MODELLING CONSUMER’S PURCHASE BEHAVIOR AS A STOCHASTIC PROCESS Thesis for the Degree of Ph. D. MICHIGAN STATE UNIVERSITY TANNIRU R. RAO 1968 INN-4b 0-169 M1Club.- . date University w This is to certify that the thesis entitled Modelling Consumer's Purchase Behavior as a Stochastic Process. presented by Tanniru R. Rao has been accepted towards fulfillment of the requirements for ML degree in M i/M / Major professor Date g’g’u‘fl X Z /yéIJ} ——. ABSTRACT MODELLING CONSUMER'S PURCHASE BEHAVIOR AS A STOCHASTIC PROCESS by Tanniru R. Rao The behavior of the consumer and an understanding of the why's and ways of her purchase decisions are topics of growing interest in marketing. However, not much progress has been made in building realistic models of purchase be- havior as a function of the dynamic enVironment in which she makes her buying decisions. Descriptive models of mar- ket behavior are still the focus of much research activity since they are a prerequisite for building causal models of a market; a market is treated as the composite behavior of all individual consumers. Published evidence of brand choice models incorporating marketing variables, such as price, advertising, distribu- tion, et cetera, is sparse. On the other hand, Bernoulli, Markov, and learning models, the stochastic models widely used in the literature, describe the consumer's brand choice as a function of her past purchases. Tanniru R. Rao Purchase data of three consumer goods (a paper product, a drug product, and a food product), made avail- able by the Chicago Tribune form the data base for this in- vestigation. Probabilistic analyses of data reveal that housewives exhibit strong bias in the selection of a store for the purchase of any product and that a housewife's brand choice is different in different stores, suggesting that the choice of the store is a major intervening variable in executing the consumer's brand preferences. Accordingly, existing models of brand purchase have been extended by in- corporating the place of purchase (store) as a variable. The housewife's decisions regarding the size of purchase, the aggregate effect of store—brand interaction, and the effect of price on the market share of a brand are some of the issues considered in this investigation. Also, the in- creased number of private label purchases among store loyal customers and the lack of differentiation among private labels suggest the existence of certain market segments that are more prone to purchase private labels than others. Properly identi- fied, these would help both the retailer and the manufacturer in planning and allocation of their marketing efforts. This study is a first step in identifying the major com- ponents of the marketing system that have considerable effect (individual or interactional) on a consumer's purchase de- cision. More research is needed to include components such as advertising exposure, rate of consumption, time lapse between purchases, etc. This would enable the researcher Tanniru R. Rao not only to effectively simulate market behavior and pre-test marketing strategies or policy alternatives, but also to simultaneously study all the variables of the purchase decision for building dynamic aggregate models of the consumer's decision-making process. MODELLING CONSUMER'S PURCHASE BEHAVIOR AS A STOCHASTIC PROCESS By Tanniru R. Rao A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Marketing and Transportation Administration 1968 I p 1 Copyright by TANNIRU R. 1968 RAO In memory of my father, Tanniru Krishnamoorthy, a model of the ideal parent, international and compassionate human being .... citizen 'I ACKNOWLEDGMENTS I am very grateful for the support, advice, criticism, effort, time, and encouragement that I received from numerous persons in completing this study. Dr. Jerome D. Herniter, chairman of my diSsertation committee, interested me in the field of consumer buying behavior, and our many discussions provided the focus for my research. Dr. E. J. McCarthy and Dr. B. J. LaLonde offered constructive criticisms and considerable encourage- ment throughout the study. Data for the study was made available by the Chicago Tribune. The allocation of computer time for analyzing the data was granted by the Computer Institute for Social Science Research, Michigan State University. To dean C. Edward Weber of the School of Business Ad- ministration, University of Wisconsin-Milwaukee, my special appreciation for the research support that he made possible. A special research grant for the preparation of the manuscript which included some computer time, was received from the Food Marketing Program of the Department of Market- ing and Transportation Administration, Michigan State Uni- versity. I am very much indebted to Susan Czajkowski whose ii careful editing contributed to the manuscript. Thanks also to Mrs. Clara Crook and Mr. William Kraus of UWM School of Business Administration for their valuable advice and assistance. Mrs. Winifred Bachman, Mrs. Bette Heaton, and Miss Nancy Henke provided quick and efficient typing. iii TABLE OF CONTENTS ACKNOWLEDGMENTS LIST OF TABLES LIST OF APPENDICES Chapter I INTRODUCTION Background Scope of the Problem Statement of the Problem Statement of Hypothesis Method of the Study Limitations of the Study Organization II REVIEW OF THE LITERATURE ON MODELS OF BUYING BEHAVIOR . . . . . . Conceptual Model Macro Models Micro Models Bernoulli Models Markov Models Learning Models Brand and Store Loyalties iv Page ii vii ix ll 12 15 16 I7 21 3M “2 TABLE OF CONTENTS (Continued) Chapter Page III DESIGN OF THE STUDY . . . . . . . . . . . . . . 46 Introduction to Data Base . . . . . . . . . . 46 Research Design . . . . . . . . . . . . . . . u7 Method of Analysis . . . . . . . . . . . . . . A9 Product Descriptions . . . . . . . . . . . . . 52 IV ANALYSIS AND FINDINGS . . . . . . . . . . . . . 6O Hypothesis 1: Consumer's Loyalty to a Store . 6O Hypothesis 2: Consumer's Loyalty to the Type of Outlet . . . . . . . . . . . . . . . 65 Hypothesis 3: Interaction Between Brand Choice and Store Choice . . . . . . . . . . 68 Hypothesis A: Consumer's Decision on Size of Purchase . . . . . . . . . . . . . . . . 87 Hypothesis 5: Consumer's Purchase of Private Labels . . . . . . . . . . . . . . . . . . . 9H Hypothesis 6: Macro Analysis of Store-Brand Interaction . . . . . . . . . . . . . . . . lOu Summary . . . . . . . . . . . . . . . . . . . 112 V CONCLUSIONS AND MODELLING SIMPLICATIONS . . . . 116 Conclusions . . . . . . . . . . . . . . . . . 116 Modelling Implications . . . . . . . . . . . 118 Bernoulli Models . . . . . . . . . . . . . . 118 Markov Models . . . . . . . . . . . . . . . 125 Learning Models . . . . . . . . . . . . . . 129 Simulation . . . . . . . . . . . . . . . . . 142 Private Label Proneness of a Consumer . . . . iuu Future Research . . . . . . . . . . . . . . . luS TABLE OF CONTENTS (Continued) Page APPENDIX . . . . . . . . . . . . . . . . . . . . . . 1A7 SELECTED BIBLIOGRAPHY . . . . . . . . . . . . . . . . 219 vi Table 10. ll. 12. 13. 14. LIST OF TABLES PRODUCT, NUMBER OF FAMILIES, AND PURCHASES "PER FAMILY" . . . . . . . . . . . . . . . . FREQUENCY DISTRIBUTION OF PURCHASES AMONG FAMILIES O O O O O O I O O O O O O 0 O I 0 O O I PRODUCTVS. NUMBER OF COMPETING BRANDS PRODUCT VS. DISTRIBUTION OF MARKET SHARE AMONG ITS BRANDS . . . . . . . . . . . . . . . . . . . TYPE OF RETAIL OUTLET VS. PRODUCT SALES PRODUCT VS. DISTRIBUTION OF MARKET SHARE AMONG THE STORES PRODUCT VS. MARKET SHARE OF 10 MAJOR STORES . PRODUCT, LEADING BRANDS,AND THEIR MARKET SHARE PROPORTION OF HOUSEWIVES PURCHASING PRODUCT A IN THE STORE GIVEN THE PAST HISTORY OF THREE PURCHASES . . . . . PROPORTION OF HOUSEWIVES PURCHASING PRODUCT A IN THE TYPE OF OUTLET GIVEN THE PAST HISTORY OF THREE PURCHASES . . . . STORE CHANGE VS. BRAND CHANGE IN TWO CONSECUTIVE PURCHASES . . . . . . . . . . . . . . . . . . REPURCHASE RATE OF THE BRAND VS. STORE CHANGE PROBABILITY OF A HOUSEWIFE PURCHASING BRAND Al GIVEN THE HISTORY OF HERoPAST TWO BRAND PURCHASES AND THE CORRESPONDING STORES VISITED LISTING OF THE COMPARISONS CONSISTENT WITH THE HYPOTHESIS . . . . . . . . . . . . . vii Page 53 53 54 54 57 57 58 58 62 66 71 74 77 8O Table Page 15. PROBABILITY OF A HOUSEWIFE PURCHASING BRAND A GIVEN THE HISTORY OF HER PAST THREE BRAND PURCHASES AND THE CORRESPONDING STORES VISITED . . . . . . . . . . . . . . . . . 82 16. LISTING OF COMPARISONS CONSISTENT WITH THE HYPOTHESIS . . . . . . . . . . . . . . . . . . . 85 17.. PROPORTION OF HOUSEWIVES CHANGING THE SIZE OF PURCHASE OF PRODUCT A VS. THE PURCHASE PATTERN . 89 18. TESTING THE EFFECT OF STORE CHANGE AND BRAND CHANGE ON THE SIZE OF PURCHASE . . . . . . . . . 90 19. AN OVER-ALL MEASURE OF STORE AND/OR BRAND CHANGE ON THE SIZE OF PURCHASE . . . . . . . . . . . . 90 20. STORE LOYALTY VS. FRACTION OF PRIVATE LABEL PURCHASES OF COFFEE . . . . . . . . . . . . . . 95 21. REPURCHASE RATE OF THE PRIVATE LABELS VS. STORE CHANGE . . . . . . . . . . . . . . . . . . . . . 98 22. PROBABILITY OF A HOUSEWIFE PURCHASING PRIVATE LABELS OF COFFEE GIVEN THE HISTORY OF HER PAST TWO BRAND PURCHASES AND THE CORRESPONDING STORES VISITED . . . . . . . . . . . . . . . . . 99 23. MEASURE OF THE CARRY—OVER EFFECT IN PURCHASING THE PRIVATE LABELS . . . . . . . . . . . . . . . 103 24. SUMS OF PRODUCTS AND SUMS OF SQUARES . . . . . . . 107 25. ANALYSIS OF COVARIANCE FOR PRODUCT A . . . . . . . 108 26. TESTING THE LINEARITY OF BRAND x STORE INTERACTION 108 27. TESTING THE REGRESSION . . . . . . . . . . . . . . 108 28. RESULTS OF THE ANALYSIS OF COVARIANCE . . . . . . 110 29. PROBABILITY OF PURCHASING THE BRAND VS. THE HISTORICAL SEQUENCE OF PAST TWO BRAND PURCHASES. 120 30. PROBABILITY OF PURCHASING THE BRAND VS. THE HISTORICAL SEQUENCE OF PAST THREE BRAND PURCHASES . . . . . . . . . . . . . . . . . . . 122 viii LIST OF APPENDICES Appendix Page I NATURE OF PANEL DATA: AN OVERVIEW . . . . . . 187 Introduction to Panel Data . . . . . . . . 1u7 Panel Description and Administration . . . ing Panel Accuracy . . . . . . . . . . . . . . 153 II DEFINITIONS AND NOTATION . . . . . . . . . . . 157 IIII INDIVIDUAL ANALYSIS OF THE THREE PRODUCTS: COMPLETE SET OF TABLES . . . . . . . . . . . . 162 IV ANALYSIS OF TOOTHPASTE DATA . . . . . . . . . 202 V ANALYSIS OF COVARIANCE . . . . . . . . . . . . 210 ix CHAPTER I INTRODUCTION 8 a ckground Market experimentation is a rapidly expanding area of knowledge in the marketing discipline today. Scientifically p lanned eXperimentation can be viewed as a means to observe the effectiveness of small or large changes in the value of the controllable inputs.l With the increasing complexity of marketing management, demands are placed more on scientific re search than on limited fact finding activity. At the present stage of development, the operations research approach is the increasingly popular methodology in marketing. The Operations research approach, systems approach and model l3L15~1ding approach are treated as synonymous terms in des- cribing certain phases of research'in the literature. The need for understanding market behavior in solving marketing problems and in developing an effective marketing pr“CDgicam is obvious. This has given impetus for the develop- \ .i 1 William C. Hoofnagle, "Experimental Designs in Measur- rléi Effectiveness of Promotion," Journal of Marketing Re— M, (May, 1965), pp. isu—iez. 2 ment of various theories of market behavior. Formal state- ments of such theories are generally referred to as models. 3 . . . Day: In most buSiness Situations there are a few central factors which are of overriding impor- tance in determining the outcome. A model can be confined to these few major factors and it specifies the nature of the important relation— ships among these variable factors. In other words, a model is a theory of the business system or process. My major concern here is the study of "models of c:c>rusumer's buying behavior.” Such models of buying beha- \7:i<3r are in great demand today as manufacturers are trying t:c> out—guess their competitors by developing sophisticated Citlsstomer—oriented marketing programs. The complexity of the ITlEiI?ket1ng task makes model building extremely difficult, V111:ile the very nature of such complexity makes the model h i ghly desirable.” _§i<2<>pe of the problem Identification of the central variables in any business =3 i-TIuation constitutes an important step in developing models. qrrléere is often a great tendency on the part of the research— EBI‘ to restrict himself to a few variables to make the models "léirlageable. The very purpose of model building may become seaClondary in importance in this urge toward simplification. FI‘Om this standpoint, this study takes a critical look at \ 2 . . C2 Ralph L. Day, Marketing Models (International Text Book Ompany, 1964) p. 14. Ibid., p. 4. Ibid., p. 5. 3 some of the existing models of consumer buying behavior; major attention is focused on micro models - models based on an indi- vidual consumer's buying behavior. The central thrust of the investigation is the study of -t1162 inter—relationships among the various selected elements of -t11e3 consumer's purchase decision (store visited, brand purchased, 5 j_2:e of purchase, price of purchase) and their implications for 11:11ding realistic models of buying behavior. The study also lb 11.i_g;hlights some hypotheses of special interest such as consumer's I) and its relation to store loyalty. Ineeference for private labels The approach to the study is descriptive; the consumer has eaean studied in terms of what she did and not in terms of what U c:éaiised her to act the way she did. At times the cause and effect Gaileationship has been studied on an inferential basis. Even i.t:h this limitation, the study should be helpful (1) in de- 2 'I < €3.113ping more realistic models of consumer's brand choice as a frtlrlction of her environment, and (2) in developing an effective 3 lJniulation of the consumer's decision—making process. Eilijzjiement of the problem The housewife's purchase decision can be viewed as the (>‘1‘t<:ome of a set of mutually related alternatives available to F1631? .in the market. In any purchase decision, the housewife, i‘n‘IDSLicitly or explicitly, has selected a particular combina— tIi-CDIi of store, brand, size and price. The decisions on these valFicus aSpects of the purchase are not completely independent d. . . . . . . . . . . . L163 ‘to the limitations imposed by diss1milar distribution, in- S ItTC’I‘e services, advertising and promotion, and the dealing Ll activities of competing brands and stores. Due to the complexity of the problem, a considerable amount of research effort has culminated in descriptions of purchasing behavior in terms of the brands selected by the housewife. Accordingly, models published in the literature have incorpora— ted only the information‘on the past history of brands purchased to predict the probability of subsequent brand purchase. Even here, empirical evidence is sparse in the literature. Where the models have incorporated other marketing variables such as price, store, advertising and so on, empirical evidence is even 8 p arser. In this study, brand choice will be described as a function 0 f the consumer's past history of brand purchases and stores Visited. The aggregate effect of a price differential on the market share of a brand, the store selection patterns of the con- 8 umer, and the consumer's decision on the size of purchase as affected by the brand or store change are studied in detail. In addition, the loyalty of the consumer to private brands and the frequent visiting of a store as it affects her preference for the store's private labels are studied. The specific focus of the study, in terms of hypotheses, are given in the following 8 e C‘tion. S1:flement of Hypotheses (l) A consumer's selection of a store is not completely b . . andcm (i.e., has an equal likelihood of selecting each store); 8 he exhibits bias in her choice. a) The more recent her purchase eXp . . . erzience in a particular store, and b) the more frequent her Visits to the store, the more likely she is to repurchase the product in that store. (2) As a corollary, consumers exhibit bias in the selection ‘of: the type of retail outlet (drugstore, food store, etc.) in hflhLiCh they would shop for a particular product. (3) Store switching increases brand switching; the more a i1c>tisewife changes stores, the more she changes the brand she p u rchases . (4) Consumers change the size of their purchase when they c:riéange the store or brand; in general, they decrease rather than .i.r1<:rease the size of their purchase with a change in store or 132r~aind. (5) Loyalty (measured by the repurchase rate) to a particu- J.611? store increases the preference for the private brands spon- E3C>r-ed.by the store. As a corollary, a housewife loyal to a pri- "Ei‘t€3 brand sponsored by a particular store is loyal to private l—EiIDeals regardless of store. (6) Store—brand interaction is statistically significant Eli:‘tfereliminating the effect of price. As a corollary, the eifrfFect of price on market share is significant and the interaction C>f: Ibrand and store cannot be explained by any linear function of “tfl‘a corresponding price difference. Mod of the Study In the probabilistic approach to the purchase decision EDIICDCZess, the housewife's purchase decision is treated as the begsStilt of the underlying parameters (probabilities of choosing d . 