsolescence. Also, the analysis of the relationship between teachers' qualifications and students' academic achieve­ ment has provided mixed findings. Several investigators have found a positive relationship between these two fac­ tors (Bowles, 1969; Cheal, 1962; Ratzman, 1968; New York State Education Department, 1967a; Summers & Wolfe, 1975). On the other hand, Riesling (1970) found both positive and negative relationships between these two factors. In a few other studies, no relationship was evident between teachers' qualifications and students' academic achieve­ ment (Burkhead, Fox, & Holland, 1967; Hanushek, 1970; Riesling, 1967; Smith, 1972). Several researchers have attempted to interpret mixed findings like the ones reported above concerning the relationship between teachers' qualifications and stu­ dents' academic achievement, the most frequently discussed argument being the inadequate control for students' 50 background factors given their correlation with school resources (see, especially, Bowles & Levin, 1968a, 1968b? Hanushek & Kain, 1972? Spady, 1973). The present researcher regards the above findings as to be expected from input-output studies since the approach used does not take into consideration that organi­ zational attributes of schools and districts (such as teachers' qualifications) may mediate the relationship between environmental input factors (such as fiscal resources) and aggregate student academic achievement (see Bidwell & Kasarda, 1975). In light of this argument, inconsistent findings from input-output studies concerning the relationship between other factors regarded as organizational attri­ butes and students' academic achievement are also expected. Two other organizational attributes analyzed in the context of input-output studies are of interest in this investiga­ tion: administrative characteristics and pupil-teacher ratio. Only a few input-output studies reviewed by this researcher have examined the relationship between adminis­ trative characteristics and students' academic achieve­ ment. Benson et al. (1965) found the ratio of teachers to administrators to be negatively related to students' aca­ demic achievement for small and middle-sized school dis­ tricts and to be positively related to students' academic 51 achievement for the largest school districts. Kiesling (1965) reported a significant negative relationship between administrator-pupil ratio and students' academic achieve­ ment. Burkhead, Fox, and Holland (1967) and Kiesling (1969, 1970), on the other hand, found no relationship between administrator-pupil ratio and students' academic achievement. mixed results: Finally, Cohn and associates (1975) reported positive and no significant relationships between administrator-pupil ratio and students' academic achievement. In several of the input-output studies reviewed in this section, the relationship between pupil-teacher ratio and students' academic achievement was examined. and Sanday (1973), Campbell et al. Boardman (1968), Katzman (1968), Kiesling (1965, 1968), and Mollenkopf and Melville (1956) found significant relationships between these two factors. Yet Kiesling (1969, 1970) reported both a sig­ nificant relationship and no relationship between these two factors. Finally, Benson et al. (1965), Bowles (1970), Burkhead, Fox, and Holland (1967), Cohn (1968), Katzman (1971), Kiesling (1967), and Raymond (1968) found no relationship between pupil-teacher ratio and students' academic achievement. The preceding summary of research findings from many input-output studies showed the failure of the inputoutput approach to yield consistent results, which has been 52 the focus of much criticism (Alexander & Eckland, 1975; Averch et al., 1972; Richer, 1975; Spady, 1973). Averch et al. As (1972) observed, The results from the input-output approach do not mean that school resources fail, actually or poten­ tially, to affect student outcomes. We simply observe that so far these studies have failed to show that school resources do affect student out­ comes (p. 148). Aside from the methodological criticisms summar­ ized by Spady (1973), recent criticisms have been addressed to the atheoretical nature of "school effects" studies (Alexander & Eckland, 1975; Richer, 1975). As the New York State Education Department (1972) observed, In the absence of a well specified theory of produc­ tion for education, the investigator is relegated to the role of guessing or playing his hunches about what variables play an important role in the crea­ tion of some definition of educational output (p. 10). It seems that "the absence of a well specified theory of production for education," which underlies input-output studies, is a result of the failure of advocates of such an approach to take into consideration the characteris­ tics of educational organizations (see Bidwell & Kasarda, 1975). That is, any attempt to specify a theory of pro­ duction for education must take into account how components of educational organizations (e.g., structure, technology, and performance) relate to each other and to environmen­ tal factors (see Bidwell, 1979; Bidwell & Kasarda, 1975; Steers, 1977; Zey-Ferrell, 1979). 53 In light of these considerations, the inconsis­ tent findings from input-output studies might be tenta­ tively interpreted as the result of not accounting for the distinctive characteristics of educational organiza­ tions. If this interpretation is valid, the analysis of "school effects" from the organizational-effectiveness perspective adopted in this investigation (the combined approach discussed in Chapter I) might provide more con­ sistent results than the ones found by input-output researchers. Organizational-Effectiveness Studies Only two studies of "school effects" upon aggre­ gate levels of student academic achievement from an organizational-effectiveness perspective were found in the pertinent literature. These two investigations were conducted recently by Bidwell and Kasarda (1975) and Wagenaar (1978). The study by Wagenaar (1978) involved a sample of 135 out of 233 elementary schools in a large midwestern city. The limitations of Wagenaar's study are evident because by adopting the closed-system strategy, which entails the goal approach for studying organizational effectiveness, he disregarded the dynamics that govern the relationships between schools and their environments. Using the school as the unit of analysis, Wagenaar examined 54 the relationship between students' academic achievement aggregated at the school level (criterion variable) and several structural attributes (explanatory variables), with and without controlling for students' families' socioeconomic status. The statistical technique used for data analysis was stepwise multiple regression. The findings of Wagenaar's study relevant to the variables of interest to this investigation were as fol­ lows: 1. A mild positive relationship between special­ ized training (teachers' qualifications) and aggregate student academic achievement, 2. A positive relationship between students' families' socioeconomic status and aggregate student aca­ demic achievement, 3. An indirect positive effect of socioeconomic status on aggregate student academic achievement through specialized training, and 4. No relationship between school size and aggre­ gate student academic achievement. The finding of no direct relationship between school size and aggregate student academic achievement is to be expected, given the aforementioned argument that size may be related to academic achievement primarily indirectly through its intermediary effect on organizational attri­ butes that may be related to academic achievement. 55 Surprisingly, Wagenaar, who specifically stated in his study that "size may not be as important in and of itself as it is important for its effect on other internal struc­ tural variables" (p. 612), adopted an approach for study­ ing organizational effectiveness that did not allow him to test for indirect effects of school size on aggregate student academic achievement. Bidwell and Kasarda's (1975) study "is an unusu­ ally well-conceived" (Erickson, 1977, p. 119) investiga­ tion of school district effectiveness in the state of Colorado. These authors suggested a new analytical frame­ work for studying the effectiveness of educational organi­ zations that is basically in line with the combined approach to the study of organizational effectiveness dis­ cussed in the first chapter of this dissertation. The question posed by Bidwell and Kasarda was "whether and how attri­ butes of school district organization affect the trans­ formation of environmental inputs into students' aggregate levels of academic achievement" (p. 56). To answer this question, the authors investigated 104 out of 178 public K-12 school districts in Colorado during the 1969-1970 school year. Using the school district as the unit of analysis, they examined the relationships between five environmental input factors (school district size, school district fiscal resources, percentage of disadvantaged students, education of parent-risk population, and 56 percentage of nonwhite population), four organizational attributes (pupil-teacher ratio, administrative inten­ sity, professional support staff, and certificated staff qualifications), and the organizational-effectiveness criterion, aggregate student academic achievement. These variables were linked in a causal recursive model in which environmental input factors were hypothesized to affect aggregate student academic achievement primarily through their effects on the intervening organizational attributes. Regression analysis techniques were used to test the pos­ ited hypotheses and the goodness of fit of the causal model. Bidwell and Kasarda's findings are summarized below: 1. Relationships between environmental input fac­ tors and organizational attributes: a. Administrative intensity was affected only by school district size, declining across districts as size increased. b. School district fiscal resources showed a significant positive effect on the relative num­ bers of professional support staff; the larger the amount of fiscal resources, the larger the proportion of professional support staff. c. Percentage of disadvantaged students and education of parent-risk population showed no effect on professional support staff. 57 d. School district size showed a significant positive effect on pupil-teacher ratio; as enroll­ ment increased, so did the average number of stu­ dents per teacher• e. School district fiscal resources showed a significant negative effect on pupil-teacher ratio; the larger the amount of fiscal resources, the smaller the number of students per teacher. f. School district size, school district fis­ cal resources, percentage of disadvantaged stu­ dents, and education of parent-risk population1 showed a significant positive effect on certifi­ cated staff qualifications. g. Percentage of nonwhite population showed no influence on pupil-teacher ratio, administrative intensity, professional support staff, or certifi­ cated staff qualifications. 2. Relationships between environmental input fac­ tors and aggregate student academic achievement, control­ ling for the intervening organizational attributes: a. Percentage of nonwhite population showed a negative effect on aggregate student academic achievement. Defined in terms of "the percent of males 20-49 years old and females 15-44 years old residing in the school district who had completed at least 4 years of high school education" (Bidwell & Kasarda, 1975, p. 59). 58 b. School district size, school district fiscal resources, percentage of disadvantaged students, and education of parent-risk population showed no direct effect on aggregate student aca­ demic achievement. 3. Relationships between organizational attri­ butes and aggregate student academic achievement: a. Pupil-teacher ratio showed a significant negative effect on aggregate student academic achievement; as pupil-teacher ratios declined, across districts, aggregate student academic achievement rose. b. Administrative intensity showed a signifi­ cant negative effect on aggregate student academic achievement; as administrative intensity rose, aggregate student academic achievement declined. c. Certificated staff qualifications showed a significant positive effect on aggregate student reading achievement and no effect on aggregate student mathematics achievement. d. Professional support staff showed no effect on aggregate student academic achievement. 