'lifriFerent alternatives). Following the axioms of probability 6 theory, the probability of a consumer purchasing any brand is measured by a number in the closed interval (0, 1). Since the housewife has to select one or another of the available brands, tide probabilities of purchasing different brands of the product .acici up to one. This type of probabilistic approach can be used j.r1 any situation where one has to select from a set of mutually ea>cc21usive and collectively exhaustive alternatives. Kuehn:5 The probabilistic approach provides a useful conceptual framework for considering the ex- pected behavior of consumers. When the ex— pected behavior of an individual is viewed as a set of probabilities related to the available brands, a richer and more flexible concept of brand loyalty is provided. Simple probability models are useful as building blocks in the construction of dynamic, aggre- gate models of consumer brand choice behavior. The probabilistic approach has some definite advantages. CDIuea can measure the effectiveness of advertising, promotion, Eirlci distribution strategies by comparing the probabilities of E>Lllechasing different brands before, during, and after eXperi- meBl’i‘tation. In each period a simple weighted average of these P>I‘C>babilities over various individual consumers in the market ('V’Eiighted by the frequency of purchases or rate of consumption) degtermines the market share distribution of brands. In this ESTIlldy, purchase histories of consumers over a period of three 3’EEEirs form the data base for the analysis. Sequences of two, three, and four purchases are aggregated .._‘_~_‘ .8 5 Alfred A. Kuehn, "Probabilistic Modelsof Consumer Buying ehéivior,” Journal of'Marketing, 28 (October, 1964), pp. 27-31. over individual consumers to describe purchasing behavior at the micro level in terms of conditional probabilities for three different products (paper product, drug product, and food pxroduct). At the macro level, the statistical technique of [irialysis of Covariance has been used to study the interaction c>f: brand and store. The detailed aspects of the research de- 5 ign and techniques are presented at a later stage. Discussing the present stage of development of the proba- 13:1 listic models of consumer behavior, Kuehn said that the em- ;311easis has been on understanding the influence of marketing Vréainiables on the consumer's decision process.6 If a particular ;p>1?<>babilistic model gives good predictions of market behavior, t:11£3 reasons the model works are of more importance than the fréiCZT that it does work. Lai;niitations of the Study Kuehn:7 The more fundamental problem facing marketing science is the development of a model which will allow the simultaneous study of all the major marketing variables. Such a model would provide an extremely powerful tool, for the study of the effects of past purchase policies could serve as a basis for pre-testing proposed policies, and would provide an extremely sophisticated sales forecasting model. Needless to say, the mathematical formulation of such a Inc>C1el is a formidable task. With the increasing uncertainties C31? such a task, simulation offers some immediate solutions; hc>‘Never, knowledge of the inter—relationships among the major ~‘_‘_‘_‘ 6 Ibid. Ibid. 8 variables of the consumer's marketing environment would be a prerequisite for purposes of constructive simulation. With tliese broad goals in mind, this study has been limited to the deascriptive aspects of the consumer's interaction with the rnéiirketing environment as a first step. In order to model the consumer's purchasing behavior as a. ciynamic stochastic process, the requirement of data on the c2c>rusumer covering a period of time is essential. Panels have t>€3e3n the major source of such information. In general, panels reeaczord the information on brand, store, size, price, and time <>:f= each purchase for a selected sample of families over a period c>:f: time. However, panel data do not give any information re- gg.EiI‘ding the advertising and promotions of stores or brands and (DIrIILy limited information on the presence of deals and price Ei.1.1:ernatives available to the consumer in the store on any pur- Clli.éise occasion. The presence of deals on a particular brand 1—13- a store can be inferred from data only if the actual purchase i‘ES Inade against that deal. Similarly, the panel data supply the E’1?.i.ce paid by the housewife but do not shed any light on the F’ITWi.ces of competing brands available to her at the time of pur- C:}1£343e. Added to these, the availability of brands, possible S1:‘Dck-outs, and the location and size of displays are variables t:}1é35t enter into the consumer's decision which, at best, can only t>€3 1>rought into focus with specially designed experiments. These lI‘lrnitations of data often leave no way for an investigator to t . . €1531<1e some of the detailed aspects of the consumer's purchaSing b O I O O EE}1§3V10P except on an inferrential baSis. Ry 9 To offset some of the said limitations of the data for the study of store-brand interaction, a portion of this in- vestigation'has been limited to the major national brands of the product-lines, as well as to the major retail outlets in the Chicago area where the specific brands have near 100 per— cent distribution. The structure of the competitition in the product lines, along with the market shares of the specific brands and stores selected, are presented in detail at a later stage. Organization The second chapter reviews the published literature on micro models of consumer buying behavior. Major importance is given to the models developed on the basis of panel data; the limitations and the underlying assumptions of the models are discussed in detail. For the purpose of convenience in presenta- tion, the models have been grouped into broad categories such as: (1) Conceptual Models; (2) Bernoulli Models; (3) Markov Models; (4) Learning Models. The third chapter deals with research design, the nature of panel data, and product descriptions. Research design includes the purpose of selecting the three specific products for this study and a description of differences among them in terms of consumer use, structure of competition, etc. A detailed account of the published literature, critical and supportive, of the panel data and its validity as a representative sample of the total consumer population, is presented in Appendix 1. 10 The fourth chapter deals with the analysis and the findings in regard to the varification of the hypotheses proposed in the earlier section. The empirical verification of each of the hypotheses has been presented in appropriate tables. Some of the statistical techniques used in the analysis are described in detail in Appendix V. The presentation of the study is concluded with the author's remarks, where the findings have been discussed in terms of their implications to the task of building realistic models of consumer's buying behavior. CHAPTER II REVIEW OF THE LITERATURE ON MODELS OF BUYING BEHAVIOR Models are of two types, descriptive and causal. A des- criptive model describes the observed phenomena and, at best, the causal relationships involved can only be drawn on an inferrential basis. In a causal model, the experimental design facilitates the understanding of the cause and effect relationships involved in the behavior. Herniter:l Of primary importance to the marketing executive is a knowledge of how his company's promotional and advertising activities causally affect the sales of its products in a competitive environ- ment. Unfortunately, the marketing process is so complex and our knowledge of it so rudimentary that the achieve- ment of this goal is a problem in re- search rather than in application. As a step toward creating a causal model of the market, it is necessary to con- struct a descriptive model that reveals how the market is behaving. That is, before we can offer the reasons for the markets' behavior, we must be able to describe the behavior itself. Considerable research effort is being directed toward developing various descriptive models of the consumer's buy- ing behavior under different sets of assumptions. 1 Jerome D. Herniter and Ronald A. Howard, "Stochastic Marketing Models," working memorandum of Arthur D. Little, Inc. (Not dated). 11 l2 Descriptive models can be purely conceptual or mathema- tical formulations. A conceptual model of the consumer and her interaction with the marketing environment is constructed using the existing knowledge of the marketing system and its components. Models of economic, affluent, limited rational, and social class consumers are examples of conceptual models based on different sets of assumptions and are widely published in the literature. One specific formulation presented by Breyer is discussed in detail at a later stage in view of its significance to the present study. Mathematical models are conceptual. In addition, in a mathematical model all the variables are quantified for measure- ment and more often the mathematical models are based on em- pirical verification. Mathematical models of consumer behavior can be further classified into Micro and Macro models. A micro model describes the individual consumer's purchase behavior, and the market is treated as a composite behavior of many individual consumers. As panels are a major source of information on indi- vidual consumer purchases, most of the existing micro models make use of panel data. A macro model describes the over-all behavior of the market without any reference to the individual consumer. Macro models are also known as flow or gross models. Conceptual Model A discussion of the conceptual framework suggested by Breyer follows.2 The model basically describes the consumer . 2Ralph F. Breyer, "Proposal Formation and Programmed Market- ing," unpublished article, Pennsylvania State University. ... c. ”I u. ”I ... .o. .. ..— .~ C. ..- .. c. .. .v. r. r. ... .. \.. .~‘ i.\ ,v c. , 13 and her interaction with the marketing environment. According to Breyer, the two elements of the consumer's purchasing en- vironment are: (1) consumer make up; and (2) the total situa- tion. Consumer make up includes the conditioning of the house- wife's buying behavior by the past history of brand purchases, advertising exposure, and the exposure of the consumer to the promotional mix of all the competing brands in the market prior to her entering the store to make her purchase. In other words, Breyer coins the words "consumer make up" to include the psycho- logical attitudes of the housewife toward the brand before she enters the store and "total situation" to signify the promotional environment of the brand that the housewife is eXposed to in the store at the time of the purchase. Total situation is fur- thur classified as the physical setting, the proposition of the brand, and the broad environmental factors in the store. The proposition consists of the physical product, the price, and the accompanying services after the sale. The physical setting refers, among other things, to the quality and size of the dis- play, sales talk, and in—store promotional services of the brand that would enhance the sales environment of the brand. In every purchase decision of the housewife, all the sub-elements and elements of this framework play their own important part. Assum- ing that the basic objective of the firm is to secure the pur- chase decision of the housewife in favor of the firm's brand, the manufacturer should carefully structure the marketing en- vironment of its brand in each and every retail outlet. The wider implication of the statement is to argue for efficient 14 channel management in addition to the management of advertising and promotion. For example, consumer make up is influenced by media advertising and promotional campaigns, proposition in— fluenced by product development and pricing, and physical set- ting influenced by the distribution and good working relations at the retail level. Breyer pursues this framework further to argue for the optimal allocation of marketing effort among the various functions and suggests some alternatives for an efficient ”programmed marketing." In the case of frequently purchased consumer goods, price is the only important element of the proposition, as the physi— cal product and accompanying services are more or less same among different brands of the product. However, consumer's relative preferences for different brands are widely varying as evidenced by the frequently observed phenomena of loyalty to brands. Thus, the consumer make up can be described by the past history of the consumer's brand purchases of the product. The physical setting of the brand is likely to be different from store to store. As a first step, let us assume that the brand's relative physical setting within a store remains the same over a period of time. Accordingly, the past history of brand purchases, the price of the product, and the store visited are the three major aspects of the consumer's purchase decision process. It is to be noted that these three elements of purchase decision occupy a central part of my investigation. This con- ceptual model has a close relationship to this investigation in that housewives with the same history of brand purchases visiting 15 two different stores are likely to choose different brands due to the differences in price and physical setting of the brand between stores. In other words, store-brand interaction should be a major consideration in planning promotion and dis— tribution strategies. Macro Models I shall not discuss Macro models in detail as they are not of immediate relevance to the purpose of my study. However, a brief mention of them is in order. Macro models depict the over—all behavior of the market with no consideration of the individual consumer. Frank and Massey3 analyzed the time pattern of the marketsflmres due to the changes in prices and the deal magnitudes, by fitting a multiple regression of current and lagged price and lagged market share on the current share of the brand in the market. Herniter and Mageeu discussed some of the advantages of describing the over-all market behavior as a Markov process. Farley5 hypothesized that the differences in the degrees of loyalty among consumers in different product lines can be explained by the structural variables in the market in which products are sold, such as: (l) the number of brands in Ronald E. Frank and William F. Massey, "Short Term Price and Dealing Effects in Selected Market Segments," Journal of Marketing Research, 2 (May, 1965), pp. 171—185. Jerome D. Herniter and John F. Magee, "Customer Behavior as a Markov Process," Operations Research, 9 (January-February, 1961), pp. 105-122. John U. Farley, "Why Does Brand Loyalty Vary Over Products?" Journal of Marketing Research, 1 (November, 196A), pp. 9-14. 16 the product line; (2) the average rate of consumption by the consumer; (3) the degree of the price activity in the product line; (A) the multiple usages of the product; (5) the intensity of the distribution; and (6) the domination of the market by the leading brands. Micro models Herniter:6 There is a growing body of literature on the analysis of panel data for frequently purchased, low cost consumer items. One of the methods of analysis has been the development of market models. The detailed structure of a model of a process is dependent upon the data that is available. Since panel data yield detailed consumer purchase histories, market models have been developed which describe the purchase behavior of individual consumers. As stated earlier, micro models of buying behavior deal with the individual consumer's purchase decision process. The marketing manager's objective is to achieve the short and long run profit goals of the company. In achieving these goals, he uses different strategies, such as dealer promotions, price pro- motions, media advertising, et cetera, primarily to change the consumer's purchase decision in favor of his brand. Hence, a model that describes individual purchase behavior should help a marketing executive in allocation of his marketing effort. Jerome D. Herniter, "Stochastic market models and the analysis of Consumer Panel Data," presented at the twenty- seventh National Meeting of the Operations Research Society of America, Boston, Massachusetts, May 6-7, 1965. 17 . 7 . . . Herniter: The behaVior of the market is the compOSite behavior of many individual consumers. As a result, the market is a complex proba- bilistic system that is complicated in its interactions and difficult to observe. Yet, if there is to be any progress in controlling the market process as a whole, we have no alternative but to attempt to analyze it at its most fundamental level -— the activities of the individual consumer. One particular method of describing individual consumer's purchase behavior is by means of a set of purchase proba- bilities. It would be very useful if the model could provide a method of revising the set of probabilities due to the passage of time, new purchase eXperiences, and other marketing . 8 . . . . . . influences. With this brief introduction, I shall reView some of the micro models. Bernoulli Models The simplest postulated brand switching model is the Bernoulli trLfl.model based on the following assumptions: "(1) In a K brand market each customer has a set of probabilities, pj, j = l, 2, . . , K, which define her probabilities of purchasing each brand. The. customer maintains this set of probabilities in- definitely. (2) Each purchase is independent of the customer's previous purchases. Jerome D. Herniter and Ronald A. Howard, "Probabilistic Consumer Models," unpublished paper, (Not dated). 