4. Direct and indirect causal effects of environ­ mental input factors on aggregate student academic achieve­ ment, based on the full model, including all possible causal paths: 59 a. School district size showed no direct effect on aggregate student academic achievement. Its indirect effects were opposing: Large size improved aggregate student academic achievement by decreasing administrative intensity and raising certificated staff qualifications, and it lowered aggregate student academic achievement by increas­ ing pupil-teacher ratios. b. School district fiscal resources showed no direct effect and a significant indirect effect on aggregate student academic achievement through lowering pupil-teacher ratio and raising certifi­ cated staff qualifications. c. Percentage of disadvantaged students showed no direct effect and no indirect effect on aggregate student academic achievement. d. Education of parent-risk population showed no direct effect on aggregate student reading achievement and a direct positive effect on aggre­ gate student mathematics achievement. Its indirect effects, through raising certificated staff quali­ fications, were positive on aggregate student reading achievement and negligible on aggregate student mathematics achievement. e. Percentage of nonwhite population showed a negative direct effect on aggregate student 60 academic achievement, independent of other vari­ ables in the causal model (pp. 63-68). On the basis of these findings, Bidwell and Kasarda concluded that organizational attributes are significantly related to aggregate student academic achievement. They interpreted the failure of input- output investigators to find consistent and articulated results of "school effects" as a result of the fact that these investigators did not take into account the char­ acteristics of educational organizations. That is, input- output investigators did not consider that organizational attributes could mediate the relationships between envi­ ronmental input factors and the output, aggregate student academic achievement. Conclusions From the Review In the first part of this chapter, the inputoutput approach for studying the effectiveness of schools was presented along with a summary of research findings from many input-output investigations. It was observed that the input-output approach failed to yield consis­ tent results. This lack of consistency of findings was interpreted as resulting from the failure of inputoutput investigators to take into account that attri­ butes of educational organizations may mediate the rela­ tionships between environmental input factors and aggregate 61 student academic achievement. Therefore, it was sug­ gested that the analysis of "school effects" from the organizational-effectiveness perspective adopted in this dissertation (the combined approach discussed in the first chapter) could provide more consistent results than the ones provided in input-output studies. In the second part of this chapter, the results of the only investi­ gation in which the combined approach was used were reported. These results provided evidence of the fruit­ fulness of the framework of analysis proposed by the authors, basically supporting the posited causal model. Based on the results of this study, the authors concluded that attributes of educational organizations do have an effect on their academic output. In synthesis, the combined approach for studying the effectiveness of educational organizations seems to yield meaningful results, as illustrated by the only investigation that has used the approach until now. Further work is not only advisable but highly necessary to accumulate empirical evidence that would provide for an adequate assessment and elaboration of the approach. The need for further work is especially evident, given the implications of findings from investigations of school effects for educational policy and practice. As a conse­ quence, the present study was designed to test a causal recursive model of school district effectiveness formulated 62 on the basis of the theoretical frame of reference of this combined approach (presented in detail in the first chapter), the findings of empirical research reported above, special features of the study population, and anticipated data availability. CHAPTER III A MODEL OF SCHOOL DISTRICT EFFECTIVENESS Overview The presentation in this chapter is divided into three sections. In the first section, a causal recursive model of school district effectiveness is introduced; for clarity, the diagrammatic representation of the model comes first and the discussion of the postulated rela­ tionships follows. In the second section, "Method of Analysis,” the technique used to test the assumed causal scheme is discussed and the path diagram of the postulated relationships is drawn. Finally, in the third section, a brief description of the study population is provided, along with a discussion of data-collection procedures and some comments regarding the variables indicated in the model. A Causal Recursive Model of School District Effectiveness In the first chapter, it was suggested that the combined approach for studying the effectiveness of organizations is the most suitable one because it allows for the recognition that environmental factors as well as the technology and internal structural attributes 63 \ 64 of the organization serve to inhibit or facilitate the extent to which goal achievement is optimized. Based on the combined approach and the conceptuali­ zation of educational organizations as bureaucracies that are loosely coupled in terms of instructional activities and tightly controlled in terms of ritual classifications and categories, this researcher discussed how environmen­ tal factors, technology, structural attributes, and the selected operative goal (aggregate student academic achievement) of educational organizations are likely to be related to each other. Basically, it was suggested that school district organizational attributes (classified as task-facilitating and task-inhibiting attributes) may mediate the relationships between environmental input factors and aggregate student academic achievement. Given this theoretical frame of reference, research findings reported in Chapter II, and anticipated data availability, the researcher proposes an explanation of school district effectiveness, which is diagrammatically represented in Figure 1 and discussed in detail on the fol­ lowing pages. The causal model represented graphically in Figure 1 is recursive, which means that there are no feed­ back loops or reciprocal linkages; i.e., the causal flow is unidirectional. variables: The model contains three types of exogenous, endogenous, and residual. The SRACE SFRAT SIZE FACQUAL SA FA C D IST RESOURCES ADMDIFF INCOME Figure 1.— A causal recursive model of school district effectiveness. o\ U1 66 exogenous variables are assumed to be predetermined; i.e., their variability is assumed to be caused by fac­ tors outside the causal model under consideration. No attempt is made to explain their variability or their intercorrelations since this is not a problem to be con­ sidered for the posited system. Thus, the intercorrela­ tions (noncausal correlations) between exogenous variables are symbolized by two-headed curvilinear arrows to dis­ tinguish them from causal arrows. The endogenous vari­ ables are taken to be influenced by exogenous variables and by exogenous and/or other endogenous variables in the model. Finally, the residual variables1 indicate the variance of the endogenous variables that is not explained by variables included in the model (see Kerlinger & Pedhazur, 1973;Land, 1969). 2 Variables included in the model (Figure 1) are as follows: a. Exogenous variables factors): (environmental input SRACE = student racial characteristic SIZE = school district size The residual variables are not represented in Figure 1, to simplify the drawing of arrow diagrams. See Figure 2 for a technical representation of the model. 2 The operational definitions of these variables are provided in Appendix A. 67 RESOURCES = school district fiscal resources INCOME = average income of families in the school district b. Endogenous variables (school district organi­ zational attributes): SFRAT = student-faculty ratio FACQUAL = faculty qualifications FACDIST = faculty distribution ADMDIFF = administrative differentiation c. Endogenous variables goal = output): (school district operative SA = aggregate student academic achievement The postulated causal relations between the vari­ ables included in the model are represented by unidirec­ tional arrows extending from the variables taken as causes to those taken as effects. For example, SFRAT is con­ sidered to be dependent on SIZE and RESOURCES. Plus signs are used to indicate direct positive effects from the variables taken as causes to those taken as effects. Minus signs indicate direct negative effects from the variables taken as causes to those taken as effects. The dotted lines symbolize relationships that could not be hypothesized. The meaning of the two dotted lines in the model is further clarified in the following dis­ cussion, under the headings "School district fiscal resources and aggregate student academic achievement" and 68 "School district size and aggregate student academic achievement." The Postulated Relationships: Explanation and Discussion Bidwell and Kasarda (1975) observed that the "problem for school districts is to transform such inputs as students, resources, staff, technology and community preferences into such outputs as student achievement, operating within limits set by law and public policy" (p. 57). Thus, certain environmental constraints consti­ tute the conditions under which a school district must operate. The relationships between the three sets of variables— environmental input factors, organizational attributes, and aggregate student academic achievement— are postulated on the following pages. School district fiscal resources and aggregate student academic achievement.— One environmental constraint is the amount of fiscal resources that a school district receives in a given year in order to carry out its activi­ ties. Following Bidwell and Kasarda's work (1975), this investigator proposes that fiscal resources affects the out­ put, aggregate student academic achievement, primarily through its effects on intervening organizational variables. In other words, fiscal resources by itself does not affect the output; it affects the output through its effects on 69 intervening organizational variables that are related to the output. This researcher points out that this proposition is contingent on the intervening organizational variables included in the causal model, given the zero-order corre­ lation coefficients between fiscal resources and output and between fiscal resources and other environmental input factors. That is, given the intercorrelations between environmental input factors, if the suggested causal model is fully specified (i.e., it contains all significant intervening organizational variables between fiscal resources and output), then no direct effect of fiscal resources upon the output would be observed. Conversely, given the zero-order correlation coefficient between fis­ cal resources and output and the intercorrelations between fiscal resources and other environmental input factors if the suggested causal model is not fully specified, then three alternative results are conceivable, depending on the task-facilitating and the task-inhibiting intervening variables included in the model: fiscal resources on output, (1) no direct effect of (2) a direct positive effect of fiscal resources on output, and (3) a direct negative effect of fiscal resources on output. Previous researchers have not determined the signifi­ cant intervening organizational variables between fiscal resources and output that are to be included in a causal 70 model within this framework of analysis; therefore, any of the preceding three conceivable alternatives may occur as a result of testing for the relationship between fiscal resources and output. exception. The posited causal model is no In this research, analysis might reveal that fiscal resources has no direct relationship to output or that it has a direct positive or negative relationship to output. As a consequence, no hypothesis concerning the direct relationship between fiscal resources and output is advanced; only hypotheses concerning the indirect effects of fiscal resources on output through intervening organizational variables are stated in this investigation. The result of testing for the direct relationship between fiscal resources and the output, aggregate student academic achievement, is analyzed on the basis of the preceding con­ siderations . The hypotheses concerning indirect effects of fis­ cal resources on aggregate student academic achievement through the selected intervening organizational variables are as follows: Hypothesis 1 : School district fiscal resources will show an indirect positive effect on aggregate student academic achievement through its effect on student-facuity ratio. Hypothesis 2 : School district fiscal resources will show an indirect positive effect on aggregate student academic achievement through its effect on faculty qualifications. 71 Hypothesis 3 : School district fiscal resources will show an indirect positive effect on aggregate student academic achievement through its effect on faculty distribution. Hypothesis 4 : School district fiscal resources will show an indirect negative effect on aggregate student academic achievement through its effect on administrative differentiation. It seems that the preceding proposition (and conse­ quent considerations and hypotheses) more adequately reflects the pattern of relationship between resources and output than does the proposition underlying the "inputoutput approach"— that fiscal resources is directly and positively related to student academic achievement. School district fiscal resources and organizational attributes.— The rationale for each hypothesis concerning the relationships between fiscal resources and organiza­ tional attributes is given below. The relationships between organizational attributes and output are examined later in this section. In Chapter I, educational organizations were con­ ceptualized as being loosely coupled in terms of instruc­ tional activities. Meyer et al. According to Meyer and Rowan (1978) , (1978), and Weick (1976), the instructional looseness of educational organizations is a result of the uncertainty and ambiguity that surround the technology of instruction. For example, "the technology of teaching is notoriously unclear" (Meyer et al., 1978, p. 236) and 72 "education is a diffuse task, the technology is uncer­ tain" (Weick, 1976, p. 12). The uncertainty and ambiguity of educational tech­ nology provide for and are evidenced by the fact that in educational organizations, instructional activities typi­ cally are not subject to systematic evaluation and inspec­ tion (Bidwell, 1965; Dornbusch & Scott, 1975; Dreeben, 1973; Lortie, 1973). instructional work It follows that the link between (technical means) and students' aca­ demic achievement (operative end) is unclear (Bidwell, 1965; Dornbusch & Scott, 1975). Within educational organizations, the allocation of resources to the production process is not based on previous assessment of alternative technical means to achieve the operative end. The basic expenses of a school district organization concerning its production process conform to prevailing institutional rules of the wider system. That is, the widely shared understandings about the nature of education create a context within which enough agreement exists to direct allocation of fis­ cal resources to organizational attributes that legitimize and give meaning to school production procedures. One such organizational attribute is studentfacuity ratio. The institutionalized rule concerning this variable is that the smaller the number of students assigned to each teacher, the greater the level of students' academic 73 achievement (Meyer & Rowan, 1978? Meyer et al . , 1978). It is to be expected, then, that school district organiza­ tions use fiscal resources to lower the number of stu­ dents assigned to each teacher. This proposition was tested by Bidwell and Kasarda (1975), who found the hypothe­ sized negative relationship between fiscal resources and student-facuity ratio to be statistically significant. On the basis of these arguments and findings, the following hypothesis is examined: Hypothesis 5 : School district fiscal resources will show a d i r e c t negative effect on studentfacuity ratio. Another organizational attribute selected to be examined here is faculty qualifications. The institution­ alized rule concerning this variable is that betterqualified teachers (as indicated by academic degrees and courses in particular topic areas from accredited insti­ tutions) render better services, which increases the level of students' academic achievement (Meyer & Rowan, 1978; Meyer et al., 1978). Thus, it is to be expected that school district organizations use fiscal resources to increase the proportion of better-qualified faculty in the district. Bidwell and Kasarda (1975) tested this proposi­ tion and found the hypothesized positive relationship between fiscal resources and faculty qualifications to be statistically significant. hypothesis is examined: Therefore, the following 74 Hypothesis 6 : School district fiscal resources will show a direct positive effect on faculty qualifications. A third organizational attribute selected to be examined here is faculty distribution, which is a measure of the degree of functional division of labor within school district organizations. Faculty distribution indicates the extent to which faculty members are within a rela­ tively small number of the 81 faculty assignment categories (reading, mathematics, elementary education, and so on) or are evenly distributed across a broad range of these assignment categories. This variable indicates the extent of faculty specialization within and among more general teaching assignment categories such as elementary education and social sciences. It also indicates the breadth and depth of curricular topics offered by school districts (Richardson, 1978). Using the formula^- introduced by Gibbs and Martin (1962) and further discussed by Gibbs and Browning (1966), faculty distribution is a better indi­ cator of depth than of breadth of curricular topics. It seems reasonable to assume that diversification and depth of curricular topics are valued by educators and the community, especially when considered in terms of the higher grade levels. It is to be expected that school ^1 - [ZX2/(ZX)2] = formula for the measurement of the degree of division of labor. 75 district organizations use fiscal resources to achieve a greater faculty distribution. Consequently, the following hypothesis is suggested: Hypothesis 7 : School district fiscal resources will show a direct positive effect on faculty distribution. The final organizational attribute selected for examination here is administrative differentiation. According to Richardson (1978), administrative differen­ tiation refers to the functional division of managerial and administrative labor in school district organizations, and thus provides a context for the consideration of both hierarchy of authority and administrative appa­ ratus (p. 125). It is expected that school district organizations direct a small amount of fiscal resources to administra­ tive differentiation. This statement follows the adopted conception of educational organizations as being loosely coupled in terms of instructional activities and tightly controlled in terms of ritual classifications and cate­ gories. Since tight organizational control is only exer­ cised over matters of categorization (such areas as the credentialing and hiring of teachers, the assignment of students to classes and teachers, and scheduling), the need in educational organizations for highly specialized administrative tasks is somewhat lowered. As Meyer and Rowan (1978) observed, in educational organizations the "logic of confidence" is adopted: 76 Higher levels o£ the system organize on the assump­ tion that what is going on at lower levels makes sense and conforms to rules, but they avoid inspect­ ing it to discover or assume responsibility for inconsistencies and ineffectiveness (p. 80). Therefore, Meyer and Rowan observed, "Administrators and other district staff make up a very small proportion of the total employees of most school districts" (p. 91). In light of these arguments, the following hypothesis is examined: Hypothesis 8 : School district fiscal resources will show a small direct positive effect on admin­ istrative differentiation. School district size and aggregate student academic achievement.— Concerning the environmental input factor, school district size, it is also proposed here that it affects the output, aggregate student academic achievement, primarily through its effects on intervening organizational variables (Bidwell & Kasarda, 1975; Wagenaar, 1978). In other words, size per se does not affect output; rather, it affects output through its effects on intervening organizational variables that are related to output. It is advanced here that this proposition is con­ tingent on the intervening organizational variables included in the model, given the interrelationships between size and other environmental input factors. That is, given the intercorrelations between size and other environmental input factors if the suggested causal model is fully speci­ fied, then no direct effect of size on output would be 77 observed. On the other hand, given the intercorrelations between size and other environmental input factors if the causal model does not contain all significant interven­ ing organizational variables between size and output (i.e., the model is not fully specified), then three alternative results are conceivable, depending on the task-facilitating and the task-inhibiting intervening vari­ ables included in the model: on output, (1) no direct effect of size (2) a direct positive effect of size on output, and (3) a direct negative effect of size on output. Previous researchers have not indicated whether the suggested causal model contains all significant interven­ ing organizational variables between size and output; hence any of the three conceivable alternatives may occur as a result of testing for the relationship between size and output. For this reason, no hypothesis concerning the direct relationship between size and output is advanced. Only hypotheses concerning the indirect effects of size on output through intervening organizational variables are stated. The result of testing for the direct relation­ ship between size and output, aggregate student academic achievement, is analyzed on the basis of the preceding considerations. The hypotheses concerning indirect effects of size on aggregate student academic achievement through the selected intervening organizational variables are as follows: 78 Hypothesis 9 : School district size will show an indirect negative effect on aggregate student academic achievement through its effect on studentfacuity ratio. Hypothesis 10: School district size will show an indirect positive effect on aggregate student aca­ demic achievement through its effect on faculty qualifications. Hypothesis 11: School district size will show an indirect positive effect on aggregate student aca­ demic achievement through its effect on faculty distribution. Hypothesis 12: School district size will show an indirect negative effect on aggregate student aca­ demic achievement through its effect on adminis­ trative differentiation. School district size and organizational attri­ butes .— The rationale for each hypothesis concerning the relationships between size and organizational attributes is given below. The relationships between organizational attributes and output are examined later in this section. Size is one of the ecological variables that has received a great amount of attention from organizational researchers (Wagenaar, 1978). Size is the environmental variable most frequently conceptualized as being associated with organizational structure (Zey-Ferrell, 1979). Corwin (1974), Hall (1977), and Zey-Ferrell (1979) observed that there has been an intense dispute among organizational analysts concerning the significance, strength, and direc­ tion of the association between size and organizational structure. 79 Hall (1963) and Hall, Haas, and Johnson (1967) stated that size is no more important than other factors in understanding organizational structure. On the other hand, Blau (1970), Blau and Schoenherr (1971), and Meyer (1972a, 1972b) suggested that size has a causal effect on organizational structure. Meyer's (1972b) longitudinal analysis supported the argument that size might have a causal effect on some aspects of organizational structure. This researcher concurs with the latter argument, assuming that size has a causal effect on some structural variables. In adopting this perspective, the investigator goes against Woodward (1965) and Thompson's (1967) argument that the tasks and technology of organizations are better predictors of structure than is size. This researcher's position is based on the adopted conception of educational organizations as being loosely coupled in terms of instruc­ tional activities and tightly controlled in terms of ritual classifications and categories. As previously observed, at least in reference to educational organizations it seems that environmental factors are better predictors of struc­ ture than are tasks and technology since instructional work and structure are loosely coupled (Meyer & Rowan, 1978; Meyer et al., 1978; Weick, 1976). Given these considerations, the environmental variable, size, is regarded here as causally related to the four organizational attributes examined in this 80 investigation: student-faculty ratio, faculty qualifica­ tions, faculty distribution, and administrative differen­ tiation. Bidwell (1965) and Bidwell and Kasarda (1975) observed that school district organizations are not able to select students in terms of total number to be served or in terms of their ability and motivation since educa­ tional policy requires the enrollment of all students who present themselves in any given year. According to these organizational analysts, input buffering and rationing are the basic means available to school districts for adapting to student input since fiscal resources is relatively fixed in the short run. In other words, "given the high probability of rationing as a response to growths in enroll­ ment and to large enrollments given fixed resources, perpupil shares of teachers should decline across districts as enrollment increases" (Bidwell & Kasarda, 1975, p. 61). These researchers found evidence to support this hypothe­ sis in their 1975 study of 104 school districts in Colorado. Conversely, given relatively fixed fiscal resources, it is to be expected that decline in enrollment will lower the number of students assigned to each teacher. As a conse­ quence, the following hypothesis is examined: Hypothesis 13; School district size will show a direct positive effect on student-faculty ratio. 