8 Alfred A. Kuehn and Ralph L. Day, "Probabilistic Models of Consumer Buying Behavior," Journal of Marketing, 28 (October, 196”), pp. 27-31. 18 (3) For each pj there is a distribution of pj over the population."9 Assuming a beta distribution of pj over the population, HerniterlO tested the model with purchase data of different products. The results are not encouraging in terms of the model describhg the observed brand switching behavior. The basic disadvantage of the model is that the probability of pur- chasing a particular brand depends on the number of purchases made by the individual consumer in her purchase history and independent of whenthey occurred in the sequence. This does not conform with the observed behavior where the recent pur- chases have more effect on brand choice than the earlier ones. However, if all the previous purchases had been of one particu- lar brand, the model predicts that the probability of subse- quently purchasing the same brand increases, and this conforms with the observed behavior. Let bj(n) 1 if brand j is purchased by the consumer h . nt time, = 0 otherwise. According to the Bernoulli model, if the customer has a probability of purchasing brand j (pj), then according to the model Jerome D. Herniter, "Stochastic Market Models and the Analysis of Consumer Panel Data," working memorandum, Arthur D. Little, Inc., (Not dated). 10 Ibid. n = 2, 3, u, ql, q2’ '0, qn_l : 0,1 where EU} indicates the probability of the event U, and K is the number of brands in the market. Using the definition of conditional probability, we obtain 2 {bj(n) - l lbj(n—l) - qn-l’ bj(n-2) - qn_2, .., bj(l) - qL; :fbj(n) : l, bj(n-l) : qn-l’ bj(n-2) : qn_23 ’, bj(l) : ql} gbj(n-l = qn-l’ bj(n-2) = qn_2, .., bj(l) = ql} Suppose pj has a beta distribution with parameters r' and n' over the population in the market. Then, {bj(n) = l .bj(n-l) = qn bj(n-2) = q :5 to U \0 U‘ {—1. A P v n D H vvv -l’ N b l j(n) Z l, bj(n"l) Z qn-l, bj(1’1-2) 2 qn-2’.’bj(l) : qllpj}{pj} J {b (n-l) = qn-l’ bj(n—2) = qn_2, .., bj(l) = q1 Ipl}{;j} J I Pi I p. n-l-c -1- (pjc(l_pj)n c > where < > is used to indicate expected values r'+c n'+n-l where c is the number of purchases of brand j in the past (n-l) A“ a~ a». . - 2O purchases of the consumer. Note that the ratio (r'+c)|(n'+n-l) is affected only by the number of the purchases made by the consumer and not when they occurred in the sequence. Frankll used Bernoulli Trial model (although he did not use the name) to analyze panel data for coffee purchases. A run in a purchase sequence is defined as the number of success- ive purchases of a particular brand by an individual consumer. Frank tested his hypothesis by using the distribution of runs in the purchase sequences of individual consumers. He found a considerable number of families with varying probabilities of brand purchase over time, thus rejecting his hypothesis. Howard,l2 expanding the simple Bernoulli model by incorpora— ting another stochastic process, suggested an interesting con- cept for describing the consumer's brand choice. The model is described in detail here in view of its implications to my study, though empirical verification of the model is lacking in the literature. A problem constantly facing the analysis of business systems is that of modeling situations where the under- lying statistical parameters of the process may change from time to time. In other words, the parameters of one process are affected by another stochastic process. A method of analysing such a situation is to assume probability distributions of the 11 Ronald E. Frank, "Brand Choice as a Probability Process," Journal of Business, 35, (January, 1962), pp. 43-56. 12 Ronald A. Howard, "Dynamic Inference," Operations Re— search, 13 (September-October, 1965) pp. 712-733. 796'? * * Cu 0 0.0A2(13011) 0 067(7653) _,1- -0,u67(1106)“_9;338(731) M5 37 * * * Significant at 1% level * Significant _ _ Not significant at 5% level 75 estimates have been based. ‘ According to the hypothesis, a housewife who did not purchase the brand the last time has a higher probability of purchasing the brand if she changes the store than if she visits the same store. Similarly, a housewife who purchased the brand the last time has a lower probability of purchasing the brand if she changes the store than if she visits the same store. In all twenty cases of the ten brands tested, the tendency of the observed estimates are consistent with the hypotheSis. In eight of the ten cases the differences in probability estimates due to store change are found statistically Significant at the 5% level of significance and, thus, the hypothesis that store change is independent of the re-purchase rate of a brand is re— jected. Similarly, the three purchase sequences of a housewife are aggregated over the individual consumers and time to estimate the probabilities of a housewife's purchasing a given brand, as a function of her past two brand purchases and the correspond- ing stores visited. With our notation of "S's" and "D's" for store chOices, there are five possible ways of classifying the housewife's past two store visits, as shown below. The housewife can be uniquely claSSified in terms of her two previous brand choices (00, 01, 10, 11). Given the history of a houseWife's two past brand choices and stores visited, along with the store of her subsequent purchase, she occupies a unique position in the u x 5 matrix of Table 13. The condi— tional probabflity in each cell of this u x 5 matrix is calcula- 76 ted by obserVing the actual fraction of housewives belonging to that cell and purchasing brand ”1” on their subsequent pur— Hypothetical Store Visits in Sequence 2nd Subsequent Background of 'Recent Purchase Recent Purchase Purchase Stores Visited Indicated by ._—— 7 “FA 8 P A 8 P A 8 P SS A 8 P Kroger A 8 P SD Kroger A 8 P A 8 P DS Kroger Kroger A 8 P DlDl Kroger Jewel ’ A 8 P DIDZ chase. The last column of the table is a weighted summation of the first five columns, which gives the conditional proba- bility of a houseWife purchasing brand ”1" given the history of her two previous brand purchases, Without taking into con- sideration the pattern of store viSits. The figures in the parentheses indicate the sample Sizes on which the corres- ponding probability estimates are based. According to the hypothesis, people SWitch brands when they switch stores. Accordingly, a housewife who has not pur— chased brand '1' the last two times (sequence 00) is more like— ly to purchase brand '1' for her subsequent purchase if she visits a store different from the earlier two rather than if she visits the same store all three times. It is observed that in the cases of store sequences DlDl and D1D2 corresponding to the brand sequence '00', the probabilities of a housewife pur— chaSing brand '1' are .163 and .172 respectively, compared to 77 TABLE I3 PROBABILITY OF A HOUSEWIFE PURCHASING BRAND A1 GIVEN THE HISTORY OF HER PAST TWO BRAND PURCHASES AND THE CORRESPONDING STORES VISITED PRODUCT A (Paper Product) BRAND A1 l-Purchased Brand A1 O—Not Purchased Brand A1 Historica1.Past H: Lstory of Stores Visited Irrespecfive Sequence 1 of the of Brands 1 SS SD DS DlDl iDlD2 Store Choice Purchased ' (over—all) 00 0 116 0 119;0 109 0.163 0.172 0 139 (336) (210)1(256) (276)i(377) (1“55) 1 i 10 o u81 0 u58!0.372 0.u77|0 675 0.u55 (10M) (59) (78) (65) ((118) (820) 01 O 567 0.339 0.673(0.583‘0.A90 0.5A] (90) (59) ((92) ((60) |(lOO) (401) 11 0.874 0.867éo 8M2 0 79010,77i 0 833 (435) (188)11214)1(2“5)1(253) (1338) FOOEEQEEEE Indicating the past two purchases by l and 2, and the subsequent purchase by 3 the notation stands for the following events: Stores Back- groun Event SS 5(1) = 8(2) SD 8(2) # 8(1) DS 8(1) # 8(2) 0101 8(1) = 8(2) 0102 8(1) ¢ 8(2) ha t3 t1: t2 = 1: 2s = 5(3) = S(3) or sh(2)¢sh(1)=sh(3)=1 = 5(3) or sh(1)¢sh(2)=sh(3)=1 ¢ S(3) or Sh<1>=Sh(2>#Sh(3>=l St(1)=St(2)=l for a t # h R° # 8(3) or Sh(l)=Sh(2)=Sh(3)=1 R0 or Sh(l)=Sh(2)=Sh(3)=l H) O "S U) 0 3 ('D :3‘ for some h St2(1)=l, Stl(l)=l for t1¢t2 78 the probability of .116 while visiting the same store (SS). (Refer to Table 13). As another example, suppose a housewife has her brand history given by 01. Under the hypotheSis, if the pattern of ,her store visits is given by SD, the probability of her pur— chasing brand '1' for her subsequent purchase is lower than if she visits the same store all along (SS), because the consumer's selection of brand '1' on her last purchase might have been prompted by her store change at that time rather than by any higher preference for brand '1'. If the same housewife has the pattern of store visits given by 08, her probability of pur- chasing brand '1' subsequently increases for the same reason as explained above: her purchase of some other brand on her second most recent purchase might have been due to her visiting a different store at that time rather than due to any higher pre— ference forsome other brand. The probabilities, as estimated by data in Table 13, are given below: Pattern of Probability of Brand Sequence Store Visits Purchasing'Brand 'l 01 SS 0.567 01 SD 0.339 01 DS 0.673 The observed trend is consistent with the hypothesis. By looking at the observed magnitudes of the estimated proba- bilities, the numbers of comparisons that are consistent and inconsistent with the hypothesis are liSted in Table 1A. In all, eight comparisons are possible in this A x 5 matrix to 79 test the validity of the hypothesis. The expected trends in the probability estimates under the hypothesis are shown below: \_ ItLStOPlcal Past History of Stores Visited Secluence of Brnands SS SD DS D D D D Ptirchased l 1 l 2 00 X1 Greater Greater than Xl than X1 01 X2 Less than Greater X2 than X2 10 X3 Greater Less than than X3 X3 11 X Less than Less than 4 X X 4 1+ $3.1.nce the analysis has been repeated over all the ten leading lDr‘ands of the products, there are a total of eighty such com- P>éi:bisons possible for the verification of the hypothesis. The i-T1<:lividual analysis of the ten brands, describing the house— ‘VSL ire's probability of purchasing a brand given the history of 13€3 I“ past two brand purchases and the corresponding store vis1ts, Eir‘EB presented in Appendix 3. (Refer to Tables 3.7 to 3.16). 'F}1€3 null hypothesis that the observed pattern in probability ess‘t.inmtes can be attributed to purely chance factors is tested. Irl (ather words, the hypothesis implies that store change has no efzi‘eact on the probability of a brand purchase by a housewife. Urléiear the null hypothesis, the probability estimates will not héi"€a any specific pattern related to the stores viSited, and as; ssuch, it is expected that in only 50% of the comparisons ST:CNbe change reduces the probability of purchasing a brand. 80 TABLE I“ LISTING OF THE COMPARISONS CONSISTENT WITH THE HYPOTHESIS w - "___—w—w‘w—‘c ___—'7 —~—.———-.——_-—— -- NumEEETSf Number of , Comparisons Comparisons jReference No. I Consistent with Inconsistent with _LAppendix III) the Hypothesism_m____the Hypothesis 3.7 7 1 3.8 7 l 309 7 1 3.10 6 2 3.11 7 1 l | i 3.12 7 1 1 ,1 e 3.13 i 8 ; 0 ) t 3.1M I 8 0 3.15 1 8 0 3.16 8 0 Total 5 73 7 I’ercentage of Comparisons Con- ; Esistent with the Hypothesis 4 91-2 Null Hypothesis: H = 0-50 n = 80 Alternate Hypothesis: n>0 50 Observed value of p = 0.91 Z = Normal deviate under the = Q 2%;2g§g_= 0,A1 V320 = 7.38 hypotheses '(0;5§g_5) .7 80 - Z being greater than 2.33 (from Normal curve tables), the.null hypothesis is rejected at 1% level of significance. 81 The observed value of 91% of the comparisons where store change has reduced the probability of purchasing a brand falls well in the crithu.region of the test, thus rejecting the null hy- pothesis. Accordingly, store switching increases brand switch- ing. Details of the test of binomial proportions are presented following Table 14. In sequences of four purchases a similar type of analysis has been repeated and presented in detail below. As earlier, sequences of 1's and 0's represent the past brand purchases of the consumer, and sequences of S's and D's represent the stores visited. Instead of presenting the 8 x 8 pOSSible matrix of the ccniditional probabilities, only estimates that are relevant for dernonstrating the hypothesis are presented. The complete set Of" tables describing the conditional probability of a housewife pLIrchasing brand '1', given the history of her three past brand lerchases and the corresponding stores visited, are presented in ADpendix III (Refer to Tables 3.17 to 3.26). The ten tables refer to the analyses done separately for each of the ten major bbands. For the purposes of illustration, the analysis of brand A is given on the following page. (Refer to Table 15). The l. 1Eist column of the table gives the conditional probability of a housewife's purchasing brand '1' given the history of her tklree previous brand purchases irrespective of the pattern of S"Sore visits. With our notation, brand code '1' stands for the pairticular brand in the analysis, and the figures in parentheses I‘EEfer to the sample sizes on which the corresponding estimates C’f: probabilities are based. 82 TABLE 15 PROBABILITY OF A HOUSEWIFE PURCHASING BRAND A1 GIVEN THE HISTORY OF HER PAST THREE BRAND PURCHASES AND THE CORRESPONDING STORES VISITED PRODUCT A (Paper Product) 1-Purchased Brand A1 BRAND Al O-Vot Purchased Brand A1 HIStorical ___, Irrespective Sequence Past History of Stores Visitgd - of the of Brands SSS DDD . Store Choice Purchased __*__(gygr:all) 000 0.067 0.132 0.101 (165) (416) (1143) 010 DSD SDS 0.478 0.412 0.125 0 377 0.383 (23) (17) (16) (69) (167) 001 DDS SSD 0.393 0.655 0.077 0.459 0,462 (28) (29) (13) (61) (182) 011 DSS SDD 0.562 0.750 0.389 0.532 0 614 (32) (28) (18) (62) (197) 100 SDD DSS 0.378 0.389 0.375 0 306 0.335 (37) (18) (16) (85) (209) 110 SSD DDS 0.595 0.524 0.414 0 508 0.522 (42) (21) (29) (59) (207) 101 SDS DSD 0.667 0.800 0.417 0.558 0 622 (36) (15) (12) (52) (180) 111 0.921 0.825 0 877 (241) (314) (1033) vn N? (I! (I) 83 Under the hypothesis, a housewife with the brand history given by the sequence of 001 has a higher probability of pur- chasing brand 'l' subsequently if her pattern of past store visits is DDS rather than SSS, because her purchasing of other brands the first two times might have been induced by her visit- ing a different store rather than by her higher preference for some other brand. The same housewife has a lower probability of purchasing brand '1' if her pattern of past store visits is SSD rather'thaiSSS for the same reason. Her recent purchase of brand '1' might have been caused by her visiting a different store at that time. The observed estimates in regard to the purchase of brand A are (Refer to Table 15) given below: 1 Brand Purchase Pattern of Probability of Pur- Sequence Store Visits chasing Brand '1' 001 SSS 0.393 001 DDS 0.655 001 SSD 0.077 There are in all fourteen such comparisons possible, and the eXpected magnitudes of these probabilities under the hypo— thesis are given in the following page. The comparisomshave been made against the columns of S or SS or SSS (visiting the same store), since the hypothesis points to dunging the store as a major factor in eXplaining a part of the variation in brand choice. Thus, the hypothesis Historical Sequence of Past History of Stores Visited Brands Purchased SSS DDD 000 Xl Greater than X 1 001 X2 DDS SSD Greater Less than than X2 X2 010 X3 DSD SDS Greater Less than than X3 X3 011 X14 DSS SDD Greater Less than than Xu XL+ 100 X5 SDD DSS Greater Less than than X5 X5 101 X6 SDS DSD Greater Less than than X6 X6 110 X7 SSD DDS Greater Less than than X7 X7 111 X Less than 8 x8 is checked by comparing brand purchase probabilities while switching stores as opposed to visiting the same store. 16 evaluates the validity of the hypothesis by listing the proportionate number of comparisons that are consistent with the hypothesis, considering the analysis of data on sequences of four purchases. Table 85 TABLE 16 LISTING OF COMPARISONS CONSISTENT WITH THE HYPOTHESIS Number of Comparisons Number of Comparisons Table Reference No. Consistent with the Inconsistent with the (Appendix III) Hypothesis Hypothesis 3.17 12 2 3.18 11 3 3.19 11 3 3.20 11 3 3.21 12 2 3.22 12 2 3.23 14 0 3.24 14 0 3.25 14 0 3.26 13 ' 1 Total 124 16 Percentage of Comparisons Consistent 88.6 with the Hypothesis Null Hypothesis: H = 0.50 n = 124 Alternate Hypothesis: H>0.50 Observed value of p = 0.89 Z = Normal deviate Under the hypothesis = 9'89 ‘ 0'50 = 0.39 (560 = 9.24 (0.5 x 0.5) 140 Z being greater than 2.33, (from Normal curve tables) the null hypothesis is rejected at 1% level of significance. 