81 Concerning the relationship between size and faculty qualifications, Bidwell and Kasarda (1975) observed that since enrollment is usually a correlate of community size, number of pupils should have a positive direct effect on teachers' qualifications. Larger places are likely to have larger pools of well-qualified teachers to draw from, to provide attractive employ­ ment for the spouses of married teachers and to afford more of the amenities of life that attract and hold competent teachers (p. 61). These researchers found evidence to support this hypothe­ sis in their 1975 study of selected Colorado school dis­ tricts. The following hypothesis is examined in the present research: Hypothesis 14: School district size will show a direct positive effect on faculty qualifications. The third organizational attribute selected here as being affected by the environmental input, size, is faculty distribution, which is an indicator of the school district functional division of labor. Richardson (1978) observed that "one consistent finding in the organizational research literature is the positive correlation between size and the complexity of an organization's division of labor, regardless of the indicators used to measure either vari­ able" (p. 24). Corwin (1970) also found a positive rela­ tionship between size and several indicators of the division of labor, which included a measure of faculty specializa­ tion. In view of these findings, the following hypothesis is examined: 82 Hypothesis 15; School district size will show a direct positive effect on faculty distribution. The fourth organizational attribute selected here as being affected by the environmental input size is administrative differentiation, which is an indicator of the degree of functional division of managerial and admin­ istrative labor in school district organizations. It is expected that a direct positive effect of size on adminis­ trative differentiation will be found. This statement is supported by the research of Blau and Schoenherr (1971), Child and Mansfield (1972), and Pugh and associates (1969, 1970), who found size to be a major determinant of organi­ zational structure. Richardson (1978) found size (indi­ cated by the total number of school district faculty) to be positively related to administrative differentiation. The following hypothesis is examined in the present study: Hypothesis 16: School district size will show a direct positive effect on administrative differ­ entiation. Average income of families and student racial characteristic .— Average income of families in the school district is a direct indicator of the socioeconomic level of the community. In the school effects literature, average family income is one of the frequently used indicators of students' socioeconomic status State Education Department, 1972). (New York Student racial 83 characteristic^" is regarded here as a proxy measure of community and students' socioeconomic level, reflecting additional variance of socioeconomic status, which is not represented by the single indicator, average income of families in the school district. These two environmental input factors are regarded here as (1) proxy measures of parental and community pref­ erences and expectations concerning the school district and (2) proxy measures of aggregate student cognitive ability and motivation (see Bidwell & Kasarda, 1975, 1976a, 1976b). Furthermore, the inclusion of these two factors in any school effects study is regarded as crucial since they have consistently been noted to affect students' aca­ demic achievement, as observed in the summary of research findings from school effects studies in Chapter II. In this investigation the organizational perspec­ tive for studying the effectiveness of school district organizations is employed; hence this researcher proposes that these two environmental input factors (average income of families in the school district and student racial ^This variable is frequently used in school effects studies as reflecting both sociocultural and socioeconomic factors (State of New York, 1974). Given the ambiguity that surrounds the sociocultural dimension of this vari­ able (see Chapter II of this paper), this researcher decided to take into consideration only its socioeconomic dimen­ sion, also discussed in the second chapter of this paper (see, for example, Bowles & Levin, 1968a; Cohen, Pettigrew, & Riley, 1972) . 84 characteristic) primarily and directly affect aggregate student academic achievement, and affect student achieve­ ment only secondarily through their effects on the inter­ vening organizational attribute, faculty qualifications. The proposition concerning the direct effects of these two environmental input factors on the output, aggre­ gate student academic achievement, follows research findings summarized in the second chapter of this dissertation. The proposition that these two factors also affect the output through their effects on faculty qualifications follows Bidwell and Kasarda's (1975) argument that the higher the socioeconomic level of the community, the higher the community's demand for better-qualified teachers. Therefore, the following hypotheses concerning these two environmental input factors are examined in this investi­ gation : Hypothesis 17; Average income of families in the school district will show a direct positive effect on aggregate student academic achievement. Hypothsis 1 8 : Average income of families in the school district will show a direct positive effect on faculty qualifications. Hypothesis 1 9 : Average income of families in the school district will show an indirect positive effect on aggregate student academic achievement through its effect on faculty qualifications. Hypothesis 2 0 : Student racial characteristic will show a direct positive effect on aggregate student academic achievement. 85 Hypothesis 21: Student racial characteristic will show a direct positive effect on faculty qualifications. Hypothesis 22: Student racial characteristic will show an indirect positive effect on aggregate student academic achievement through its effect on faculty qualifications. Organizational attributes and aggregate student academic achievement.— Previous investigators (see Chapter II of this paper) have found either a relationship between student-faculty ratio and students' academic achievement or no relationship between these two variables. However, most of these investigators have used the input-output approach, which is not adequate— either theoretically or methodologically— to represent the complex set of relation­ ships that characterize school or school district academic process of production. The only research known to the writer that has used an organizational-effectiveness perspective following the framework of analysis adopted in this investi­ gation was carried out by Bidwell and Kasarda (1975), who found evidence that the smaller the student-faculty ratio, the greater the aggregate level of student academic achieve­ ment. The basic argument posited by these organizational analysts to support this hypothesis and finding follows the conception of instruction as being labor-intensive, involving feedback-responses between teacher and student, and taking place in the isolation of classrooms; thus, the smaller the teacher's span of control, the more adaptive 86 to specific performances and characteristics his/her response to students is likely to be. On the basis of these considerations, the following hypothesis is exam­ ined: Hypothesis 23: The task-facilitating studentfaculty ratio will show a negative direct effect on aggregate student academic achievement. Investigators using the input-output approach, discussed in Chapter II, have reported mixed findings concerning the relationship between teachers' qualifica­ tions and students' academic achievement. As already observed, however, the input-output approach is not theo­ retically and methodologically adequate to represent the complex network of relations that characterize school or school district academic process of production. Wagenaar (1978), using an organizational-effectiveness approach but following a framework of analysis that differs from the one adopted in this research, found a positive relation­ ship between teachers' qualifications and students' academic achievement. Employing the framework of analysis adopted in this research, Bidwell and Kasarda (1975) also found teachers' qualifications to be positively related to the school district's level of student academic achievement. The basic argument supporting these findings is that the teacher-intensive character of instruction requires improved teaching skills, which is assumed to be related to higher levels of college training. Based on these 87 arguments and findings, the following hypothesis is examined: Hypothesis 2 4 : The task-facilitating faculty qualifications will show a direct positive effect on aggregate student academic achievement. The third organizational attribute selected to be examined in relation to the school district's level of student academic achievement is faculty distribution, which is a measure of the functional division of labor of school district organizations. As previously observed, faculty distribution indicates the extent of faculty specialization within and among more general teaching assignment categories; it is a better indicator of extent of specialization within than among teaching assignment categories. Given the nature of this variable, it is expected it will be positively related to aggregate student academic achievement. forward: The rationale for this prediction is straight­ because of the labor-intensive character of the technology of teaching, it is to be expected that more specialized teachers can provide better services in such crucial areas as reading and mathematics than can less specialized teachers. Pelz This prediction was supported by (1956), who noted that differentiation among and within occupational specialties may contribute to a higher degree of organizational performance. tion was supported by Price's Also, this predic­ (1968) proposition that 88 "organizations which have a high degree of division of labor are more likely to have a high degree of effective­ ness than organizations which have a low degree of division of labor" (p. 16). On the basis of these arguments/ the following hypothesis is examined: Hypothesis 25: The task-facilitating faculty distribution will show a direct positive effect on aggregate student academic achievement. The fourth and last organizational attribute to be examined in relation to the school district's level of student academic achievement is administrative differen­ tiation, which is an indicator of the functional division of managerial and administrative labor of school district organizations. Overall, this variable is regarded as a task-inhibiting organizational attribute. As such, it is expected to be negatively related to aggregate student academic achievement. This prediction is supported by the posited argument that schools are loosely coupled, and therefore some organizational attributes constrain instruc­ tional activities. Since administrative components are mainly derived from the institutionalized rules of the environment and not by the coordinative requirements of instruction, it is likely that administrative differen­ tiation mainly constrains the instructional work of teachers, consequently depressing the district's level of student academic achievement. That is, as administrators are more highly differentiated among more highly specialized 89 positions and functions, their coordination and control over matters of categorization should increase at a rate not overcome by their contributions toward the instruc­ tional work of teachers; thus, in balance, they should divert teachers from their instructional activities. As a consequence, the amount and quality of professional ser­ vices provided by teachers to students is lowered, which depresses the district's level of student academic achieve­ ment {see Biddle, 1970; Bidwell & Kasarda, 1975; Blau, 1960; Leavitt, 1958; Williams, 1971). Based on these argu­ ments, the following hypothesis is examined: Hypothesis 26: The task-inhibiting administrative differentiation will show a direct negative effect on aggregate student academic achievement. Method of Analysis The preceding material was an extended discussion of how environmental input factors and school district organizational attributes relate to each other and to aggregate student academic achievement. The postulated system of relationships among these variables consti­ tutes a theory of school district organizational effec­ tiveness. Given that these variables are assumed to be measured on an interval scale and that the relationships among the variables in the explanatory scheme are assumed to be unidirectional, linear, additive, and causal, path analysis is the technique used to test the theoretical 90 model. Another assumption that must be met for the proper use of path analysis is that the residuals are mutually uncorrelated and also uncorrelated with other variables in the system (see Heise, 1969; Kerlinger & Pedhazur, 1973; Land, 1969). Provided the foregoing assumptions are met, path analysis is a suitable analytical tool for testing the proposed theoretical model. It is important to observe that path analysis is not a method for generating theory. Rather, it is a technique appropriate for testing theory; i.e., it gives the implications of a particular system in which the causal ordering and the nature of the causal connections of variables have already been specified. By using path analysis, it is possible to verify whether a pattern of correlations for a set of observations is con­ sistent with the postulated explanatory scheme Kerlinger & Pedhazur, 1973). (see In brief, path analysis allows the researcher to evaluate the causal process assumed to operate among the variables considered in the theoreti­ cal model through the decomposition of the zero-order correlation between variables into a sum of simple (direct effect of one variable on another) and compound paths (some being meaningful indirect effects and others perhaps not) (Alwin & Hauser, 1975; Asher, 1976). Given these preliminary considerations, the pro­ posed theory of school district effectiveness is 91 represented in the path diagram depicted in Figure 2, where: X^, X2 , X 3 , and X^ are identified as exogenous variables since they are assumed to be pre­ determined; Xg, Xg, X y , Xg, and X g are considered endogenous variables because they are taken to be influ­ enced by other variables in the model; X,, Xu , X„, X , , and Xrt are residual or unmeasured a d c' d e variables that are introduced to account for the variance of the endogenous variables not explained by variables included in the model; The path coefficients (p’s) indicate the direct effect of one variable on another; and The zero-order correlation coefficients (r's) rep­ resent noncausal correlations between exogenous variables. The causal recursive model depicted in the path diagram in Figure 2 can be expressed mathematically in a set of structural equations. Since only the endogenous variables are to be explained, the following set of recur­ sive equations emerges'*': ^It can be observed that there is no constant term in the equations; this is due to the assumption that all variables are normalized with mean of zero and stan­ dard deviation of one (Blalock, 1969). X, 6b SFRAT £1 ’95 SIZE 13 FACQUAL '96 23 14 FACDIST RESOURCES 24 83 64 aomdiff INCOME 7c 8d X X1 (SRACE) *2 (SIZE) *3 * student-faculty ratio X5 “ school district site X6 (FACQUAL) (FACDIST) = X7 (ADMDIFF) = X8 (SA) X9 {RESOURCES) « school district fiscal resources (INCOME) *4 4 (SFRAT) = student racial characteristic * average incose of families in the school district faculty qualifications faculty distribution administrative differentiation aqqregate student academic achievement Figure 2.— The basic model of school district effectiveness. 93 X5 " P52X2 + P 53X 3 + P 5aXa X6 = P 61X1 + P62X 2 + P63X 3 + P64X4 + p 6bX: X7 = P72x2 + P73X 3 + p7cXc X 8 = P82X2 + P 83X 3 + p8dXd X9 = P9ixi + P94X4 + P95x5 + P96X 6 + P97X P9eXe Using this set of recursive equations, it is pos­ sible to estimate the path coefficients1 for the hypothe­ sized linkages through ordinary least squares, provided the previously stated assumptions that underlie the appli­ cation of path analysis are met (Asher, 1976). The evaluation of the causal process assumed to operate among the variables in the proposed model by decom­ posing the zero-order correlation coefficients into a sum of simple and compound paths follows the approach sug­ gested by Alwin and Hauser (1975), who emphasized the need to distinguish between the concepts of total association and total effects. According to these authors, the total association between two variables is given by their zeroorder correlation, which entails causal and noncausal components. The causal component of association is the 1Since all variables in the model are expressed in standard form, the path coefficients become standardized regression coefficients obtained in the ordinary regres­ sion analysis. 94 total effect (direct effect, if any, plus indirect effect(s), if any) of one variable on another that is not due to noncausal components of association (i.e., neither due to their common causes, to correlation among their causes, nor to unanalyzed effects due to association of exogenous vari­ ables) . Furthermore, the direct effect of one variable on another is part of the total effect, if any, that is not mediated by intervening variables. Conversely, the indirect effect of one variable on another is transmitted through intervening variables. As these authors observed, the distinction between direct and indirect effects as well as between causal and noncausal components of associa­ tion refers to a specific model. In terms of total effect, for example, depending on the model postulated by the researcher, one variable may have only a direct effect on another, or only an indirect effect, or both effects. The decomposition of the causal component of asso­ ciation between two variables (total effect) into direct and indirect elements is relatively simple to carry out. However, calculating the noncausal component of associa­ tion between two variables may be tedious and cumbersome, depending on the number of variables and linkages indi­ cated in a specific model. Fortunately, Alwin and Hauser (1975) provided a much simpler procedure: "The sum of the noncausal components of association may be found as the 95 difference between a total effect and the corresponding zero-order measure of association" (p. 42). Since the simpler procedure for decomposing zeroorder correlations between variables in the proposed causal system has been adopted in this investigation, the test of the model indicates whether the omitted linkages between variables that were hypothesized to have path coeffi­ cients equal or close to zero do, in fact, show path coef­ ficients of zero magnitude. The criteria for the deletion of path coefficients ("theory trimming")^are statistical significance and mean2 ingfulness. Path coefficients that are found to be sig­ nificant at the .05 level and of magnitude greater than .05 will be retained; if they do not meet these criteria, they will be deleted. The plan of analysis to be chapter involves followed in the fourth (1) theory trimming by estimating all the path coefficients in the recursive model through ordi­ nary least squares (including the omitted linkages between variables that were hypothesized to have path coefficients equal or close to zero), using the criteria of statistical ■'"The reader is referred to Heise (1969) and Kerlinger and Pedhazur (1973) for a discussion of this term. Land (1969) recommended that path coefficients lower than .05 can be regarded as not meaningful. This researcher followed Land's recommendation, treating path coefficients lower than .05 as not meaningful. This deci­ sion was made in view of the large number of cases (n = 508) used in the analysis. 96 significance (.05 level) and meaningfulness (coefficients lower than .05) for deletion of paths; and (2) decomposi­ tion of the total effect of independent variables on dependent variables in direct effect, if any, and indirect effects, if any, in order to obtain more information about the patterns of relationships between these variables. Population and Data Collection1 To test the recursive model presented in the fore­ going sections, Michigan K-12 school district organiza­ tions were selected as the study population in view of their considerable variability with respect to the vari­ ables indicated in the model and their similarity "with respect to charter, goals, polity, technology and day-today activities" (Richardson, 1978, p. 73). In the 1975-76 school year, there were 530 K-12 school districts in Michigan with a total enrollment of 2,124,221 elementary and secondary school students. The smallest school district enrolled only 113 students, and the largest enrolled 250,000 students. The typical school district provided educational services for 4,019 students. For a detailed description of the study population and data-collection procedures, the reader is referred to Richardson (1978), who collected the data used in this research and provided the information for the description of the study population. 97 In addition, the size of the geographical areas served by these school districts ranged from approximately two square miles to over 1,200 square miles. Considerable variation in the socioeconomic status of the community served by these school districts was also observed: the average income of the families in the typi­ cal school district was approximately $11,000, with a range in income from a low of $5,112 to a high of $33,972. The amount of fiscal resources per pupil received by these school districts from local, state, and federal sources in order to meet basic expenses ranged from a low of $729.91 to a high of $2,279.50, with an average of approximately $1,200 in the 1975-76 school year. The variability of Michigan K-12 school districts with respect to the variables of interest in this study can be observed by examining Table 1. The summary measures displayed in Table 1 were computed from a data file of 508 school district organizations out of the existing 530 pub­ lic K-12 school districts in Michigan during the 1975-76 school year. For 22 school districts, data concerning the variables included in this study were lacking because (1) information for two school districts was both incom­ plete and inaccurately recorded in one of the documentary sources and (2) the remaining 20 school districts did not have data for a critical variable— average income of the families in the school district. Table 1.— Mean and standard deviation of variables indicated in the model. Variable Mean Standard Deviation n 95.08 33.68 508 School district size (enrollment) 4125.69 12130.01 508 School district fiscal resources 1196.47 182.52 508 Average income of families in the school district 10914.21 2737.86 508 Student-faculty ratio 21.06 2.18 508 Faculty qualifications 31.34 13.05 508 Faculty distribution .82 .04 508 Administrative differentiation .29 .17 508 75.27 5.70 508 Student racial characteristic Aggregate student academic achievement 99 Richardson (1978) found no significant differences between the means of the two populations N = 508) in a series of Z-tests. (N = 528 and Further, multiple regres­ sion equations using both data sets (N = 528 and N = 508) "produced virtually identical results" (Richardson, 1978, p. 90). Because the set of recursive equations (without X 4 = average income of the families in the school district) identified in the proposed model of school district effec­ tiveness also yielded "virtually identical results" using both data sets (N = 528 and N = 508), it was decided to perform this investigation based on 508 school districts. The data used in this study were obtained by Richardson (1978) from official documents and records.^" The documentary information used in this investigation is straightforward, as can be observed in Appendix C. All of the data, with the exception of those obtained from the Executive Office of the Governor, are collected routinely by various divisions of the Michigan Department of Educa­ tion and are recorded either in departmental publications or on magnetic tape. Some of these variables were merely transcribed since they were used as originally measured; measures for a few of them were created by manipulating the ^A list of the sources of documentary information is furnished in Appendix C. 100 original information to obtain ratios, percentages, pro­ portions, and so on. Richardson (1978) verified the reliability of the data concerning several of the variables by cross-checking information that was duplicated in different documentary sources. Information derived from a survey instrument he administered enabled him to verify the reliability of information from documentary sources regarding the vari­ able, administrative differentiation. Variables Although most of the variables 1 used in this study are straightforward and self-explanatory, some additional comments are provided here: 1. The measure for average income of the families in the school district was derived from 1970 Census data. Hence it reflects conditions at least five years before the conditions represented by the other variables indi­ cated in the model. However, this source was the best available for such a variable at the time of the data collection. 2. In the review of related literature, it was observed that the two teacher characteristics most 1In Appendix A, the operational definitions of the variables used in this study are provided. In Appendix B, the mean, standard deviation, and number of cases are listed for each variable. 101 frequently analyzed in school effects studies have been teachers' qualifications and teachers' experience. Since these two variables are highly correlated, this researcher decided to include only one of them in the model. Teachers' qualifications was selected over teachers' experience because of the possible nonlinear relationship between the latter variable and students' academic achievement (Spady, 1973). 3. Two indicators of the functional division of labor of school district organizations were available for use in this study: (a) faculty differentiation, which indicates the proportion of 81 teaching-assignment cate­ gories actually occupied as first or second assignments by district faculty members during the 1975-76 school year; and (b) faculty distribution, which indicates the extent of distribution of district faculty within occupied facultyassignment categories*" during the 1975-76 school year. Both variables measure the extent of faculty specialization: the former is a better indicator of specialization among teaching-assignment categories and also of breadth of cur­ ricular topics offered by school districts; the latter is a better indicator of specialization within teachingassignment categories and also of depth of curricular ^Reading, mathematics, and elementary education are examples of faculty-assignment categories, as stated earlier in this paper. 