86 The null hypothesis that the observed pattern of proba- bility estimates could have arisen because of chance factors have been tested on the same lines as explained earlier. The observed value of 89% of the comparisons is well above the expected value of 50%; thus, store switching increases brand switching. Details of the statistical test of binomial prOpor- tions are presented following Table 16. In analyzing the sequences of two, three,and four pur— chases, this study arrived at the consistent finding that store change has increased the probability of brand change. This general finding has been consistent over all the national brands of the three products. Brand switching due to store switching ~is of extreme importance to manufacturers in: (1) developing effective distribution strategies, and (2) identifying the stores where the firm's brand has been losing or gaining custo- mers. So far the study has been concerned with the consumer's brand choices as she shops in different stores. However, from the manufacturer's point of view, another closely related and important characteristic of the consumer's choice is the size of her purchase. The market share of any brand (by dollar volume) is a simple multiplicative function of the unit price, the size of the purchase, and the probability of purchasing the particular brand. The size of the purchase, as used here, is the total number of units of a product purchased by a housewife on any one particular purchase occasion and, as such, it should not be confused with the package size. In the next hypothesis, we 87 look into changes in the size of purchase as a housewife changes her store or brand or both. HYPOTHESIS 4: Consumers change the size of their purchases as they change the store or brand; in general, they decrease rather than increase the size of their purchase with a change in store or brand. Changes in purchase size may be prompted by many factors, such as: (1) the availability of different package sizes in different stores; (2) the lack of a uniform package size among different brands; (3) the unit price differential on higher package sizes; and (4) the customer's inherent demand variation in the use of the product. In addition to these, a housewife might be decreasing the size of her purchase as she changes brand because of her lack of familiarity with the new brand. Also, a housewife who visits a different store because of some advertised price promotion in the store is likely to increase the size of her purchase over the usual. Not much research has been published on the factors contributing to a housewife's decisions on purchase size. In this study, the proposition that a housewife's decision on purchase size is random is re- jected, and some tendencies influencing change in her size of purchase are observed. One can visualize the range of variation in the size of a purchase on a continuum from zero to infinity, and minor changes inevitably caused by package differences are quite likely to exaggerate the magnitude of the observed variation in the size of purchase. As such, using the distribution of sales over different sizes, the observed range in size of purchase has been 88 grouped into low, medium and high volume categories. Only housewives changing from one category to another for two conse- cutive purchases are counted as changing their size of purchase. Table 17 presents the proportion of housewives who increased, decreased, or retained their purchase size as they visited different stores or purchased different brands while buying product A. The complete set of tables are given in Appendix III. (Refer to tables 3.27, 8.28, and 3.29). The null hypothesis that size of purchase is independent of brand or of store change has been tested by computing the value of statistical x2. Table l8 presents the value of x2, which is significant in all three cases; thus, rejecting the null hypothesis. Hence, choice of brand and store has signifi- cant effect on the purchase size decision. Assuming that the effects of store and/or brand change on purchase size are in- dependent of the product type, Table 19 summarizes the findings. Reading from Table 19, among the housewives visiting the same store and purchasing the same brand in two consecutive purchases, only 13% decreased their purchase size as opposed to 10% who increased their purchase size. But with a change in the brand of purchase, an additional 11% of the houseWives decreased their purchase size while only an additional 6% in- creased their purchase size. With a simultaneous change of brand and store, an additional 15% of the housewives decreased their purchase size as opposed to 11% who increased their pur- chase size, The differences between all these estimates of proportions of housewives increasing or decreasing the size of purchase caused by a brand and/or store change are found to 89 TABLE 17 PROPORTION OF HOUSEWIVES CHANGING THE SIZE OF PURCHASE OF PRODUCT A VS. THE PURCHASE PATTERN PRODUCT A (Paper Product) Increased No Change Decreased 7 Pattern Of Two the Size in the the Size Consecutive Si f M Purchases of ze o of arginal Purchase Purchase Purchase Total Same Store & 0.124 0.784 0.092 0.312 Same Brand (152) (963) (113) (1228) Same Store & 0.212 0.574 0.214 0.131 Different (112) (303) (113) (528) Brand Different 0.184 0.630 0.186 0.333 Store & (240) (820) (243) (1303) Same Brand Different 0.236 0.521 0.243 0.224 Store & (208) (460) (214) (882) Different Brand Marginal '0.181 0.646 0.173 1,000 Total (712) (2546) (683) (3941) 13.30 + BC X 7.00 + SC x 4.20 10.80 + BC x 8.95 + SC x 6.15 90 TABLE 18 TESTING THE EFFECT OF STORE CHANGE AND BRAND CHANGE ON THE SIZE OF PURCHASE Rgference TIA gTest of Product Table No. Value of x2 Significance A 3.27 180.2 * * B 3.28 276.3 * * c 3.29 1606.7 * * * * Significant at 1% level. TABLE 19 AN OVER-ALL MEASURE OF STORE AND/OR BRAND CHANGE ON THE SIZE OF PURCHASE Percentage of housewives ! Decreased Increased No change the size Source of the size of in the size of Variation purchase of purchase purchase Same Store 13.10 77-07 9'83- Same Brand (1503) (11220) (126:) Same Store 19 27 60.36 20.37 Different (1115) (4225) (118C) Brand Different 17.17 65.60 17.23 Store & (1191) (4680) (1194) Same Brand Different Store & 24.03 51.14 24 3 Different (2021) (4422) (2( 2) Brand NOTE: Figure in the parentheses indicate the sample sizes on which the corresponding probability estimates are based. PD = 10.56 + BC x 9.07 + 30 x 5.93 PI = 12.92 + BC x 6.52 + SC x 4.42 91 be statistically significant at the 5% level. A brief explana— tion of the test is in order: With a pair of proportional estimates, p1 and p2, based on two independent samples of sizes n and n respectively, 1 2 the standard error of the difference (pl - p2) is given by //Sl(1-pl) p2(l-p2) o = ———————— + ___—___. n n 1 2 The maximum value of p(l-p) is equal to 1/4 when p = 1/2. In Table 19, the minimum sample size for an estimate is 1100. Hence, the maximum value of the standard error of the difference between any two estimates is given by 1 1 1 _ //VK (1100 I 1100) ‘ 0'0213 In testing the equality of the binomial proportions, the obser- ved difference is compared with the critical value (20 limit) at 5% level of significance. Maximum value of the 20 limit in our case is .0426. In Table 19, all the differences between observed estimates corresponding to the effect of store and/or brand change on the increase or the decrease in purchase size exceed the critical value of 4.3%. As such, all the effects are statistically significant. Note that there is a greater tendency for consumers to decrease rather than to increase their size of purchase follow- ing a change in the brand purchased, or the store visited, or both. In Table 19, if 100 consumers visit the same store and purchase the same brand, we eXpect an average of ten consumers to decrease their size of purchase and thirteen to increase Pb 92 their size of purchase. But if 100 consumers change their brand or store, or both, we expect an average of twenty-one consumers to decrease their size of purchase. This is obtained by taking a simple average of the three estimates for decreasing purchase size with a brand and/or store change ((20.37 + 17.23 + 24.83)/3 = 20.81); similarly, we expect twenty consumers to increase their size of purchase. Comparing the above estimates, the change in brand and/or store has caused, on the average, an additional eleven house- wives to decrease the size of their purchase and an additional seven to increase the size of their purchase. Accordingly, for every 100 housewives who increase purchase size with a change in brand and/or store, there are, on the average, 157 (2 11 x 100/7) who decrease purchase size. Treating the data resulting from a simple designed experi— ment, a linear regression model is fitted between the percentage of housewives increasing or decreasing their purchase size and the factors of brand change and store change. The linear additive models are: PI = a + 8 x BC + y x SC PD = a1 + 81 x BC + yl x SC Where PI = Percentage of people increasing the size of their purchase PD = Percentage of people decreasing the size of their purchase 93 l a and a are constants 8 and 81 are brand change effects Y and yl are store change effects BC and SC are the variables that take the values of '0' and '1' in the following manner: BC _ {1 if there is a change in the brand - 0 if there is no change in the brand SC {1 if there is a change in the store 0 if there is no change in the store The regression equations are presented following each of the product data tables as well as the summary table. (Refer to Tables 17, 19 and 3.27 to 3.29). Note that from the esti- mates of 8, y, Bl and yl the following relations are consistently observed: This shows that brand change has a more pronounced effect on the decrease or increase of purchase size than store change. However, both brand change and store change cause more people to decrease their purchase size than to increase their purchase size. The next topic of my discussion is how store SWitching affects the store's private lable purchases. Private labels have limited distribution compared to national brands since they are available only in their sponsor stores. But private labels have one thhm;in common; they have, in general, a price advantage over national brands, and stores usually allocate more shelf space and better displays to their own private labels 94 than to national brands. With these advantages, it is likely that a housewife loyal to a store may tend to purchase the store's private labels, and that a housewife loyal to a private label may tend to treat all private labels as substitutes regardless of the store she visits. The next hypothesis deals in detail with these two propositions. HYPOTHBSIS 5:, Loyalty (measured by the re-purchase rate) to a particular store increases the preference for the private brands sponsored by the store. As a corollary, a housewife loyal to a private brand sponsored by a particular store is loyal to private labels regardless of store. Among the three products of my study, only coffee has a considerable number of strong private labels in the market; therefore, this hypothesis has been tested with coffee data only. A store loyalty index has been calculated for each housewife by computing the fraction of times she has Visited the same store for every pair of consecutive purchases. The families have been grouped into eleven categories depending on their store loyalty index, as shown in Table 20. Three major food chains marketing private labels of coffee have been selected, and the fraction of coffee purchases made by each of the family groups in these three stores, as well as the fraction of their purchases in favor of the private labels of the three stores, are presented in columns (2) and (3) of the table respectively. However, only families who purchased the product on at least ten different occasions over the period of three years are included in this analysis. Column (1) of the table gives the total number of purchases made by each 95 m:s.o moz.o mam o mom oo_H mam o m mmfl.o am: 0 amsm as o-oa.o mm:.o s:o.o _ m:m.o mam.o am:.o Hw:.o Beam mm ouom o mnz.o c s:m.o mmm.o Hmwm ms.o|os.o mmm.o W msm.o Hsz.o mmwm mo.olom.o mm:.o mmm.o amm.o Hom.o mom.o mam.o momm mm.oiom.c H::.o :mm.o omm.o msmm m:.oto:.o Hmm.o sma.o Hom.o oozm mm.ouom.o mom.o mmm.o mma.o m:a.o osm.o so:.o mow mm.onom.o mam.o mma.o wmm.o mmm ma.ouoa.o 000.0 000.0 mmm.o ma mo.osoo.o Ame .Hoo + Amv .900 Amy Amv AHV ozonu onoum onu.:H mow: mommzondm ozone onoum .mommco meCH mommconsm no noossz Honmq opm>apm ocp CH ,Insm mo mpamzoq Hmpoe on» on o>Hu mo coflunooonm moms mommconsm nocezz mnopm ImHmm mommconsm Honda mo coapnooonm Hmpoe mum>whm mo :ofipAOQOAm mchco boom no we conga "msohwlmnOpm Ammmmoov "economm mmmmoo mo mmmHmm mo ZOHBo wBA¢wOA mmOBm om mqm<8 96 family group. Grouping into sets of three, as shown in the table, it is evident that the proportion of private label pur- chases increased from .135 to .409 as we move in the ascending order of the loyalty index. Simultaneously, the proportion of purchases made in the store group (the three food chains) in- creased from 37% to 55% approximately. To adjust for the obvious positive association between store traffic in terms of product purchases made in the store 'group, and coffee purchases in favor of their private labels, the last column indicates the proportion of private label pur— chases made by the family group relative to the number of total purchases made in the store group. With the same grouping, as done earlier, the proportion of private label purchases in- creased from .365 to .745 as we go from low to high store loyalty groups. This clearly states that after adjusting for store traffic figures the proportion of private label purchases in the stores has a high degree of association with the store loyalty index; the higher the store loyalty index of a housewife, the greater is the chance of her purchasing private labels. Looking at the estimates, private labels enjoy almost twice the propor— tion of sales from a completely loyal customer than from her counterpart, after adjusting for differences in the frequency of store visits. Accordingly, stores have more to gain in their sale of private labels by promoting the habit of store patron- age. Thus loyalty of a housewife to a store is positively asso— ciated with her purchase of private labels in the store. In the second part of the hypothesis, I am questioning 97 the existence of consumer loyalty for private labels; do con- sumers differentiate the private labels of a product or treat them on an equal basis? At the outset, it is to be noted that this type of behavior may be observed by combining any set of national or regional brands, which is known as a brand-mix loyalty or loyalty to a group of brands. But one clear dis- tinction in terms of the distribution is to be kept in mind. National or regional brands are available in many stores, but no two private labels are marketed in the same store. Loyalty to private labels has been studied by calculating the proportion of housewives who purchased private labels while visiting the same or different stores in sequences of two and three purchases; Table 21 presents the probability estimates for sequences of two purchases and Table 22 for sequences of three purchases. Stores 1, 2, and 3 in both tables are food chains in the Chicago area marketing their own private labels of coffee, along with national and regional brands. A housewife's purchase of the store's private label of coffee in store 1, 2, or 3 is denoted by '1', whereas her purchase of another brand in that store obviously a national or regional brand, is denoted by '0'. Aggregating over all the housewives who made two con— secutive purchases in one of these stores, the proportion of housewives who purchased private labels are compared in refer- ence to the background of their store visits and brand purchases. If the phenomenon of loyalty to private labels does not exist in a consumer's mind, the past selection of a private label should not in any way influence her subsequent selection of a different store's private label. 98 TABLE 21 RE-PURCHASE RATE OF THE PRIVATE LABELS OF COFFEE VS. STORE CHANGE PRODUCT: C 1-Purchased the store’s private labels (Coffee) 0-Not purchased the store's private labels Store Brand Probability of a Housewife Purchase Purchase Purchasing Private Labels Sequence Sequence of Coffee in the Store 1 ‘ 2 ' 3 0 0.152 0.106 0.221 (768) (85) (95) l 1 0.926 0 424 0,577 (1756) (59) (222) 0 0.432 0.092 0.197 (102) (892) (198) 2 1 0.710 0.727 0 569 (31) (275) (51) 0 1 0.534 0.153 0 128 i (188) (190) (1951) 3 l 5 0.895 0 440 0 840 g (153) (59) (1452) 99 TABLE 22 PROBABILITY OF A HOUSEWIFE PURCHASING PRIVATE LABELS OF COFFEE GIVEN THE HISTORY OF HER PAST TWO BRAND PURCHASES AND THE CORRESPONDING STORES VISITED PRODUCT: C l-Purchased the store's private labels (Coffee) O-Not purchased the store's private labels Historical Probability of a Housewife Past History Sequence Purchasing Private Labels of of Stores of Brands Coffee in store Visited Purchased 1 2 3 00 0.049 0.100 0.136 (510) (20) (22) (l, l) 11 0.952 0.263 0.603 (1322) (38) (73) 00 0.306 0.054 0.067 (36) (552) (60) (2, 2) 11 0.750 0 825 0 455 (4) (149) (11) 00 0.455 0.152 0.065 (44) (66) (1347) (3, 3) 11 0.998 0 550 0.900 (55) (20) (972) 00 0.231 0.043 0 128 (1,2), (2,1) (121) (185) (172) (2,3), (3,2) (1,3), (3,1) 11 0.920 0.714 0.791 (138) (35) (153) 100 In other words, a housewife's selection of the private label in store 2 or 3 should be independent of her earlier brand selection in store 1. However, as shown in Table 20, about 42.4% and 57.7% of the housewives elected to continue with the purchase of private labels in stores 2 and 3 respect— ively, following their purchase of the private label in store 1. Only 10.6% and 22.1% of the housewives chose to purchase private labels in stores 2 and 3 respectively, following their purchase of some other brand in store 1. On the average, the carry-over effect of purchase preference from one private label to another is around 36%. This figure is obtained by taking the weighted average of the six estimates for the six possible cross-store traffic combinations. ((l,2L(l,3),GhlL(2,3),(3,1), (3,2)). From the third column of the table, it is seen that store l's private label is relatively stronger than others. Considerable proportion of consumers purchased store 1's private label even though they didn't choose to purchase the private labels in Suns 2 or 3 on their previous purchase. Looking into the sequences of two consecutive purchases, the existence of carry-over effect in loyalty from one private label to another is evident. Table 21 presents findings of similar effect in sequences of three successive purchases. The first column of the table refers to the stores visited by the housewife for her past two purchases. Though the past two store Visits can be classified in nine different combinations, only repeated purchase visits to the same store have been separately identified, leaving the six other combinations grouped together because (7131') two , 11., are” who can ef (D (D :3 C. (1) (N ( ) (I) \J r'f (I) I" .1 5 Q1 rt .’ (T Y) LA (I) (f) ('3 (0 all . 9 (1.." i;r smal '1 .L _ b‘ S A 15:9." .9}, Of T”res ases c r1y P" . sele Lected giy cfl' re- the n ased t (I) ., (T) Jisited. : . TH e sample size“ (mirchasing priva heir 165: two brand n be ch porticnal eStimates ted in the last two 7m last two times) ugh, the estimates ely small sample si (able 1* “.3 r1 (f‘ h a S e 5 he txur different way (,1) !\l e r+, mber 2f coffee gurqha Hfiwerer, 1: is r: be or three surcessi e in The analysis L“ :hise :casi ns uenr (urchase of 2 purchased the try “ts, whereas h usew W 1 .L .L F . 71 S (0 5186 brand hi Z‘I‘e h h (I) b (I) U) E ... h B \ j ( Wl' T. ab: presents /\ x J ‘R I) C.» \J (3 S (w 1e U) aiThC sales 1 I1 d t f t" (I) tor nding s) and T. ugh lDT. the da /. hat the 1 1') I“! SDLIICh parfnased 4 a , h be house .he p W per:- . i s trina: r\ O. . In ‘th:: w,rds, due to the ab:11‘3 t purchasing fhe private .ur times Sim:;ar observations 0 s'. res show that the probability (:3 n V I" .J 1 - he he ta 1 V *J’ rt 11 D e La (:3 |‘\ ore, g e of the (‘- O - (private Trible 22 are ‘hree Chicag. base are :>n51mtrs htee st-ces r on 0 store 3 n, a:.ume re du"1.g he nativnaL e A will Kc.” 1“ . L d 1.! L“? 1 ’3 T I ‘9' " : 0 ( 1 J. U) U) k.) \D ‘h “r m 1mg 102 has been increased approx1mately four times. The average increase in (he probability (weighted by the sample size) due to the carry-over effect has been around 44%. The estimates of the carryover effect, as obtained from Tables 21 and 22, are summarized in Table 23. This strong carry-over effect suggeSts that in certain segments of the market, housewives feel that one private label can be substituted far another. In general, private labels have an advantage of price differential over national brands. Thus, it is likely that the observed purchasing behavior could be due to the housewife's price—consciousness. This inference has not been pursued further since the data does not supply the If (1‘) price alternatives available to the housewife in the sfcr should also be kept in mind that private labels enjoy better in-store promotiinal services than national or regional brands, and this could be another causal factor in the observed ca'ry~ over effeCt. further research by designed experimentation is necessary t: test these cause and effect relationships. Thus far, we have shown that a housewife's loyalty to a st re in- :he probability of her purchasing the store's priVa e *5 (D L11 U) (I) (J) labels, and that a housewife's loyalty to one private label positively influences her decision to a spbstantial degree t3 purchase pritate labels in a different store. A: the micrn level we have been considering the consumer's many available alternatives in deciding among different brands, steres, and product sizes. Thus far, the discussion has center- ed around topics such as: (l) the effect of store SWitching MEASURE OF THE 103 TABLE 23 CARRY-OVER EFFECT 1N PURCHASING THE PRlVATE LABELS OF COFFEE Probability of purchasing private 'abels while visiting a store other than S. 1 Purchase History .,. _ . 3 . . :,- . (Figures in parentheses indica the sample Size for correspon- ding probability estimates; Purchased the nattxml or regional brand in Store S 0.28 85p on the previous purchase occaSifin Purchased the private label in Stirs S. on the 0.64 575 previous purchasd occasion Purchased national o- regicnal brands in S :e 0.20 (248. 3, en the two previou- par base .asions Eur:hased the p11 ate labels in Store S. on the 0.64 20.) two preai.us pur-hase CC 13.312115: 10% on brand choice; (2) the loyalty of a housewife to a particular store and its effects on her purchase of private labels; and (3) the effect of store or brand change on the Size of her pur- chase, et cetera. Although these findings are of considerable importance to the manufacturer, helping him to understand con- sumer buying behaVior and to develop suitable marketing strate— gies, often the manufacturer initiates price promotions on his brand, either to meet the competitor's actions or to encourage an increase in the sales of his brand. A considerable amount of price actiVity is common in the market for frequently pur- chased consumer goods, initiated either by the manufacturer or the retailer. The assumption underlying price actiVity is that a housewife knows the price of a product because of her frequent purchases, and so any reduction in price should attract a greater volume of sales. Since this seems logical, it IS interesting to explore the over-all market share variation as affected by prices over time. We shall also study the inter- action between bzand and store at an aggregate market share level, after suitably adjusting for price variation. This is an eXtension of our second hypotheSis that store switching of hOUSEleeS increases brand switching. HYPOTHESIS 6: Store-brand interaction is statistically Sig- nificant after eliminating the effect of price. As a corollary, the effect of price on the market share is Significant and the interaction between brand and Store cannot be explained by any linear function of the corresponding price difference. In the ideal situation of a housewife purchasing the same brand in whatever store she visits, there would be no inter— 105 action between brand and store. It is assumed here that the over-all distribution of consumers shopping in different stores remains more or less the same in terms of their prefer— ences for brands. Under this assumption and the ideal situa- tions, a brand will maintain the same market share in each of the stores, and so the differences between two brand shares over all the stores remains the same; hence, no interaction between the brand and the store. Testing the interaction be- tween brand and Store would be difficult in real situations due to existing distribution differences; all brands are not available in all the stores. Therefore, four major brands of each product and ten stores that carry all these brands (as evidenced by actual purchases) were selected for the study. For each month, the market share and the average price of each of the four brands in each of the ten stores are cal— culated. The price differential of the brands is one of the important external variables that affects the market share of the brand. In many situations it may be impracticable or un— economicaito keep conStant all the other variables that affect the marketsrare of a brand in a store; for example, the effect of variation in price levels is confounded in the observed differences in market shares. By measuring these extraneous variables or concomitant variables in statistical analysis, it is possible to adjuSt for their variations by the technique of Analysis of Covariance. The price of the brand has been treated as the concomitant variable in performing the Analysis of Covariance. A detailed l06 description of the technique is presented in Appendix V. Analysis of Covariance is done twice for each product, by calculating the market share of the brand first by the pro- portionate number of purchases and second by the proportionate volume of sales. In all, the analysis has been repeated six times for the three products. Each analysis is presented in sets of four tables. For the purposes of illustration, one set of tables in connection with the analysis of product A is presented below. (Refer to Tables 24 to 27). The first table (Table 24) tabulates the sums of products and the sums of squares (estimates of variation and the corresponding source of variation) for the market share variable (Y) and the con- comitant variable, price (X). The second table (Table 25) is a part of the Analysis of Covariance for testing the null hy- pothesis that there is no interaction between the brand and the store after adjusting for the effect of price variation. The third table (Table 26) similarly tests the null hypothesis that the observed interaction (store x brand) is explained by a linear function of the corresponding price difference. The last table (Table 27) tests the null hypothesis that price has no over—all effect on the market share of the brand. All these hypotheses have been tested for their significance at both 5% and 1% levels. Two asterisks in the F-ratio column of a table indicates that the corresponding hypothesis has been rejected at the l% level. A single asterisk indicates the rejection of the hypothesis at the 5% level. No asterisk means that the corresponding hypothesis has been accepted. The complete set 107 TABLE 2“ SUMS OF PRODUCTS AND SUMS OF SQUARES Product A (Paper Product) No. of Brands a No. of Stores 10 No. of Periods 36 Yijk‘ Market Share of Brand i in Store j and Period k as determined by number of purchases. Xijk: Average Price of Brand 1 in Store j and Period k. ’— Source of Degrees Sums of Sums of Sums of Regression Variation of Squares Products Squares Coefficient Freedom (yz) (xy) (X2) Between Brands 3 91 353 -0.261 0.033 -7.903 Between Stores 9 2.785 0.901 0.945 0.95M Between Periods 35 1.309 0.562 0 573 0.981 Brand x Store Inter— action 27 9.135 0.073 0,107 0.683 Brand x Perod Inter— action 105 11.U53 —0.l25 0.115 -1 086 Store x Period Inter— action 315 7.879 3.333 5.156 0.6U6 Error 9M5 82.518 0.252 1.082 0 233 Total 1339 206.933 4 736 8.012 0.591 eme,o oea.mm Jam Locum . mmo.o so: mm sea eonmm cofipom cofim Inmch smo.o mmo o mmo.o H Imonwmm **mm.m m:m.o mmo.m om mAOpm o» mom x ocmum Eoommnm Eoomopm owpmmlm mopmzdm mopmzom mo coapmflnm> oflcmm mmpmsom mopwoom mo coapmfipm> saw: no masm momnmma mo ransom um cam: mm masm mmmummo mo monsom onBo oopmono< momnmma oopmsno< QOflmmopmom wo masm mo meow mo meow mmommoa wo ochzom f Aposoopm Loommv Ammmmcopsm mo Lopezzv < Bozmomm mom mozoo mo mHqu (300) (M15) (,766) 01 0.375 0.323 0.307 0.22M 0.350 (738) (“3“) (306) (A28) (2752) 121 information on the historical sequence of the past two purchases: corresponding to the store background 58 (visit- ing the same store three times). Similar figures are given in Table 30 for sequences of four purchases, corresponding to the store backgroumiSSS. Under the null hypothesis, the probability estimates do not show any effect of the recency of brand purchase. Thus: H(Ol) = H(lO) (l) H(OOl) = H(OlO) = H(lOO) (2) H(Oll) = H(lOl) = H(llO) where H(abc) indicates the probability of purchasing brand 1 corresponding to the past purchase sequence given by abc. However, if the recency effect of the brand purchase (historical weighting of past purchases) is present, we expect H(01) > H(10) (3) H(001) > n(010) > H(100)g (q) “(011) > H(101) > H(llO) In nine out of the ten cases (refer to Table 29), the observed estimates are consistent with the relation given in (3), H(Ol) > H(lO), suggesting the effect of the recency of brand purchase in sequences of three purchases. In seven out of the twenty cases corresponding to sequences of four pur- chases (Refer to Table 30), the observed estimates are con— sistent with the set of equations given in (H). The signifi- cance of the hypothesis in this case is tested on the following lines. Even under the null hypothesis, the conditional proba- 122 TABLE 30 PROBABILITY OF PURCHASING THE BRAND VS. THE HISTORICAL SEQUENCE OF PAST THREE BRAND PURCHASES Brand Purchase Sequence \\ Al A2 B1 B2 B3 B4 100 0.378 0.372 0.164 0.324 0.182 0.119 (37) (43 (173) (74) (77) (59) 010 0 478 0.308 0.219 0.338 0.187 0.269 (23) (39) (64) (80) (64) (56) 001 0.393 0.309 0.295 0.361 0.365 0.328 (28) (42) (61) (97) (74) (64) 110 0.595 0.464 0.511 0.490 0.510 0.387 (42) (28) (45) (51) (49) (31) 101 0.667 0.438 0.683 0.652 0.500 0.365 (36) (16) (41) (46) (42) (23) 011 0.562 0.372 0.468 0.750 0.47 0.455 ~ 1 ' (32) (24) (47) (60) (46) (33) Irrespective Purchase of the brand Sequence C1 C2 C3 C4 (Over—all) 100 0,269 0.243 0.124 0.170 0.232 (390) (251) (185) (247) (1436) 010 0,271 0.273 0.145 0.244 0.253 (365) (242) (165) (246) (1344) 001 0.270 0.270 0.258 0.203 0.275 (397) (237) (186) (246) £1u32) 110 0.523 0.459 0.370 0.293 0.463 (218) (122) (81) (82) (749) 101 0.560 0.481 0.519 0.238 0.509 (209) (108) (52) (84) (657) 011 0.553 0.482 0.449 0.419 0.513 (217) (114) (78) (74) (725) I23 bility estimates may follow a pattern consistent with the set of relations given in (4) due to sampling fluctuations, suggesting an effect of the recency of brand purchase. The probability that the observed set of estimates corresponding to a brand may form a pattern consistent with either one of the relations given in (4) is 1/6 because the six possible permutations are equally likely under the null hypothesis. But in seven out of the twenty triplets, the observed esti- mates follow a pattern consistent with either of the relations given in (4). Accordingly, a simple binomial test of prOpor- tions with r = 7, n = 20, and H = l/6 is valid here. From the tables of the binomial probabilities: P(r:7/n 2 20, H : l/6) = 0.04 Thus the hypothesis is rejected at the 5% level, suggesting an effect of the recency of brand purchase. However, the magni- tude of this effect appears to be very small. The aggregation of the consumer's purchasing in different stores may contribute to the overeestimation of the recency effect of brand purchase. Though the purchase data confirm the tendency consistant with the following relations, the differences are statistically insignificant. H(Ol) > H(10) H(OOl) > H(OlO) > H(lOO) H(Oll) > H(lOl) > H(llO) The maximum value of the standard error of the difference between any two proportional estimates p1 and p2 is given below for various sample sizes. 124 I + Standard error of (pl-p2) n1 n2 <—l-(£+-l-)=£ifn=n=n 4 n n 2n 1 2 l 2 Standard error of Sample Size pl - p2(o) 2o limit (5% level) 50 0.100 0.200 75 0.082 0.164 100 0.071 0.142 200 0.050 0.100 300 0.041 0.082 400 0.035 0.070 500 0.031 0.062 Testing for the significance of the differences in the probability estimates, only in seven out of the seventy possible comparisons the findings show a substantial effect of the re- cency of brand purchase. The seven cases are: H(Ol) > H(10) -——C3 H(Oll) > H(110) B2 H(001) > H(100)----—C3 H(001) > H(010) B3 H(001) > H(Oio)———C3 H(001) > H(100) Bu H(Oll) > H(lOl)———Cu Thus, the recency effect of brand purchase in the purchase history is very small, when the consumer visits the same store successively for the purchase of a product. Accordingly, a simple Bernoulli model reasonably approximates the purchase behavior of a housewife in a particular store. This throws some serious doubts on what causes the apparent learning effect observed by Kuehn in brand choice. If the increase in the probability of buying a brand is completely due to past pur- chases in favor of the brand, then such learning should be more pronounced while visiting the same store since the external 125 influences would be relatively less time-variant. However, it is to be noted that the linear learning model has the recency effect built into the model. Detailed analysis of purchase data by the store may highlight some of the under- lying aspects of the consumer's brand choice, and the inter— action with the choice of the store and external environment. Markov models Defining the state of the system by the brand purchased, the consumer's brand choice has often been described by a Markov process. In a K—brand market, a first order stationary Markov process is described by the transition matrix given below: :;\ Final \\\\ State Initial “ l 2 . j . K State ‘ 1 p11 p12 le 2 p21 p22 p2K i pij K pKl pK2 ° ° ' pKK pij = {b(n)=j'b(n—l)=i} b(n) indicating the brand purchased in the nth state. In a stationary Markov process, transition probabilities (pij) are independent of time. Much of the published work made this assumption and the additional assumption that the 126 that the transiinnimatrix (P) is the same for all individuals. However, the bias of consumer toward a store, the interaction between store choice and brand purchase, and the variation in the distribution of brands make these assumptions untenable. So,a realistic attempt to describe the brand choice as a Markov process should not only incorporate the place of pur- chase (store), but should also assume a distribution of transi- tion probabilities in the market. A simple way of incorporating the effect of the place of purchase into the model is through conditional probabilities. Let qij indicate the probability that the purchase of ah brand j in store h follows the purchase of brand 1 in store a, in a K-brand and R—store market for a product. With my earlier notation of b(n) and s(n) indicating t . brand and store selected for n h purchase respectively, we have \’ . -- - -1 qij.ah 2s(n)-h, b(n)-j s(n-l)-a, b(n—l)-ij. i,j=1,2,...,K a,h:l,2, ,R Defining the state of the system by the combination of brand purchased and store visited, we can describe the brand choice by a Markov process whose transition matrix 'Q' is of the order of KR. The transition probabilities (qij.ah) can be estimated by observing the fraction of times a housewife has purchased brand j in store h following her purchase of brand 1 in store a. The general form of the transition matrix (Q) is given in the following page. 127 Transition Matrix (0) .