102 topics offered by school districts. In this study, faculty distribution was preferred over faculty differen­ tiation because (a) faculty differentiation is highly correlated with administrative differentiation (r = .84), the selected indicator of the formal structure of authority relations in Michigan K-12 school districts; and (b) since faculty distribution is a better indicator of specializa­ tion within teaching-assignment categories (e.g., reading, mathematics) and also of depth of curricular topics offered by school districts, it would likely reveal a higher rela­ tionship with aggregate student academic achievement than would faculty differentiation--besides, the correlation between faculty distribution and administrative differen­ tiation is low (r = .29). 4. Administrative differentiation was selected over other available indicators of hierarchy of authority and administrative apparatus because as an overall measure of the complexity of the administrative division of labor (it indicates the proportion of 24 administrative-assignment categories occupied as first or second assignments by dis­ trict administrators during the 1975-76 school year) it provides a context for the consideration of both hierarchy of authority and administrative apparatus. Other avail­ able indicators of hierarchy of authority, besides being more specific (indicator of horizontal differentiation, indicator of vertical differentiation), are dependent on 103 the extent of administrative differentiation son, 1978, pp. 124-42). (see Richard­ Also, available indicators of administrative apparatus are very sensitive to measure­ ment error since they express proportional relations between functions that are not necessarily mutually exclusive cate­ gories in every school district. Summary In this chapter, the causal recursive model of school district effectiveness was introduced. After an extended discussion of how the variables indicated in the model are assumed to relate to each other, the technique of path analysis was discussed since it is used to test the model in Chapter IV. A brief description of the study population was also provided, along with a discussion of data-collection procedures. Finally, some comments were made regarding measures selected for variables included in the model. CHAPTER IV EVALUATION OF THE BASIC MODEL Introduction In this chapter, the causal recursive model of school district effectiveness postulated in Chapter III is evaluated. For the sake of clarity, the hypothesized relationships between variables in the posited causal sys­ tem are discussed in stages, each stage corresponding to the explanation of one endogenous variable in the model. In the last stage, in which the ultimate endogenous vari­ able (aggregate student academic achievement) in the model is explained, the model as a whole is considered in the interpretation of results. It is in this stage that the goodness of fit of the whole model is discussed. The presentation format followed in each stage involves: (1 ) presentation of a path diagram for a sub­ section of the model with all path coefficients estimated through the use of ordinary least squares; coefficients are provided not only for hypothesized linkages between variables but also for linkages that were omitted in the basic model since they are expected to have path coeffi­ cients equal or close to zero; (2 ) preliminary analysis of the path coefficients to assess if the hypothesized 104 105 linkages between variables are statistically significant and if the linkages that were omitted in the basic model do, in fact, show path coefficients that are not statistically significant; (3) presentation of a trimmed path diagram for the subsection of the model under consideration, with path coefficients resulting from regressing the variable to be explained for just those variables found to be significant in the previous diagram; and (4) interpretation 1 of the results of the final form of the subsection of the model. In the last stage, in which the model as a whole is analyzed, the importance of all variables in the causal system supported by the data in explaining aggregate stu­ dent academic achievement is considered. This is achieved by decomposing the total effects of the variables in the causal chain into direct and/or indirect effects on the ultimate dependent variable. Tables for Figures 3 through 10 are presented in Appendix D. mation: Those tables contain the following infor­ the standardized regression coefficient (beta), the unstandardized regression coefficient (B), the standard error of the unstandardized regression coefficient (SEg), the magnitude of the regression coef­ ficient relative to the magnitude of its standard error, the coefficient of multiple correlation (R), the 1See Appendix F, where the criterion for the inter­ pretation of the magnitude of the path coefficients (direct effect of one variable on another) is furnished. 106 2 coefficient of determination (R ), and the number of cases (n). In Appendix E r the matrix of simple correla­ tion is furnished. The Explanation of Student-Faculty Ratio What environmental input factors influence the ratio of students to faculty in Michigan K-12 school dis­ tricts? In Chapter III, it was predicted that only two out of the four environmental input factors included in the model influence the ratio of students to faculty: school district fiscal resources (Hypothesis 5) and school district size (Hypothesis 13). School district fiscal resources was hypothesized to show a direct negative effect .on student-faculty ratio, and school district size was hypothesized to show a direct positive effect on studentfacuity ratio. The result of regressing student-faculty ratio on all four environmental input factors is shown in Figure 3. As expected, the paths from student racial characteristic to student-faculty ratio (P5 1 “ -.018) and from average income of the families in the school district to studentfaculty ratio (p5 4 = -.018) do, in fact, show path coeffi­ cients close to zero. Dropping these two variables with not statistically significant coefficients, a final path dia­ gram may be drawn for this subsection of the model, as shown in Figure 4. It can be seen that the diagram in 107 SRACE -.086 -.124 P5a =.72 SIZE 383 070 SFRAT ‘r e s o u r c e s 559 427 .69 INCOME .48 n where: 508 X x (SRACE) Student racial characteristic X2 (SIZE) School district size (log) X3 (RESOURCES) School district fiscal resources X4 (INCOME) Average income of families in the school district Xg (SFRAT) = Student-faculty ratio Figure 3.— Path coefficients between environmental input factors and student-faculty ratio. 108 Figure 4 corresponds with the hypothesized linkages between variables for this subsection of the basic model represented in Figure 2. The path coefficients for the final form of this subsection of the model are based on regression with the variables found to be statistically significant in Figure 3, as predicted. 5a SIZE = .72 SFRAT .383 RESOURCES = .69 = .48 n where: X, (SIZE) X- (RESOURCES) = School district fiscal resources (SFRAT) = School district size = 508 (log) = Student-faculty ratio Figure 4.— Significant path coefficients between environ­ mental input factors and student-faculty ratio. Recursive equation: X,- = Ps2X 2 + ^53X 3 + p 5ax a' It maybe observed that there is no loss of informa­ tion from Figure 3 to Figure 4, which includes only the environmental input factors that were hypothesized to affect student-faculty ratio (R = .69; R ses 5 and 13 are supported by the data: significant predictors at the .01 level. 2 = .48). Hypothe­ Both variables are School district size shows a moderately strong direct positive effect on student-faculty ratio (p5 2 = .428), which supports the prediction that increases in school district enrollment are followed by increases in the average number of stu­ dents assigned to teachers. Conversely, school district fiscal resources has a strong direct negative effect on student-faculty ratio (P5 3 - -.737); the larger the amount of fiscal resources received by the school district, the smaller the average number of students per teacher. This finding demonstrates that school districts do conform to the prevailing institutional rule of the wider system— that by providing for a lower student-faculty ratio, the level of students' academic achievement will be improved. These findings also demonstrate that school districts with fewer fiscal resources are less able to lessen the impact of size than are wealthier school districts. These two environmental input factors account for 2 48 percent (R = .48) of the variance in student-faculty ratio, leaving 52 percent of the variance in this organi­ zational attribute unexplained. The residual path coeffi­ cient equals .72 since the square root of the unexplained variation for student-faculty ratio is pea = /1-.48 = .72. 11 0 The Explanation of Faculty Qualifications In the preceding chapter, it was hypothesized that all four environmental input factors indicated in the model would affect the level of qualifications of faculty employed by the school districts: and 21. Hypotheses 6 , 14, 18, All these factors (student racial characteristic, school district size, school district fiscal resources, and average income of the families in the school district) were hypothesized to have a direct positive effect on fac­ ulty qualifications. In Figure 5, the result of regressing faculty qualifications on all four environmental input factors is represented. As predicted, all path coefficients in Figure 5 are statistically significant at the .05 level. All paths, except the path from student racial character­ istic to faculty qualifications, were also statistically significant at the .01 level. The four environmental 2 input factors explain 55 percent (R = .55) of the vari­ ance in faculty qualifications. The unexplained variance in this organizational attribute is 45 percent. The path / coefficient for the residual variable is .67. All four variables in Figure 5 are in accord with the hypothesized direction of the effects. Ill SRACE X, -.086 = .67 p 6b = -.124 SIZE 070 383 FACQUAL X, 559 RESOURCES .427 R = .74 R 2 = .55 NCOME where: n = 508 X x (SRACE) Student racial characteristic X2 School district size (log) j (SIZE) (RESOURCES) = School district fiscal resources X 4 (INCOME) X g (FACQUAL) Average income of familes in the school district = Faculty qualifications Figure 5. -Significant path coefficients between envi­ ronmental input factors and faculty quali­ fications. Recursive equation: Xg ~ P61X1 + P 62X2 + P 63X 3 + P 64X 4 + P 6 bXb* 112 The greatest contribution is given by school dis­ trict fiscal resources, which shows a moderately strong positive impact on faculty qualifications (Pg 3 = .422); the greater the amount of fiscal resources received by school districts, the greater the proportion of betterqualified faculty in the district. Also concerning this variable, the evidence is that school districts follow the institutionalized rule of the wider system— that expenditures on better-qualified faculty are worthwhile since they will provide better services, which will increase the level of students' academic achievement. In terms of magnitude of influence, school district size ranks second among the environmental input factors, showing a moderate direct positive effect on faculty quali­ fications (pg2 = .355). This finding supports the predic­ tion that larger communities are more likely to attract better-qualified teachers than are smaller communities. The small (pg 4 = .149) but statistically signifi­ cant (.01 level) effect of average income of the families in the school district on faculty qualifications supports the prediction that the higher the socioeconomic level of the community, the higher the community's demand for better-qualified teachers. This prediction is also sup­ ported by the very small (Pg^ = *069) but statistically significant (.05 level) effect of student racial char­ acteristic on faculty qualifications. The magnitude of 113 the latter path coefficient in comparison with the mag­ nitude of the former supports the use of student racial characteristic as a proxy measure reflecting additional variance of socioeconomic status that is not represented in the single indicator, average income of the families in the school district. The Explanation of Faculty Distribution In the preceding chapter it was hypothesized that faculty distribution would be affected in a positive direction by two environmental input factors: school dis­ trict size (Hypothesis 15) and school district fiscal resources (Hypothesis 7). racial characteristic It was expected that student and average income of the families in the school district would show no effect on faculty distribution. The result of regressing faculty distribution on all four environmental input factors is shown in Figure 6 . As expected, student racial characteristic/ with a path coefficient of .071, do not influence faculty distribu­ tion at a statistically significant level. Also as pre­ dicted (Hypothesis 7), school district fiscal resources shows a direct positive effect on faculty distribution (p^ 3 = .292), statistically significant at the .01 level, which demonstrates that diversification and depth of cur­ ricular topics are valued by school district organizations 114 -.086 ' - 124 070 383 559 91 7c 5SIZE FACDIST ^RESOURCES 427 .41 .17 508 where: X^ (SRACE = Student racial characteristic X2 = School district size (log) (SIZE) X 3 (RESOURCES) = School district fiscal resources X4 (INCOME) X? (FACDIST) Figure 6 = Average income of families in the school district = Faculty distribution .