~ \\$inal \ngte Initia state (1,1) . (l,R) (2,1) . (2,R) . (K,l) . (K,R) (1’1) q11.11 ° q11.1R q12.11 ' ql2.lR ° qlK.ll ' qlK.lR (l’R) qii.Ri ' q11.RR qi2.Ri ‘ ql2.RR ' qlK.Rl ‘ qlK.RR (2’1) q21.11 ‘ q21.1R q22.11 ° q22.1R ‘ q2K.ii ' qu.lR (Q’R) 'q21.Ri ' q21.RR q22.Rl ' q22.RR ' q2K.Rl ' q2K.RR (K l) qu1.11 ° qu.lR qK2.ll ’ qK2.lR ° qKK.ll ’ qKK.lR L l l (K’R) qu.Rl ' qK1.RR qK2.Rl ' qK2.RR ' qKK.Rl ‘ qKK.RR Knowledge of consumer's brand purchases and the correspond- ing store visits enable us to estimate the transition probabili- ties. The large number of transitions can be reduced by grouping in any particular fashion without doing undue violence to the model and can be used to pre-test different distribu- tion strategies. 128 Aggregating over all the stores, we have: {b(n)=j b(n-im} R R :5: E: {b(n)=j,s(n)=h b(n-l)=i,s(n-l)=a§{s(n)=h,s(n—l)=a} a=l h=l . R R i.e. . =1h=1 We shall assume that the transition probabilities (q.. ) while switching stores (h ¢ a) are independent of ij.ah the store selected. for all a ¢ h, l < a, h < R Then’ qij.ah:qij.D — — Let us make another simplification by assuming that the transition probabilities (q ) while visiting the same store ij. ah (a = h) are independent of the store. for all a = h, l < a, h i R. Then’ qij.ah:qij.8 — Accordingly, we have: R p.. = E: q.. 58(n):h s(n-l) = h} ij ij.ah L ’ h=l R R ( + E: §:.qij.ahlS(D)-h’ s(n-l)-a} a=l hzl h¢a : qij.S i: {5(n)=h, S(n-l)=h} h‘l R R qijl) E: E: {S(n)=h, S(n-l):a} a=l h=l hfa With our earlier notation of - qij.Sgog+q qij. DiD } 'S' and 'D' for store shopping i.e., P = stSg+Qd§D£ where 08 and Qd are the transition matrices correspOHding to visiting the same store (8) or differ- 129 ent store (D) respectively. For example, we have in the case of brand Cl: 0 : [0.90 0.10] Q = [0.81 0.19] s 0.27 0.73 d 0.43 0.57 {sf : 0.63 {D} = 0.37 where the two states of the system 1 and 2 are defined by the purchase of some other brand and brand C respectively. 1 Multiplying the corresponding probabilities, the first order transition matrix without taking into consideration the store of purchase will be: P Q {81+ Odin? S 0.90 0.10 0.87 0.13 0'63 [0.27 0.73j+ 0'37 L_. . ] 0.87 0.13 0.33 0.67 The model suggested earlier can be further extended by assuming a distribution of 0S and 0d over the individuals in the market or even further by assuming a joint distribution of Q8 and {S} as well as Qd and §D§. Such a model would have taken into consideration the strong bias exhibited by the consumer in the selection of a store as well as the effect of her store switching on the brand purchase. This would allow us to bring into the model explicitly the effect of distribu- tion. Learning models With the passage of time, a housewife purchases and uses different brands of the same product and according to the learning model the probability of her purchasing a brand is changed every time she makes a purchase decision. In the 130 model, the change in the probability of purchasing a brand either by purchasing or rejecting the brand on a particular occasion, depends on the apriori probability of purchasing the brand and the slope (l-g) of the purchase and rejection operators. With our notation, the equations of the model are: 7 b(n)='ib(n—l)zi : .- E 3; S.pl] ; gU. + (l-g) H (n-l) if i : J pij 3L3 + (l-g) H%(n-l) if 1 ¢ j Where1%(n-1) is the probability of purchasing brand j prior to consumer's n—lt purchase. The graphical presentation of the model is given below: J'j l I I l l l i . ) ! 0 L. H.(n-l) U. l J J J The formulation of the learning model ignores the effect of the differences in the promotional policies of the retail outlets and the differences in the availability of brands. 131 Thus, the change in the probability caused by purchasing or rejecting the brand on a particular occasion is assumed to be independent of the store selected. A housewife with a positive probability of purchasing a particular brand (accord- ing to the model) obviously cannot purchase the brand if she makes her purchase in a store where the brand is not available. Similarly, viSiting a store that de-emphasizes a particular brand will have some negative effect on the consumer's proba— bility of purchasing that brand. In other words, the preference developed by a housewife to a particular brand due to her past usage of the brand is likely to be modified by the store environment of the brand in her subsequent purchase. This can be conceived as a two- step process in the brand choice as shown below: Past éxpéfiéfiéé Hitfi” i lConsumer's prefer-— l the usage of the brand: iencefifor_£hembrandl ,, 11.___w___ Promofionalwen:mmm Availability \; Vironment of the (__of_ the b_rand brand in the store gStore environment L of the brand ’ . l .-- ~o -. ...——~.-_.. Brand 3 Consumer's probability ' 1 choice r”m*_ E - of purchasing the brand 1 _s.— .«~J ___-_- __-_-.—-__. ___—___...— --——-—-—— - -——--_ __ ..-— .w— _‘ —— The store of purchase acts as an intermediate variable between the consumer's preference for a brand and the execution of her preference in terms of a purchase probability. In the ideal case where all stores are identical in terms of their distribution and promotion of the brands of a certain product 132 we assume that the preferences of a consumer and her purchase probabilities W111 be the same. We shall also assume that changes in the preference of a consumer for a particular brand are described by a linear learning model. The preference for a brand is measured by a number in the closed interval (0,1) and it is assumed that preference for a brand increases with the purchase of the brand and decreases with the purchase of same other brand on any purchase occasion. Let Mj(n) denote the consumer's preference for brand j prior to her nth purchase andIB(n) the probability of her purchasing brand j for her nth purchase. Assume a K-brand and R—store market for the product. 3 ”,~’ ng + (l—g) M](n-l) U. 1 The distinction between a housewife's preference for a brand, and her probability of purchasing the brand should be noted. We make an assumption here that preference for a brand is 133 affected only by her usage of the brand. However, probability of purchasing a brand is affected by her preference for the brand as well as the marketing environment of the brand in the store. If the consumer has purchased brand j on her nth pur- chase, her preference for brand 3 on her subsequent purchase is given by: M]j(n+l) = ng+(l-g)MJ(n) lijiK If the consumer has purchased brand 1' on her nth pur- chase, her preference for brand j on her subsequent purchase is M .(n+l) 2 L.+(l— )M.(n) l< #1 macaw -.. _ m meSmcoo 138 purchase with a probability of H. (n), and some other brand jh with the probabiLhy of (l-Hjh(n)). The final brand selection along with M](n) will affect her apriori preference for brand 3 on her n + lSt purchase. Equation (l) gives R Hj(n) = E: [athh+(l-Bh)Mj(n)]§s(n):h§ hel R R = E: E: [ajh8h+(l-Bh)M](n)]{s(n)=h, s(n-l) ; a; hzl azl fin-l) = afx E: SE [ajh8h+(l—Bh)MJ(r1)]{s(n);h _ {s(n—J) =a} (5) It is observed in this study that a housewife does not have a constant probability of purchasing in a store and the pattern of store choice is similar to the recency effect of brand purchases observed by Kuehn in brand choice. Now we shall incorporate the recency effect in store choice into the above model. Let 6h(n) denote the apriori probability of a housewife purchasing in store h for her nth purchase. Describing the change in the probabilities of visiting different stores by a linear learning model, the set of conditional probabilities are given by the following equations: Y 6+(1-0) 5 (n-l) if ash (6) -/Sn) : hls(n) = a? = h h L c 6+(l-9)5 (n-l) if a¢h h h h : l , 2 , C . I ,R 9 is same for all stores because of our assumption regard- ing the linearity of the model. 139 Substituting equation (6) in (5) we get, R njm) zzlajt eh H1 8 h)Mj(n)][Yh9+(l—9)5h(n-l)]6h(n-l) h h 1R R LlehZEOL 8h r(l— 8h )Mj (n)][s:h 6+(l— e)5h(n- 1)]5a (n— l) lazl afih R ::§:.[ajh8h +(l— 8 hj)M (11)][Yh9+(l-9)5h(r1-.l)15h(n-l) h=l + [ajh8h+(l_8h)Mj(n)][€h6+(l-6)5h(n-l)][la¥n—D] (7) ' o B : B : z : Case 1. l 2 ... 8R 0 Then we get, Hj(n) : Mj(n n) R R Since E: In this case, consumers execute their brand preferences L.‘ H p...- v M u o 7< a{s(n) = h, S(n-l) = a}: l 1 =1 independent of the store visited. Case ii: 9 : 0 In this case, consumers have constant probability of visiting a store. Then we get: H : a 8 -8 '- j(n) Z [ 3h h+(1 hmjmndh 3- 1, 2, K hsl . where 6h is the probability of visiting store h. Case iii: g = O In this case, consumers have constant preference for a brand. i.e. Mj(n) is same for all n, (say) Mj j = l, 2, 140 Then the above formulation becomes a simple Bernoulli model within a store where the constant probability of purchasing brand jin store h is given by aJhBhHl-maj j = l,2,...,K h = l,2,...,R If a housewife has gone to store a for her n-lth purchase, the probability of her purchasing brand 3 subsequently is given by: H, : B _B e _ j(n) [aja a+(1 a)Mj(n)][Ya +(1 6)6a(n-1)] R + E: [ajk8h+(l—Bh)Mj(n)][€h0+(l-8)6h(n-l] h=l h¢a The complete set of equations for this generalized model are: ng+(l—g)Mj(n) if b(n)=j Mj(n+l = . . ng+(1-g)Mj(n) if b(n)¢j ] z 1, 2’ ’ K n = l, 2, Hjh(n+l)= ajh8h+(1-Bh)Mj(n+1) h 1 1, 2’ , = 1, 2, ..., n = l, 2, R H.(n+l) :E: 3 a. B ( _B r 6 -6 6 - 6 _ hzl [ jh h+‘l h)Mj(n+l)] Liyh +(l ) h(n 1)] h(n l) + [l-6h(n-l)][€h9+(l-9)6h(n-l)]] j = 1, 2, ..., K n = l, 2, There is no need to assume that the relationship between Hj(n) and Mj(n) is linear. The above model can be extended on these generalized lines: Hjh(n) = fh[M3(n)] 1H1 Then the equations of the model are: ng+(1—g)Mj(n) if b(n) = j Mj(n+l) = L.+1- M.( -l 'f b( ) 3 ‘ g 3 g) 3 n ) i n j _ l, 2, , K n = l, 2, Hjh(n+l) = fhEMj(n+l)] j = l, 2, ..., h : 1, 2, ..., n = l, 2, R H (n+1) =E: 6 6 _6 6 3 h-l fhEMj(n+l)] [Th(n)[Yh +(l ) h(n)] + -6 _ [l h(n)][€he+(l e)‘5h(n)]:| jil n = l, 2, If a consumer has visited Store a for her nth purchase, then: H. = 1 - j(n+1) faEMj(n+i)][Ya6+(l 656a(n)] R c 6 _6 6 +.E: [ h +<1 ) b(n))thEMj(n+l)] h=l h¢a In addition to the task of developing a generalized relation- shi between M.(n) and H. (n), more research is needed to p 3 jh give a physical interpretation of the parameters in the model. In some sense, the parameters reflect the retail store poli— cies as well as the distribution and promotion policies of the manufacturer. Such knowledge would be of immense use to the marketing practitioner and would also justify the academic task of building marketing models. The parameters not only help us in quantifying the effects of store—brand interaction, but also provide us with some concrete criteria for discrimina— ting among the various types of outlets. The criteria can also be used to segment the retail market for effective and optimal allocation of marketing effort on the part of the manufacturer. 142 Thus far, we concentrated on the problem of incor- porating store effect in brand choice models. The other important variables such as the size of purchase, the time— lag between purchases, and the price of purchase also de- serve Special attention. This investigation has not dealt at great length with these variables and, therefore, it would be premature to make any specific suggestions regarding their incorporation into models of brand choice, except that they should be incorporated. Simulation In the face of the complex task of building a mathematical model that incorporates all the elements of a consumer's pur- chase decision, simulation offers some immediate solutions to the researcher. However, constructive simulation needs the knowledge of the relationships among the various factors of buying behavior. This study highlighted some of these factors such as: stcre selection patterns of a consumer; the inter- action between brand choice and store choice; the private label proneness of a store—loyal consumer; and the aggregate effect of price on the market share of a brand. Any of the suggested models in earlier pages can be used to simulate consumer's buying behavior. As an example, let us discuss the simulation of brand choice based upon the generalized learning model. Assume a K-brand and R-store market for the product. We must start with a set of apriori probabilities of a consumer visiting each store and apriori preferences for each brand. Let these be, with our earlier notation: 143 6h(l) h ; l, 2, ..., R M.(l) 1] j II H o R) v u Let the parameters of brand 3 in store h be (ajh,8h). h = l, 2, ..., R If a consumer selects store h for his first purchase, the 6h's for his second purchase are given by: 6h(2) : 6+(l—6)6h(1) Yb 6 (2) : c 6+(l—6)6 (l) axh; azl, 2, ..., R a a a The probability of purchasing brand j in store h is given by: H h(l) : a hBhHl-ma (1) (Assuming a linear effect 3 3 J of store x brand inter- action) Purchase of brand j or some other brand will affect her apriori preference for his second purchase as follows: gguj.(1-g)mj(1) if b(l) : j ‘M 3 ggL.+(l—g)M.(1) if b(l) 3 \ J J Using the random number generating function and the values of 6h(n), (hLl, 2, ..., R) and Hjh(n) at each Stage (n11, 2, the purchase data of a consumer in terms of her brand purchases and store visits can be simulated. The brand choice and store choice of nth purchase will modify the apriori probabilities of n + lSt purchase through the intermediate variable Mj(n+l). Starting with an initial distribution of the apriori prefer— ences for brand 3 in the market, and distributions of apriori probabilities of visiting R stores, the performance of brand j can be simulated. As a first step, the model can be tested for its accuracy by comparing the simulated data with the panel 144 data. Also, the simulated data can be used for pre-testing the policies of the manufacturer or for evaluating marketing alternatives. Private label proneness of a consumer Though the hypotheses regarding the private label pur- chases do not belong to the central theme of our discussion, they deserve a special mention in view of their importance to the retailer. The positive association between the store loyalty of a consumer and her proportion of private label pur— chases increases the importance of store patronage by a house- wife to both the manufacturer and the retailer. Store patron- age of a consumer enables the retailer not only to attract a considerable portion of the consumer's budget, but also to in- crease the preference of the consumer for the store's private labels. A consumer's store preference and her private label preference interact, positively reinforcing each other in favor of the retailer. The substantial degree of substitutability of one private label for another suggests that in certain segments of the market, consumersdo not differentiate between the individual private labels of stores. Identification of these segments through further research will help retailers to develop suit- able promotional strategies. Except for a subtle difference in distribution, the observed behavior is similar to brand- mix loyalty (loyalty to a group of brands). The different brands of a brand—mix (normally referred to in the published literature as a set of national or regional brands) are avail- 14:) able simultaneously in various stores, whereas no two private labels are available in the same store. An interesting side light of the issue is that it has been the customary practice to group all the private labels into one category while analyzing the market data. This has been especially useful while fitting a Markov chain model to the purchase data, Since the number of brands in the market are considerably reduced to make the analySis manageable. The evidence in this study supports the practice. Future Research In order to streamline future research efforts, a major goal should be to study simultaneously the major factors of the consumer's purchase decision process and incorporate them into models of buying behavior. It is a complex task, but not impossible to achieve in the author's view. One way of working toward this goal is to eXpand the exiSting models by expressing the parameters of the model as functions of the external market- ing influences. The incorporation of store effect into the models of brand choice has been studied here. Store—brand interaction observed at both micro and macro levels is only a partial reflection of the interactions among the various elements of the marketing mix: Advertising and distribution; price and distribution; product and promotion; retail store policies and manufacturers' promotions, etc. Further research, through de51gned experimentation, is necessary to understand the causal phenomena behind the observed inter- actions between the consumer and her marketing environment. 1&6 ESuch a diagnostic Study will help the manufacturer look at ‘the market situations in a more realiStic perspective and pylan and execute remedial strategies. The Size of the purchase, the time-lag between pur- cliases, the price of the purchase, and the consumer's adver— tmising exposure, are only a few of the important factors of ptirchase enVironment that should be expliCitly brought into nuodels of brand choice. These variables have not been studied 111 great detail in relation to the exiSting models of brand cchoice. Constantly fac1ng the Studies of buying behavior is the §>rc>blem of aggregation, to describe the behavior of the market Wflezi the stochastic model describes the behavior of an indi- Vlwfllial. How accurately and usefully one can interpret the mar‘ket Situation from the micro models of buying behavior is Sti_j_l a problem in research. The present method of grouping 1319 successive purchases, giVing rise to the duplication of lnd-iVidual brand purchases in estimating the conditional proba— b‘ R. ' ,. o \ 1* J—ties of brand purchase did not seem to draw universal appro- v . . . a1 among the academiCianS. A Sincere attempt should be made to test any possible alternate methods of grouping purchase datzéi to describe the consumer's buying behavior. The study has achieved its purpose if it has raised some lSESLJees regarding our understanding of consumer's brand choice a . Ild‘ 'the reliability of the existing models. APPENDIX I CONSUMER PANEL DATA: AN OVERVIEW Int_3duction to Panel Data m—_——— n— The use of the panel technique in market research can be traced back to the 1940's. In 1940 the Farm Journal's cross country survey used the continuous reporting of family (eXpenditure records to study their purchase behavior. In bday, 1941, the Industrial Surveys Company-(at present the kharket Research Corporation of America) operated a contin- ucous panel of more than one hundred families in Indiana. Ir1 the last twenty years the panel technique has gained Wiiciespread attention and has become an integral part of m531:keting research, The consumer panel, "a unique market reassearch tool," can be used to "consistently penetrate the Inirld of Mr. Consumer and discover his definite views on a b(D Sit of subjecrs affecting product acceptance or merchan- di-Sing "; The panel, in effecr, "enables the marketer to téiLte a motion picture of consumer purChase behavior, to Cl—éassify this behavior by all sorts of demographic, psycho- lC’Egical and geographic detail, and to watch these phenomena ._~_‘___ _ ._ i _— 1 H. L. Churchill, "How to Measure Brand Loyalty," AC1\7e'r't:isingand_Sel]ing, 35 (August, 1942). P» 26. T 2 _, "Consumer Panel as a Marketing QC>1," Printer's Ink, 213 (November 9, 1945), p. 25- 147 148 change through time, By use of modern mathematical ap- proaches, the panel technique may also provide the most powerful tool for predicting future behavior and determining strategy to affect this behavior‘"3 The panel technique has taide application outside the marketing world; for example, it can be used to study the dynamics of people's Opinions and attitudes, I shall restrict myself in the following pages to a discussion of panel research in the marketing sense, A panel, in a general sense, "is a group of consumers (Jrganized to serve with some continuity in an advisory, a judiciary, or fact—finding capacity."“ A panel in the Ina rketing sense is "a controlled array of original data SCDLirces which permit current and repetitive examination of S tiles phenomena through a finite time series." In other WC>rrds, a panel study enables us to study the purchase be- lianv'ior of a group of consumers as a function of time\6 The th~I‘ee functions of panels are: (l) to minimize memory loss by' obtaining a reccrd of the purchase on the day that the leEchase is made; (2) to compile a mass of essential data \\ Seymour Sudman, "Maintaining a.Consumer Panel,” EEE‘E;Beting Keys to Profits in the 1960's: :Proceedings of the £224§;3ican Marketing Association Convention;‘€1eveland (June, 19 59), pp. 322-326. P , "Consumer‘Panel as-a Marketing Tool,' -E;i;gter's Ink, 213 (November 9. 1945): P° 25* E Samuel C. Barton, "The Consumer.Pattern of Different I‘DInomic Groups,” Journal of Marketing, 8 (July, 1943), pp- 51-53. Franklin R Cawl, "The Continuing Panel Technique," ilfiiilnal of Marketing, 8 (July, 1943): PP- 45‘50- 1149 at>caut each family on a basis convenient to the researcher aricj to the respondent family; and (3) to eliminate the bias caf' the respondent's present view in reporting past events.’ PEitIEBl Description and Administration The Chicago Tribune panel consists of 750 families "vatnca keep chronological records of their purchases of food atlci household items. For each purchase in a given product C.1 6385, information is available as to the family's code t1L1tnber, selected demographic= characteristics of the family, b r‘éand purchased, date, quantity, price, type of outlet, [some méijot outlets are coded by their ownership] and whether or u(Dt‘_:a.deal was used in making a purchase."8 Since panel data PTI‘cavides a continuous record of brand choice for an extended EDGE Iriod of time, it is suitable for a study of the consumer's l3€al~mavior patterns over time. Panel designs are of two types: (1) natural; and (2? 3 quasi-experimental. NiCZOSia:9 Natural designs (Chicago Tribune, MRCA) produce the data for descriptions of gross and net change and for the prediction of change. These designs generally are not intended to yield data for the study of evaluative, prescriptive or explanatory questions. The main feature of quasi-experimental designs is the purposeful manipulation or intro- duction of one or more stimuli into a system of variables interacting in real life rather than \ E1 Samuel C. Barton, ”The Consumer Pattern of Different C’C’nomic Groups," Journal of Marketing, 8 (July, 1943\, pp . '31-'33. Ronald E. Frank, "Brand Choice as a Probability Pro- EESS: ” Journal of Business, 35 (January, 1962), p. 43. b1 Francesco M. Nicosia, "Panel Designs and Analysis in bqéilfketing,” Proceedings of the Fall Conference of American “\§ij;k§ting Association, (September, 1965), pp. 228-243. lSO laboratory settings. These are best suited to answer evaluative and prescriptive questions. Quasi-experimental designs are also a must when we want to explain changes in a variable in terms of its causal structure. So far we have been talking about the conceptual as— peer: ts of the panel technique in marketing research. Some of ‘thee problems of administering a panel and the advantages atlci disadvantages of panel data for research.purposes are dj~sscussed in detail in the following pages. Though a re- S eBearcher is not directly confronted with the.problem of panel a'iitxiinistration, it is essential that he understand some of t:klwe aspects of the maintenance of a panel as.they might re- f J—eect on the nature of the data. The first problem of panel administration is to select t311‘e panel sample. As previously mentioned, a consumer panel 1-53 a group of consumers so selected that it constitutes a representative sample of the market to be appraised. The QWC>Insumers are chosen in terms of income, age, sex, education, O'C1<:upation, size of family, and ownership or rental of homes, inI order to conform to the national, sectional, or regional F’Ei‘tterns under observation.10 Such a selected group of con- SL1triers is submitted "to a series of intermittent interviews C’]? is required to make a series of reports over a period . 1?... Of t1me."" \ 1° Archibald S. Bennett, ”Consumer Panels: Radar of e Sales Department," Sales Management, 55 (October 15, h 9 4.5), pp. 155-156. t l. 11 Robert N. Wadsworth, "The Experience of User of C:<3tisumer Panel,” Applied Statistics, 1 (November, 1952), P D . 169—178. 151 Once the panel is established, the major problem is to erifilzist the c00peration of the panel members. Various in- ceerlizive schemes are instigated as a part of the panel admin— isst:1:ation to ensure the continuity of the panel membership 12 fc31: a required time period. Sudman presents an extensive dciasczussion of these incentive schemes in a publication of tilea Journal of Marketing Research. Shafferla discusses some 035 the operational problems involved in the organization of a. (zonsumer panel, such as: "(1) how long should the report- itlzg period he; (2) on what days should the reporting period 1”Eiggin and end; and (3) should reporting be continuous or dii—sscontinuous." From the published evidence, it appears that V7€3ndents cannot be representative in their behavior if 145rage both initial and continuing participation" of mem- bta‘rrs on the panel, the mortality rate is high during the <>p>€eration, and often the causal factors are not under the r‘esearcher's control.20 A considerable amount of literature has been published (>11 various possible sources of bias in panel information and (’11 the question of whether the panel sample truly repre- S Etnts the general market behavior. Some issues concerning P anel accuracy are: (l) Bias and other effects that may be introduced by re-interviewing (2) Representativeness of the sample, since a certain proportion of peOple are not interested in panel participation (3) Errors due to memory loss and mistakes in recording (4) Possible sources of bias in recording due to the length of panel membership (5) The large number of commodities for which pur- chases are to be recorded affecting the quality of reporting (6) Possible over—statement of purchases from new panel recruits (7) Response errors from the panel members because of their self-consciousness and "expertise" attempts to look good \ 2° Francesco M. Nicosia, "Panel Designs and Analysis j‘tl Marketing,” Proceedings-of the Fall Conference of ~€§Eggrican Marketing Association, (September, 1965), pp. 28-243. 155 (8) Possible conditioning of purchase behavior be- cause of the continuous reporting of brands and the prices of past purchases (9) Representativeness of national markets limited by the geographical concentration of panel members. "Plausible as these arguments seem, the limited data axrzaxilable indicate that these effects do not occur, or occur ' l 1r1 such a manner as to offset each other.”2' Consumer 'Péitlels are continuously conducting experiments to study the 22 Sudman reports em- I>C>£ssible validity of these arguments. PIi—Irical evidence that panel membership does not condition flJ-t:ure behavior in regard-to-purchases. Nicosia claims that bZi-Eis due to the re-interviewing effect is not detrimental Sli.t1ce "it makes the respondent a better reporter of her own ac: tzions and thoughts; indeed, repreated interviewing may be til ea only way to get at routine behavior patterns and uncon- SC-::i.ously enacted psychological processes."23 Ehrenbergzk f31.t1.ds that the length of panel membership and the increase 21 James D. Shaffer, "The Reporting Period For a Con— n‘ler Purchase Panel," Journal of Marketing, 19 (January, 55 5), pp. 252-257. 22 Seymour Sudman, "Accuracy of Recording of Consumer :anels," Journal of Marketing Research, 1 (May, 1964 and ugust, 1964), pp. 14—20, pp. 69-80. . 23 Francesco M. Nicosia, "Panel Designs and Analysis in Marketing," Proceedings of the Fall Conference of “21£E;§ican Marketing Association, (September, 1965), pp. 2253 ‘2430 "A Study of Potential Biases in 2“ A. s. c. Ehrenberg, " Applied Statistics, 9 Eh Q Operation of Consumer Panel, biéirch, 1960), pp. 20-27. 156 1:1 the number of products to be reported do not affect be— 5 1121\Iior. Regarding the length of panel membership, Sandage2 ssLIIDPIiES evidence that peOple on the panel as long as eight t<3 ten years did.not exhibit any bias in their attitudes. Relatively little evidence is available on the magni— tLLicies of response errors because of self-consciousness and ' attempts to look good. However, Ehrenberg26 e xpertise' i.r1€3 riod of four to six weeks, they are included in the tabu- l—Ei tions of the entire panel.27 On the whole, evidence sup— F> r our research purposes, we can reasonably assume that t:11 eaconclusions drawn from panel data are not typical of E‘rlfiy particular sample, but-only depict the general tenden— C i-ees of consumers in the over-all market. \ 25 C. H. Sandage, ''Do Research Panels Wear Out?," -$Liilgrnal of Marketing, 20 (April, 1956), pp. 397-401. 26 A. S. C. Ehrenberg, "A Study of Potential Biases :TrI the Operation of Consumer Panel,” Applied Statistics, 9 'biiarch, 1960), pp. 20-27. 2? Seymour Sudman, "Maintaining a Consumer Panel," E§£Eggketing Keys to Profits in the 1960's: Proceedings of 75:11? American Marketing Association Convention, Cleveland ~<1n4ne, 1959), pp. 322-326. APPENDIX ll DEFINITIONS AND NOTATION FCDI‘ the sake of convenience to the reader, the ter- minologgy, the symbolism, and the notati~n used in this 1 documerit are explained in the foilcwing pages: Matrix.: An array of elements arranged in rows and columns. Order of a matrix: If a matrix has m rows and m columns, then the order of the matrix is m. Cl?Seci interval (a,b): The set of elements between a and b with the incluSion of a and b. PFSbaLDiiuty: In simple terms, probability oi an event E is a number in the closed interval (O,l) assigned to the event E and denoted by §E§ or P(E). An impossible event has probability zero and a certain event has probability one. State 3 The state is the description cf the sysrem at a particular time. The state or the system in the Markov model is defined by the last brand purchased or a combination of the las: brand purchased and the last store viSited. Trangfiit‘;n probability: Probability that the system passes through State i to state 3. Tr"EmSition matrix: A matrix whose elements are transition probabilities. 157 158 Stationary Markov process: A Markov process in which the transition probabilities are independent of time. First Cinder Markov process: In a first order Markov pro— cess, the present state is dependent on only the immediately preceding state. An extension of this is an nth order Markov process in which the present state is dependent on the immediately preceding r stateso Model: An abstraction of the reality. A model formally states the relationships among various factors of a business situation or process. Stochaistic process: A situation in which the relationships among factors are probabilistic rather than deter— ministic. NuLl fyypothe81s: In statistics, the hypothes1s that is being tested is called the null hypothesis. Level (of significance: In statis2ical inference, this is known as Type I error. In any type of Statistical testing, the researcher takes a risk of accepting wrong hypothesis or rejecting a correct hypothesis due to sampling fluctuations. The rejection of a null hypothesis at 5% level of significance means that the researcher is taking a one in twenty chance of rejecting the null hypothesis when in fact it is true. In other words Prob (Rejecting Null Hypo- thesisiNull Hypothesis is true) = 0.05. Symbols 2’ f (p5 No (_J ration \ 159 Indicates the probability of an event in discrete case or the probability density of random variable in a continuous case. Indicates the event A given the occurrence of event B. Indicates the conditional probability of A given the occurrence of B. Indicates the expected value of the random variable p . Symbols like I(intergral), E: (summation), and J [ 1, (parentheses), convey the standard meanings used in mathematics As far as possible a uniform notation has been used throughout the document for representing the market situation. - th Brand purchased by the consumer for her n purchase. . . th Store v1s1ted by the consumer for her n purchase. . . , th Preference for brand j prior to consumer s n purchase. Probability of purchasing brand j prior to consumer's th n purchase. Number of brands of a product in the market. Number of stores where the product is sold in thenarket. A typical brand. A typical store. V [0 If brand j is not purchased on n 160 H3h(n) Probability of purchasing brand j in store h for nth purchase. ajh,8h Parameters of brand j in store h. 6h(n) Apriori probability of a consumer viSing Store h for ' her nth purchase. pl] Probability of purchasing brand j following the purchase of brand 1. qu.ah Probability of purchasing brand j in store h follow- ing the purchase of brand i in store a. gsUj,IJj Parameters of the linear learning model for describing the change in the preference for brand j. G’Yh,6:h Parameters of the linear learning model for describing the change in the probability of viSiting store h. S The event of a housewife Visiting the same store in two consecutive purchases [(s(n) = h, s(n—l) = h), h - 1, 2, ..., R]. The event of a hcusew1fe viSiting different stores in two consecutive purchases [(s(n) = h, s(n-l) : a:h), lia, hiR]. Brand and Store baCkgI“O‘Linds: The notation used in describing store and brand backgrounds is explained in the beginning of the fourth chapter (Refer to Pages 70 and 72)- b (n) I If brand j is purchased on 11th purchase occasion th purchase occa- sion. 161 purchase is not made in store h I If the nth purchase is made in store h sh(n) - th 0 If the n {.1 If b(n).:bm-i) BC 0 If b(n) : b(n-l) SC _E’l If s(n)¢s(n-l) ‘\0 If s(n) 2 s(n-l) APPENDIX III INDIVIDUAL ANALYSIS OF THE THREE PRODUCTS: COMPLETE SET OF TABLES List c>f Tables Serial Reference NO. Title of the Table Product/Brand -No. 1 Proportion of Housewives Purchas— 10 11 12 ing Product in the Store Given the Past History of Three Purchases A 3.1 ” B 3.2 H C 3.3 Ibroportion of Housewives Purchas- .ing Product in the Type of Outlet C3iven the Past History of Three EDurchases A 3.4 ” B 3.5 " C 3.6 EDrobability of a Housewife Pur- czhasing the Brand Given the History (of Her Past Two Brand Purchases and ‘the Corresponding Stores Visited A1 3.7 " A2 3.8 " B1 3.9 " B2 3.10 " B3 3.11 " Bu 3.12 162 w‘clzt' 163 Serial Reference No. Title of the Table Product/Brand No. 13 E’robability of a Housewife Pur- clnasing the Brand Given the History c>f Her Past Two Brand Purchases and tflhe Corresponding Stores Visited Cl 3.13 1H " C2 3.14 15 ” C3 3.15 16 " Cu 3.16 17 Probability of a Housewife Pur— chasing the Brand Given the History of Her Past Three Brand Purchases and the Corresponding Stores Visited Al 3.17 18 " A2 3.18 19 " B1 3.19 20 " B2 3.20 21 " B3 3.21 22 " B 3.22 L1 23 H Cl 3.23 2“ " C2 3.24 25 " G3 3.25 26 n Cu 3.26 27 E>roportion of Housewives Changing “the Size of Purchase of Product \fs. Purchase Pattern A 3.27 28 " B 3.28 29 " c 3.29 30 Sums of Products and Sums of Squares (Market Share Determined by Number of Purchases) A 3.30 31 " B 3.38 32 " c 3.46 164 Serial Reference No. Title of the Table Product/Brand No. 33 .Ainalysis of Covariance for Product (Idarket Share Determined by Nnumber of Purchases) A 3.31 34 ” B 3.39 35 " C 3.47 36 'Testing the Linearity of Store x Brand Interaction (Market Share Determined by Number of Purchases) A 3.32 37 " B 3.40 38 H C 3.48 39 Testing the Regression (Market Share Determined by Number of Purchases) A 3.33 40 " B 3.41 “l " c 3.49 “2 Sums of Products and Sums of Squares (Market Share Determined Iby Volume of Sales) A 3.34 “3 " B 3.42 ”4 " c 3.50 45 [Analysis of Covariance for Product (Market Share Determined by Volume (of Sales) . A 3.35 “'5 " B 3.43 “7 " c 3.51 ”8 'Testing the Linearity of Store X Brand Interaction (Market Share Determined by Volume of Sales) A 3.36 “9 " B 3.44 50 " c 3.52 165 Serial Reference No. Title of the Table Product/Brand No. 51 T7esting the Regression (Market Slnare Determined by Volume of Sales) A 3.37 52 " B 3.45 53 " C 3.53 PMHn. - 166 TABLE 3.1 PROPORTION OF HOUSEWIVES PURCHASING PRODUCT A IN THE STORE GIVEN THE PAST HISTORY OF THREE PURCHASES l-Purchased inothe Store O-Not Purchased_in the Store PRODUCT A ( Paper; Product) fgiéfEEE-Purchase Fraction Purchasing invStore No. __fi :Sequence 1 2 3 000 0.039 0.047 O 021 (2676) (2328) (2976) 010 0.192 0.255 0.181 (114) (137) (77) 001 0.298 0.368 0.253 (13“) (152) (79) 011 O 523 O 625 0.375 (65) (104) (32) 100 0 219 0.264 0 189 (123) (170) (79) 110 0 A30 0.413 0.500 (65) (116) (32) 101 0.562 0.546 0-433 (A8) (86) (30) 111 0.717 0.710 0.621 (117) (249) (37) EELfiifia: 1: Food Chain 2: Drug Chain 3: Food Chain TABLE 3.2 PROPORTION OF HOUSEWIVES PURCHASING PRODUCT B IN THE STORE GIVEN THE PAST HISTORY OF THREE PURCHASES P RODUCT B (']?zatst Purchase Fraction Purchasing in Store No. Sequence 1 2 3 000 0.027 0.027 0.045 (16389) (18123) (14266) 010 0 312 0.244 0.300 (608) (601) (918) 001 0.334 0.301 0.322 (630) (643) (920) 011‘ 0.622 0 550 0.577 (490) (325) (675) 100 0 275 0 224 0.281 (668) (636) (938) 110 0.527 0.425 0.564 (506) (324) (684) 101 : 0.598 0.471 0 570 I (463) (282) (663) 111 0.840 O 772 0.851 (1999) (819) (2689) W 1: Food Chain 2: Food Chain 3: Food Chain II?