— Path coefficients between environmental input factors and faculty distribution. 115 since they direct a certain amount of fiscal resources to achieve a greater faculty distribution. Thus, the higher the amount of fiscal resources received by the school dis­ trict, the higher the degree of faculty distribution. However, contrary to the prediction made in this study, the path from school district size to faculty dis­ tribution, with a coefficient of .092, is not statistically significant at the .05 level. This coefficient is statis­ tically significant at the level, which does not meet . 10 the criterion adopted in this investigation. Also con­ trary to what was expected, average income of the families in the school district does show a direct positive impact on faculty distribution (P7 4 - .113) that is statistically significant at the .05 level. These unexpected findings can be clarified through an analysis of the pattern of relationships between school district size, family average income, and faculty dis­ tribution. School district size and average income of the families in the school district show a moderate zero-order correlation coefficient (r = .559), which might mean that larger communities are likely to be of a higher socioecon­ omic level. Furthermore, it may be observed that these two variables vary simultaneously with faculty distri­ bution, which show a simple correlation coefficient of .261 with school district size and of .294 with average income of the families in the school district. 116 Given this pattern of zero-order correlations among these variables and given that in ordinary regression analysis the contribution of each variable in the equation is assessed after the contributions of all other variables in the equation have been considered, each path coefficient reflects the component of variation in faculty distribu­ tion attributable to a specific independent variable; i.e., the proportion of variance in faculty distribution that is due to the shared effect of school district size and family average income is reflected in the coefficient of determination (R ) but is not attributable to either of these two variables individually. It follows that if family average income is taken out of the regression equation, school district size will increase in magnitude by the addition of the effect that it shares with family average income. In fact, taking out family average income from the regression equation, school district size shows a direct positive impact on faculty distribution (p7 2 = .145) that is statistically significant at the .01 level. Con­ versely, dropping school district size from the regression equation, average income of the families in the school district increases in magnitude (P7 4 = .159) as well as in statistical significance (from .05 to .01 level). In terms of percentage of variance accounted for in faculty distribution, the inclusion of either variable in the 117 regression equation produces virtually identical results (R2 = .16). Aside from the preceding methodological considers-* tions, it would seem that the significant direct positive effect of average income of the families in the school dis­ trict on faculty distribution results from the fact that families of higher socioeconomic status are more likely to require school districts to provide better education than are families of lower socioeconomic status. The evi­ dence from this research demonstrates that families of higher socioeconomic status require in-depth preparation of their children, which provides for a greater specialization of functions within the instructional component of school district organizations. In synthesis, the greater the average income of families in the school district, the greater the specialization within teaching-assignment categories (e.g., reading, mathematics, elementary educa­ tion) and also the greater the depth of curricular topics offered by school districts. In view of the foregoing considerations, the two variables (student racial characteristic and school dis­ trict size) with coefficients that are not statistically significant are dropped from this subsection of the model. The final path diagram for this subsection of the model is depicted in Figure 7. information from Figure It may be observed that the loss of 6 to Figure 7 is from R = .41 and R 2 = .17 to R = .40 and R 2 = .16. Hypothesis 15 is not supported by the data; Hypothesis 7 is supported. RESOURCES 7c FACDIST .427 .40 INCOME .16 508 where: X3 (RESOURCES) = School district fiscal resources X 4 (INCOME) = Average income of families in the school district Xj (FACDIST) = Faculty distribution Figure 7.— Significant path coefficients between envi­ ronmental input factors and faculty distri­ bution. Revised recursive equation: X 7 = P 73X 3 + P 74X 4 + p 7cXc* The two environmental input factors in Figure 7 2 account for 16 percent (R = .16) of the variance in fac­ ulty distribution. The unexplained variance in this organi­ zational attribute is 84 percent. The residual path coef­ ficient for this endogenous variable equals .92. The difference in the magnitude of the path coefficients for the final form of this subsection of the model is a result 119 of regressing faculty distribution only on the two envi­ ronmental input factors found to be statistically sig­ nificant in Figure 6 . The Explanation of Administrative Differentiation The fourth organizational attribute to be explained in this study is administrative differentiation. Chapter III In it was predicted that only two of the four environmental input factors included in the study affect administrative differentiation. Both school district size (Hypothesis 16) and school district fiscal resources (Hypothesis 8) were hypothesized to affect administrative differentiation in a positive direction; the latter was expected to show a small effect. In Figure 8 , the result of regressing administra­ tive differentiation on all four environmental input fac­ tors is depicted. It may be observed in Figure path from student racial characteristic 8 that the to administrative differentiation (Pg^ = -. 0 2 2 ) does in fact have a coeffi­ cient close to zero, as expected. However, the path from average income of the families in the school district to administrative differentiation, which was also hypothe­ sized to be equal or close to zero, is statistically sig­ nificant at the .05 level although the coefficient is very small (pg4 = -.063). The other two environmental input factors are related to administrative differentiation, 120 SRACE -.086 -.124 070 = .44 8d SIZE 383 ADMDIFF X8 559 ^RESOURCES 427 ^52- R = .90 R 2 = .81 NCOME where: n = 508 X x (SRACE) Student racial characteristic X2 School district size (log) (SIZE) X 3 (RESOURCES) School district fiscal resources X4 (INCOME) Average income of families in the school district Xg (ADMDIFF) Figure 8 = Administrative differentiation .— Path coefficients between environmental input factors and administrative differ­ entiation. 121 as predicted. Dropping the variable with a coefficient that is not statistically significant, a final path diagram may be drawn for this subsection of the model, as shown in Figure 9. SIZE 8d 383 559 ^RESOURCES P83 ~ ‘196 = .44 * ADMDIFF 427 'INCOME where: X2 (SIZE) (RESOURCES) = School district size (log) = School district fiscal resources X4 (INCOME) = Average income of families in the school district Xg (ADMDIFF) = Administrative differentiation Figure 9.— Significant path coefficients between envi­ ronmental input factors and administrative differentiation. Revised recursive equation: X8 = P 82X 2 + P 83X 3 + P 84X 4 + P 8 dXd* It may be observed that except for the inclusion of the linkage between average income of the families in the school district and administrative differentia­ tion, the diagram in Figure 9 corresponds with the 122 hypothesized linkages between variables for this subsec­ tion of the basic model depicted in Figure 2. The path coefficients for the final form of this subsection of the model resulted from regressing administrative differen­ tiation only on the three environmental input factors found to be statistically significant in Figure 8 . It can be seen that there is no loss of informa2 tion from Figure 8 to Figure 9 since R = .90 and R = .81 in both figures. These three environmental input factors account for 81 percent (R = .81) of the variance in administrative differentiation. The fraction of the unexplained variance in this organizational attribute is 19 percent. The path coefficient for the residual vari­ able is .44. Specifically in terms of each variable, it may be observed that school district size shows a very strong direct positive effect on administrative differentiation (Poo = .846), which is statistically significant at the .01 level. Thus, increases in student enrollment are followed by increases in the degree of functional division of managerial and administrative labor in school district organizations. This finding supports Hypothesis 16. Also as predicted (Hypothesis 8 ), school district fiscal resources shows a small direct positive effect on administrative differentiation (pg 3 = .196). The result 123 is statistically significant at the .01 level. This finding supports the conception of educational organiza­ tions as being loosely coupled in terms of instructional activities and tightly controlled in terms of ritual classifications and categories. As was observed on page 75, the need for highly specialized administrative tasks in edu­ cational organizations is somewhat lowered since tight organizational control is only exercised over matters of categorization; as a consequence, school district organi­ zations direct a small but significant amount of fiscal resources toward increasing administrative differentia­ tion. Finally, an influence that was not predicted in this study concerns the very small direct negative effect of average income of the families in the school district on administrative differentiation (pg 4 = -.068), which is statistically significant at the .05 level. lowing may explain this finding: The fol­ Poorer school districts frequently receive more fiscal resources from state and federal sources, which requires special administrative procedures; that is, there is the need to designate admin­ istrators to manage the special programs created with these funds, which provides for increased administrative differentiation. 124 The Explanation of Aggregate Student Academic Achievement: Direct Effects What environmental input factors and organizational attributes of school districts have a direct influence on students' aggregate levels of academic achievement in Michigan? In the preceding chapter, it was hypothesized that all four organizational attributes of school districts selected in this study would show a direct effect on aggre­ gate student academic achievement: Two of them, student- facuity ratio (Hypothesis 23) and administrative differen­ tiation (Hypothesis 26), would have a negative effect; the other two, faculty qualifications (Hypothesis 24) and faculty distribution (Hypothesis 25), would show a positive effect. Concerning the environmental input factors, stu­ dent racial characteristic (Hypothesis 20) and average income of the families in the school district (Hypothesis 17) were hypothesized to have a direct positive effect on aggregate student academic achievement. For the two other environmental input factors (school district fiscal resources and school district size), no hypotheses of direct effect on aggregate student academic achievement were advanced since these two variables were regarded to affect aggregate student academic achievement primarily indirectly through their effects on intervening organiza­ tional variables. It was stressed, however, that this proposition would be supported only in the case of a fully 125 specified model, i.e., only when all significant interven­ ing organizational variables between these two environmen­ tal input factors and aggregate student academic achievement were included in the model. If all of the significant intervening organizational variables between these two environmental input factors and aggregate student academic achievement were not included in the model, three alterna­ tive results are conceivable: no direct effect, a direct positive effect, or a direct negative effect of either of these two environmental input factors on aggregate student academic achievement. It was also pointed out that previous researchers have not indicated all the significant interven­ ing organizational variables between these two environmental input factors and aggregate student academic achievement that are to be included in a model postulated within the framework of analysis adopted in this investigation. (See pages 68-70 and 76-77 of this study for a further explana­ tion .) In view of the preceding considerations, the cri­ terion variable, aggregate student academic achievement, was regressed not only on the six variables hypothesized to show a direct effect on it but also on these six vari­ ables plus school district fiscal resources and school district size. The result of this regression equation revealed a path coefficient close to zero (-.025) between school district size and aggregate student academic 126 achievement and a path coefficient of -.262 between school district fiscal resources and aggregate student academic achievement, which is statistically significant at the .01 level. Do these results demonstrate that the model is fully specified concerning school district size and not fully specified concerning school district fiscal resources? Not necessarily with regard to school district size: It might mean that all significant intervening organizational variables that mediate the relationship between this vari­ able and aggregate student academic achievement were included in the model (in which case the model would be fully specified concerning this variable), or it might mean that given the intercorrelations between school dis­ trict size and other environmental input factors, the opposing indirect effects (positive and negative) of size on aggregate student academic achievement through inter­ vening organizational attributes (see the final form of the whole model in Figure 11) might have balanced each other out. If the latter interpretation were correct, the inclusion of another intervening organizational variable in the model and/or the inclusion of another environmen­ tal input factor that would break the existing balance between positive and negative components would result in a direct effect of school district size on aggregate stu­ dent academic achievement. With respect to school district 127 fiscal resources, the model is clearly not fully speci­ fied. In this case, the inclusion of another intervening organizational variable and/or the inclusion of another environmental input factor that would provide for the balancing out of positive and negative components would result in no direct effect of school district fiscal resources on aggregate student academic achievement. If this occurs, can one regard the model as being fully speci­ fied concerning this variable? Again, not necessarily. Continuous inclusion or deletion of intervening organi­ zational attributes and/or environmental input factors in a model within this framework of analysis could keep changing the relationship between each of these two envi­ ronmental factors (school district size and school dis­ trict fiscal resources) and aggregate student academic achievement up to a point where the most important envi­ ronmental input factors and intervening organizational attributes related to aggregate student academic achieve­ ment are identified. This can be achieved only through extensive research using the framework of analysis adopted in this study, aiming at increasing the explanatory and predictive power of further elaborated models. Given that the path coefficient from school district size to aggregate student academic achievement is not sta­ tistically significant, the final form for this subsection of the basic model is represented in Figure 10. The 128 SRACE X RESOURCES INCOME 9e SFRAT = .90 SA X„ FACQUAL R FACDIST = .44 R 2 = .19 n = 508 ADMDIFF where: = Student racial characteristic (SRACE) X1 = School district fiscal resources X 3 (RESOURCES) = Average income of families in the (INCOME) X4 school district X5 X6 X7 X8 X9 Student-faculty ratio (SFRAT) = (FACQUAL) = Faculty qualifications (FACDIST) = (ADMDIFF) = Administrative differentiation (SA) = Aggregate student academic achievement Faculty distribution Figure 10.- -Significant path coefficients between environ­ mental input factors/organizational attributes and aggregate student academic achievement. Extended recursive equation: Xg = P 91X 1 + P 93X 3 + P 94 4 + p95X 5 + P96X 6 + P 97X 7 + P 98X 8 + p 9eXe 129 reported path coefficients result from regressing aggregate student academic achievement on all variables indicated in the model except for school district size. All hypothesized linkages between variables for this subsection of the model are supported by the data. 2 The coefficient of determination (R = .19) shows that the four organizational attributes plus three out of the four environmental input factors explain 19 percent of the variance in aggregate student academic achievement. The path coefficient for the residual variable, which repre­ sents the square root of the unexplained variance, equals .90. The unexplained variance in aggregate student academic achievement is 81 percent. Examining the contribution of each individual vari­ able in the equation, it may be observed that average income of the families in the school district shows a mod­ erate impact on the criterion variable, aggregate student academic achievement, with a path coefficient of .364, sta­ tistically significant at the .01 level. This result sup­ ports Hypothesis 17 and is in accordance with previous "school effects" investigations, in which researchers have found different indicators of socioeconomic status of stu­ dents' families to be consistently related, in a positive direction, to students' academic achievement. Another environmental input factor, student racial characteristic (percentage of Caucasian students 130 in the school district), shows a small direct positive effect on aggregate student academic achievement (Pg^ = .116), which is statistically significant at the .05 level. This result, which supports Hypothesis 20, is also in accordance with previous "school effects" research, which has pointed out that student racial characteristic is con­ sistently related to students' academic achievement. The other environmental input factors included in the model and found to have a moderately small direct effect on aggregate student academic achievement (pg3 = -.261), statistically significant at the .01 level, is school dis­ trict fiscal resources, which was discussed at the begin­ ning of this section. Among the organizational attributes indicated in the model, administrative differentiation shows a small direct negative influence on aggregate student academic achievement (pgg = -.193), statistically significant at the .01 level. This result supports Hypothesis 26, demonstrat­ ing that the higher the administrative differentiation within school district organizations, the lower the level of aggregate student academic achievement. That is, as admin­ istrators are more highly differentiated among more highly specialized positions and functions, their coordination and control over matters of categorization are greater than their contributions toward the instructional work of teachers. This, in effect, diverts teachers from their instructional 131 activities, consequently lowering the district’s level of student academic achievement. It is pointed out that the administrative differentiation measure is made up of two components: academic administration, which is expected to be related positively to aggregate student academic achieve­ ment, and nonacademic administration, which is expected to be related negatively to aggregate student academic achieve­ ment. The fact that the path coefficient between adminis­ trative differentiation and the output, aggregate student academic achievement, is negative and of -.193 magnitude demonstrates that the influence of the nonacademic adminis­ tration component on output in Michigan K-12 school dis­ tricts must be greater since the observed path coefficient may be decreased in magnitude by the opposing influence of the academic administration component on output. Another organizational attribute included in the model is faculty qualifications. As predicted (Hypothe­ sis 24), this variable shows a direct positive influence on aggregate student academic achievement (Pgg = *182), which is statistically significant at the .01 level. Thus, the higher the qualifications of teachers employed by the school district, the higher the district’s level of student academic achievement. It may be observed that the size of the path coefficient is small. 132 A third organizational attribute used in this study is faculty distribution, which is a measure of the func­ tional division of labor of school district organizations. The path coefficient between this variable and aggregate student academic achievement is small ( p ^ = .122) but statistically significant at the .05 level, revealing a direct positive effect of this organizational attribute. This result supports Hypothesis 25 and demonstrates that the greater the specialization of functions within the instructional component of school district organizations, the greater the district's level of student academic achievement. Finally, with respect to student-facuity ratio, it can be observed in Figure 10 that this organizational attribute shows a small direct negative effect on aggre­ gate student academic achievement (p^5 = -.133), which is statistically significant at the .05 level. supports Hypothesis 23: This result The smaller the average number of students assigned to teachers, the higher the district's level of student academic achievement. It may be observed in Figure 10 that the path coefficients between organizational attributes and aggre­ gate student academic achievement are of small magnitude. It is stressed here, however, that aggregate student 133 academic achievement, the selected operative goal (out­ put variable) of school district organizations, is an indicator of school district effectiveness at the elementary-school level since the only available measure of output was at this level. Given that academic achieve­ ment of students is likely to be emphasized more in higher grades than in lower ones, it seems reasonable to assume that the organizational attributes used in this study would show a stronger effect on aggregate student aca­ demic achievement measured at the secondary-school level. Support for this assumption was provided by Aldrich (1977) , who demonstrated that as students move from lower to higher grade levels, the influence of school resources (organizational attributes) on their academic achievement increases and the influence of their background factors (family and/or community socioeconomic level) decreases. The Basic Model Revised In the foregoing explanation of each endogenous variable included in the basic model of school district effectiveness, the hypothesized linkages between variables were tested. Also, the omitted linkages between variables that were assumed to be not statistically significant were assessed through the use of a "theory trimming" approach. 134 With the exception of Hypothesis 15, all other hypotheses regarding the diredt effect of one variable on another were supported by the data— all of them according to the pre­ dicted direction of influence. All but two of the omitted linkages were not statistically significant, as predicted. The two omitted linkages that were statistically signifi­ cant concern the path from average income of the families in the school district to faculty distribution and the path from average income of the families in the school district to administrative differentiation. The aggregation of the five subsections of the basic model evaluated and represented in their final form in the preceding pages results in the slightly revised model depicted in the path diagram in Figure 11 and expressed mathematically in the following set of recursive equations: X5 = P 52X 2+ P53X 3 + p 5aXa X6 = P61X1+ P62X2 + P63X3 + P64X4 + X7 * P73X3+ P74X4 + p7cXc X8 = P82X2+ P83X 3 + P84X4 + P8dXd x9 = P91X1+ ?93X 3 + P94X4 + P95X5 + P96X6 + P97X 7 + P98X 8 + p9eXe p6bXb SRACE SFRAT 086 sizE^Tr; 124 *2 FACQUAL 383 .070 RESOURCES T 3-.295 FACDIST 135 559 ADMDIFF INCOME P7C-.92 X1 (SRACE) = student racial characteristic *= school district size (SIZE) *2 (RESOURCES) « school district fiscal resources *3 • average incone of families in (INCOME) *4 4 the school district X5 | P8d_ ^ (SFRAT) = student-faculty ratio B faculty qualifications X6 (FACQUAL) (FACDIST) - faculty distribution X7 (ADMDIFF) > administrative differentiation XB (SA) - aggregate student academic achievement X9 Figure 11.— The revised model of school district effectiveness. 136 The Explanation of Aggregate Student Academic Achievement: Indirect Effects In Chapter III, several hypotheses of indirect effects of environmental input factors on aggregate student academic achievement through intervening organizational attributes were stated. In view of the slight modifica­ tion in the basic model, a question that logically fol­ lows is: Are the hypotheses of indirect effects stated in Chapter III supported in the revised model? The answer to this question is provided in Table 2, in which the indirect causal effects of environmental input factors on aggregate student academic achievement through interven­ ing organizational variables are reported. The values presented in Table 2 were obtained by multiplying the path coefficients in the causal chain from the predetermined (exogenous) variables to the ultimate endogenous variable. For example, the multiplication of p^1 = .069 by p• "School Effects: The Case for Grounded Theory." 1975 Sociology of Education 48: 383-99. Roberts, K. H.; Hulin, C. L.; and Rousseau, D. M. 1978 Developing an Interdisciplinary Science of Organizations. San Francisco: Jossey-Bass. Smith, M 1968 S. "Equality of Educational Opportunity: Comments on Bowles and Levin." 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