“ . . 169 TABLE 3.4 PROPORTION OF HOUSEWIVES PURCHASING PRODUCT A IN THE CEYPE OF OUTLET GIVEN THE PAST HISTORY OF THREE PURCHASES PRODUCT A ( Paper Product) l-Purchased in Store Type O-Not Purchased in Store Type ——‘ Fraction Purchasing in Store Type E’aa.st Purchase Sequence 1 2 000 0.039 0.040 (2823) (2755) 010 0.198 0 157 (116) (127) 001 0.248 0 205 (37) (136) 011 0.487 0.468 (41) (47) 100 0.184 0.126 (114) p (142) 110 0.263 0.265 (38) - . (49) 101 0.366 0.529 | (137) (34) 111 0.627 0.538 "i (43) (52) 17573785 ’ 1: Discount stores 2: Independent Drugstores 170 TABLE 3.5 PROPORTION OF HOUSEWIVES PURCHASING PRODUCT B IN THE (TYPE OF OUTLET GIVEN THE PAST HISTORY OF THREE PURCHASES IF’IRODUCT B l-Purchased in Store Type ('CEoothpaste) _, O-Not Purchased in Store Type ——' Fraction Purchasing in SEore Type Past Purchase , Sequence 1 2 1 000 0.025 0.028 is (71110) (7255) ' 010 0.152 0.206 (216) (174) .‘ 001 0.206 0.357 “a; (223) (246) 011 0.482 0.543 (85) (114) 100 0.116 0.296 (265) (182) 110 0.288 0.459 (90) (87) 101 0.442 0.597 (61) (67) 111 0.814 0.780 (232) (187) E<>1zeesz 1: Independent Food Stores 2: Discount Stores "'1— 171 TABLE 3.6 PROPORTION OF HOUSEWIVES PURCHASING PRODUCT C IN THE CFYPE OF OUTLET GIVEN THE PAST HISTORY OF THREE PURCHASES P RODUCT C J;_C30ffee) 1-Purchased in Store Type 0—Not Purchased in Store Type ___i Past Purchase Fraction Purchasing in Store Type Sequence 1 2 000 0 002 0.036 (21440) (16773) 010 0.122 0.218 (57) (738) 001 0.271 0.240 (70) (756) 011 0.629 0.561 (27) (365) 100 0 111 0.179 (63) (767) 110 0.480 0.486 (25) (374) 101 0 473 0.545 (19) (343) 111 0 692 0 871 (52) (1633) 81C>13es: 1: Drug Chains and Independent Drugstores 2: Independent Food Stores GIVEN THE HISTORY OF HER P EODUCT A 172 TABLE 3.7 PROBABILITY OF A HOUSEWIFE PURCHASING BRAND PAST TWO BRAND PURCHASES AND THE CORRESPONDING STORES VISITED ( Paper Product) 1-Purchased Brand A1 IE3IRAND A1 4* __ 0- Not Purchased Brand A1 fiistorical Past Histor of Stores Visited firespective ESeequence of DD of the Store Brands SS SD DS 131131 ID? Choice I’LJrchased _ (over-all) 00 0.116 0.119 0.109 0.163 0 172 0.139 (336) (210) (256) (276) (377) (1455) 10 0.481 0 458 0.372 0.477 0.675 0.455 (104) (59) (78) (65) (118) 0424) 01 0.567 0.339 0 673 0 583 0.490 0.541 (90) (59) (92) (60) (100) (401) 11 0.874 0.867 0 842 0.790 0.771 0 833 __1 (435) (188) (214) (248) (253) (1338) TABLE 3.8 P RODUCT A C P aper Produc ’0) BRAND A2 1-Purchased Brand A2 0-Not Purchased Brand A2 IIII. storical 7 of Stores Visited TIrrespective LPast Historx SEEquence of 7 ADD of the Store Brands 38 so DS 0101 0102 Choice EUEIIPChased . _____ ___ (over-all) 00 ' 0 107 0 10270 109 0.147 0.169 0.127 I (633) (313) ((375)fi (101) (113) (2165) 10 1 0.38110 518 0 330! 0. 29610 303 I 0 356 ! (102))(56) ‘(88) . (51) (119) i (119) 01 0.390‘0.370 0 535i 0.494 0 350 0 u22 (95) |(5u) (71) (87) (120) (927) I 11 0 719 0.753 0 726 0.720 0 705 0 722 ..____ (135) (93) (106) (107) (166) (607) TABLE 3.9 PROBABILITY OF A HOUSEWIFE PURCHASING BRAND GIVEN THE HISTORY OF HER PAST TWO BRAND PURCHASES AND THE CORRESPONDING STORES VISITED P FODUCT B ( Toothpaste) BRAND Bl l-Purchased Brand B1 O-Not Purchased Brand B1 }{:i_storic§1 Past History of StoreE'Vigfregm"Igrespective"_ ESeaquence of 00 '"“"of the Store E3cr’ands SS SD DS D101 01D2 Choice E’Llrchased (over—all) 00 0.050 0.060 0.082 0.083 0 097 0.072 (1858)(765) (1012) (1008)(1310) (5952) 10 0.352 0.279 0 254 0 266 0.321 0 304 (165) (86) (114) (94) (196) (654) 01 0.409 O 333 0 558 O 359 0.382 0.398 (159) (78) (111) (92) (202) (641) 11 0.899 0.843 0.864 0.765 p 798 J O 850 (711) (191) (242) (260) (302) f7 (1705) TABLE 3 10 PRODUCT B (’]?<30thpaste) 1-Purchased Brand B2 BR AND 132 O—Not Purchased Brand 132 H'3_Storica1 Past History of Stores Visited Irrespective Secluence ofI' DD of‘ the Store Br- ands 53 so DS _ “0101 0102 Choice Eflgigzchased (over-all) 00 0.075 0.072|0.058 10.098 0.101 0,081 (2023)(759)‘(1005) (1009)(1276) (6070) 10 0.397 3.442 0.292 0.329 0.376 0.368 (179) (77) (113) (79) (157) (604) 01 0.436 0.488 0.596 0.548 0.487 0.499 (202) 84) (114) (104) (193) (697) 11 0.857 0 825 0.830 0.763 0 818 O 824 \ (489) 200) (247) (262) (384) (1581) 173 TABLE 3.9 PROBABILITY OF A HOUSEWIFE PURCHASING BRAND GIVEN THE HISTORY OF HER PAST TWO BRAND PURCHASES AND THE CORRESPONDING STORES VISITED P FODUCT B ( Toothpaste) l—Purchased Brand B1 JESIRAND Bl O-Not Purchased Brand B1 }{:istorical Past History of Stores ViEIFédw-IFrespective-_ ESeequence of ‘DD ‘r—"of the Store Brands SS SD DS 131131 13ng Choice I’larchased (over—all) 00 0.050 0.060 0.082 0.083 0.097 0.072 (1858)(765) (1012) (1008)(l310) (5952) 10 0.352 0.279 0 254 0 266 0.321 0 304 (165) (86) (114) (94) (196) (654) 01 0.409 0.333 0 558 0-359 0.382 0.398 (159) (78) (111) (92) (202) (641) 11 0.899 0.843 0 864 0.765 0.798 0 850 (711) (191) (242) (260) (302) (1705) TABLE 3.10 PRODUCT B C IPoothpaste) 1-Purchased Brand B2 BRAND 132 O-Not Purchased Brand 132 I‘“I':.'1_storical Past istory of Store; VIEIEZE Irrespective Sequence of DD of the Store Brands 33 SD DS . DID] (3ng Choice I?14rchased (over—all) 00 0.075 0.072 0.058 0.098 0.101 0.081 (2023)(759) (1005) (1009)(1276) (6070) 10 03971442 0.292 0.329 0376 0.368 (179) (.77) (113) (79) (157) (604) 01 0.436 D 488 0 596 0 548 0.487 0.499 (202) 84) (114) (104) (193) (697) 11 0.857 0 825 0.830 0.763 0 818 0 824 \ (489) 200) (247) (262) (384) (1581) TABLE 3.11 PROBABILITY OF A HOUSEWIFE PURCHASING BRAND GIVEN THE HISTORY OF HER PAST TWO BRAND PURCHASES AND THE CORRESPONDING STORES VISITED PRODUCT B C TToothpaste) BRAND 83 1- Purchased Brand B 0— IJot PurChased Brand B3 If3:istorica1 Past History of Stores Visited —I;;espective ESeequence —‘- _DD'—”“ Jof the Store <>:f Brands SS SD DS Dlul DlD§_" Choice Eidirchased_» _ _- (over—all) 00 0 051 0.062 0 048 0 094 0 074 0 064 (2239) (820) (119) (1140)(1517) (6831) 10 0 358 0.291 0 160 0 162 0 270 0.261 (171) (79) (125) (80) (163) (618) 01 0 413 0.255.0.439 0.341 0 269 0 345 (167) (96) (98) (85) (160) (606) 11 0 785 0 840 0 759 0.685 0 653 0 747 __ _ (316) (125)(137)..-,(139Lii‘10)_._.__1_<§3_921 TABLE 3.12 PRODUCT B (Toothpaste) 1- Purchased Brand Bu IBRAND Bu 0— Not Purcnased Brand Bu instorical P§;f History of Stores_V181::d IrrespeCtive Sequence I I I DB_,_ m10f the Store of Brands SS I " i Choice Purcnased +_(over- -a11) _ _ .__ 1_. I ._m_1 ___"._ 00 0 036 I 0 042 (2486) I1 (7579) I )I 10 i 0.305 0.295'0 239 i0.190 .287 0.268 ‘ (128) i<61) ‘(71) {(84) (129) (473) 01 1 0 338 I0.383Io 477 I0.362 b 266 0 366 (133) l(60) |(109) (58) {94) (454) 11 I 0 630 |O.5760.770 0.546 3.527 i 0.610 |,(146) (38) |(74) _,_(___97) 91) (446) \l (J7 TABLE 3 . .13 PROBABILITY OF A HOUSEWIFE PURCHASING BRAND GIVEN THE HISTORY OF HER PAST TWO BRAND PURCHASES AND THE CORRESPONDING STORES VISITED P RODUCT C ( Coffee) 1- Purchased Brand 01 BRAND Cl _. __ 0- Not Purchased Brand 01 Historical I___Past Histor of_' Stores 112th IFEe-sp—EFt—ive Sequence of I DD of the Store Brands SS SD DS DlD1 DlD2 Choice ‘£:}Jrchased (over-all) 00 0.069 0.098 0.083 0.190 0.178 0.100 (7114) (1658)(1741) (1983)(1328) (13824) 10 0.357 0 453 0 156 0.371 0.372 0.330 (760) (300) (456) (248) (288) (2052) 01 0 375 0 229 0.396 0 325 0.368 0 361 (738) (393) (357) (243) (339) (2070) l 11 0.879 0 786 0 798 I03 73 2 0 714 0 822 i (2.222) (477) (59.0) ___1.<._1_2.H1_-(_496,1_i_.(4180) TABLE 3.14 PRODUCT C (Coffee) 1- Purchased Brand C2 BRAND 02 i__ 0- Not PurChased Bragdnggm Historical _Pa§§__Hi_s_t9ry BEEF/.0322 _\_J_is1t_ed irrespective Sequence of I I DD of the Store :Brahds 38 SD 08 IDlDl 31D2 Choice Purchased , L. _ (over-all) w——-— -->-—-- -—1'--—=-=-——-— r—-— —-—n—»r——-—-———-—— -- ..-—.-...- -_ 00 10.032 I0 043 b 044 I0 081 0-063 0 044 :(9484)I(2363)I25531I(262O)(1895) (18915) I 10 0 312 I0. 366 0 147 :0 325 b 240 0 279 (442) I (172) (224) (123) (196) (1157) I I 01 0 323 I 0 152 I0 432 0.193 0.229‘ 0.277 (434) I(210) I183) l(161) (179) (1167) 11 709 I0 59 8 0.687 0 464 0 571 i 0.642 -1017: I 83) (94) (1.40) (.211-.. (885‘- 1.76 TABLE 3 .15 PROBABILITY OF A HOUSEWIFE PURCHASING BRAND GIVEN THE HISTORY OF HER PAST TWO BRAND PURCHASES AND THE CORRESPONDING STORES VISITED P HODUCT C ( (Soffee) l-Purchased Brand C3 BRAND C3 ______.__._1 __-. _"0- -Not Purchased Bran-d C3 Ii istorical I ”Past History of Stor:s_\_’151t_e_d_ IrrespeztI’x’xe Sequence f ADD of the. Store O f Brands I SS SD DS DlUI Dng 1 Choice Purchased. 1 ___ __ ..._.- J I (over-all) 00 _0 025 ~0 044 0,040 . 048 0 060 I 0 036 ((9692) (2435) (2646) (2652) (1959)I (19384) 10 {0217 ?0 304 0 108 0 171_ 0.218 I 0 209 ;<300I .7161) (139) (129), (147) I (876) 01 50 307 .0 119 0 441 0 243i 0.256 0 285 (306) (134) :(161) (115)] (160) (876) 11 0 807 0 796 I0 787 50.527' 0 642 0.746 .1 -..--(919... I(98) 19981.. 1.4.81.195) . (988.) TABLE 3 16 IP13ODUCT c ( Coffee) l-Purchased Brand Cu BRAND Cu O-Not Purchased Brand CLI Eis- BEL—cal 'TWTPastA history of Sta? e3 V_1517e—d- _IrPengctive Sequence i ._ -.-DD- ___; of the Store O f Brands . SS SD DS DID} D1D2 ' Choice archased _ - -1411-.- “___? . "Lover—all) 00 50.032 0 049 0 049 0 063 0.060 I 0.044 5(96111) (2427) (2597) (2629) (1990): (19254) i I I . I 10 ;0 236 0 293 .01115 0.191; 0 147: 0 204 I(415) ‘(1501 i7183) (162). (150) I (1060) 01 I0 224 20.183 I0 402 0 230 0,215 I 0 249 ((428) .(169) ;(189) (126) (149) g (1061) 11 10.723 :0 622 I0.682 0 480‘ 0 542 ' 0 649 \ (383) W83) I,(89)___.-.(_12.:.)I..<_72.)__ 1 (749) 177 TABLE 3,17 PROBABILITY OF A HOUSEWIFE GIVEN THE HISTORY OF HER PAST AND THE CORRESPONDING PURCHASING BRAND A1 THREE BRAND PURCHASES STORES VISITED IPRODUCT A C Paper Product) l-Purchased Brand A1 iEBRAND A1 O-Not Purchased Brand Al filstorical ESequence Past History of Stores Visited Irrespective of c>f Brands SSS DDD the Store Choice EDurchased (over-all) 000 0 067 0,132 0.101 (165) (A16) (11u3) DSD SDS 010 0.U78 0 U12 02125 0 377 O 383 (23) (17> <16) (69) (167) 001 DDS SSD 0 393 0 655 0.077 0 U59 0,u62 (28) (29) (13) (61) (182) 011 DSS SDD 07562 0 750 00289 0.532 0 61A (32) (28) (18) (62) (197) 100' SDD DSS 0 -78 0 389 07375 0 306 0.335 (37) (18> <16) (85) (209) 110 SSD DDS 0 595 0 52a 0 Uiu 0 508 0 522 (A?) (21) (29) (59) (207) 101 SDS DSD 0 667 0 800 0.Al7 0,558 0.622 (36) (15) (12) (52) (180) 111 07921 I 0.825 0 87’7 ‘(2U1) i (31“) (1033) 178 TABLE 3 . 18 PROBABILITY OF A HOUSEWIFE PURCHASING BRAND A2 GIVEN THE HISTORY OF HER PAST THREE BRAND PURCHASES AND THE CORRESPONDING STORES VISITED P RODUCT A C Paper Product) l-Purchased Brand A2 EBuRAND A2 O-Not Purchased Brand A2 Ififiistorical EScequence LPast History of Stores Visited Irrespective of c>;f Brands 1 .the Store Choice I?11rchased L _SS i S 1 Y T DDD j (over- all) 1 1 000 '0w0 079 I i 0 159T 0 105 (355) s , 1 (568)) (1752) i ‘ ! e 1 010 g , DSD ; SDS ; ! )0 308 0 500 g 0 277 f 0 267! 0 311 .(39) ;(16) 1 (13) (75) f (225) L ! g 1 g 001 E i 003 i SSD ; ) g07309 f0,u6u : 0.237 1 O -15 O 328 1(12) [(28) ‘ (21) : (92) (256) 011 i E DSS ; SDD ‘0 372 g 0 533 + 0 u00 0.539 0 519 t<21> 5(15) é (15) (51) (154) 100 E Q SDD I DSS 0 372 , 01348 ° 0 17m 0 300’ 0 270 (13) 1 (23) ; (23) 1 (70) ~ (211) 110 i 3 SSD a DDS I0~u6u . 0 727 0 36a 0 311 0 106 {(28) (11) (22) (M5) (155) 101 i SDS } DSD 10.138 3 0 643 o 333 , 0 571 0 593 §(16) (11) 4 (9) g (63) (135) , _ . 111 !0(775 ‘ ) 0,801 0 792 4(57) ; (151) (100) 179 TABLE 3.19 PROBABILITY OF A HOUSEWIFE PURCHASING BRAND Bl GIVEN THE HISTORY OF HER PAST THREE BRAND PURCHASES AND THE CORRESPONDING STORES VISITED I?RODUCT B ( Toothpaste) l-Purchased Brand B1 BRAND Bl O—Not Purchased Brand Bl Historical 1 Sequence Past History of Stores Visited ,Irrespective of of Brands I ‘Ithe Store Choice Purchased SSS DDD (over-all) , T 000 0.041 0.087 0.060 (118“) (1621) (5104) 010 DSD SDS 0 219 0.212 0.158 0.270 0.227 (6“) (33) (19) (126)I (348) 001 DDS ‘ SSD 0.295 0,580 I 0 250 0.292 0.329 (61.) (50) (20) (15“) (398) 011 DSS SDD 0.A68 0.692 0.619 0.52“ 0.536 (147) (26) (23) (82) (233) 100 ; SDD DSS 0.164 10.219 0.175 0,204 0 186 (73) (32) (A0) (1“?) (“24) 110 SSD DDS 0.511 :0.615 0.314 0.430 0.421 (45) (13) (35) (86) (240) 101 SDS ‘ DSD 0.683 0.727 0.333 0.1418 0.552 (141) (ll) (18) (55) (183) 111 0.952 0.812; 0 903 (505 (355) (1376) 180 TABLE 3 . 20 PROBABILITY OF A HOUSEWIFE PURCHASING BRAND B2 GIVEN THE HISTORY OF HER PAST THREE BRAND PURCHASES AND THE CORRESPONDING STORES VISITED P RODUCT B C Toothpaste) l-Purchased Brand B2 BRAND B2 O-Not Purchased Brand B2 Historical Sequence Past History of Stores Visited Irrespective of of Brands E the Store Choice Purchased 888 L DDD (over—all) 000 0.059 ‘ 0.078 0.067 (1338) (1589) (5223) 010 DSD SDS 0338 !0.A62 0.261 0.302 0.295 (80) (13) (23) (96) (308) 001 DDS SSD ‘0.361 0.569 0.3214 0.1132 0.1425 ((97) (51) (31) (158) (117) 011 1, DSS SDD '0.750 0.806 0.810 0.6614 0.715 i<6o> .(36) (21) (116) (326) 100 E SDD DSS 0.3211 i0.290 0.281 0.262 0.261 (7“) 3(31) (32) (126) (353) 110 SSD DDS 0.u90 0 500 _ 0.300 0.353 0 u80 I(51) (22) ) (30) (85) (251) 101 i SDS 1 DSD 50.652 0.865 i 0.636 0.620 0.667 :(16) (15) ; (11) (71) (201) 2 . 111 0.887 ‘ 0.811 0 860 ‘(274) ) 2 (385) g (1194) 181 TABLE 3.21 PROBABILITY OF A HOUSEWIFE GIVEN THE HISTORY OF HER PAST PURCHASING BRAND B THREE BRAND PURCHA ES AND THE CORRESPONDING STORES VISITED LEDRODUCT B ( Toothpaste) l-Purchased Brand B BRAND B3 O-Not Purchased Brand B3 Historical Sequence Past History of Stores‘ Visited Irrespective of of Brands ’ he Store Choice Purchased SSS DDD (over-all) 000 0.045 E i 0.076 0.056 (1485) i g (1887) (5984) 1 . 010 ) DSD ) SDS 0 187 . 0 185 g 0.054 . 0 200 0 174 (64) , (27) 1 (37) f (115) (368) 7 . 001 j DDS SSD 1 0 365 § 0-355 0.283 . 0 225 0.289 (74) * (45) (46) ; (138) (402) 011 l DSS . SDD 5 0 478 u 0 625 7 0 353 I 0 400 0.475 (46) ((16) (17) I (65) (198) 100 3 E SDD DSS ) 0 182 )0 294 0.093 g 0 149 0 157 (77) V34) (54) i (141) (421) I 110 E . SSD ) DDS )0 510 |0 500 I 0.237 i 0.318 0.387 :(49) ((18) (21) (66) (204) i I 101 i 1 SDS ) DSD ) :0 500 '0 643 g 0 273 0.395 0 476 (42) ‘(14) (11) (43) (135) 111 0 841 i 0.766 0.830 (183) a (171) I (624) 182 TABLE 3.22 PROBABILITY OF A HOUSEWIFE PURCHASING BRAND Bu GIVEN THE HISTORY OF HER PAST THREE BRAND PURCHASES AND THE CORRESPONDING STORES VISITED I?RODUCT B ( Toothpaste) l—Purchased Brand 83 iEBRAND Bu O-Not Purchased Brand Bu ZEIistorical Irrespective .SSequence Past History of Stores Visited of the Store 0 1‘ Brands Choice IE’urchased SSS DDD (over-all) 000 0.033 0.0A7 0.037 (1693) (2099) (6739) 010 DSD SDS 0.269 0 318 0.133 0.247 0.290 .(50) (22) (15) (89) (263) 001 DDS SSD 0 328 0.969 0.231 0.250 0 339 (6“) (A9) (13) (80) (292) 011 DSS SDD 0.U55 0 565 0.900 .472 0.999 (33) (23) (10) (53) (158) 100 SDD DSS 0.119 0 261 0 200 0.121 0.141 (59) (23) (25) (108) (326) l10 SSD DDS 0.387 0.571 0.388 0.299 0.398 (31) (7) (23) (67) (158) 101 SDS DSD 0 365 0.829 0 667 0.450 0.A62 (23) (7) (9) (“0) (119) 111 0 721 1 0.611 0.694 (61) E (90) (255) \ 183 TABLE 3.23 PROBABILITY OF A HOUSEWIFE PURCHASING BRAND C GIVEN THE HISTORY OF HER PAST THREE BRAND PURCHA ES AND THE CORRESPONDING STORES VISITED PRODUCT 0 (Coffee) l-Purchased Brand Cl EBRAND Cl 0-Not Purchased Brand Cl PIIstorical ___— ESequence Past History of Stores Visited Irrespective of c>f Brands . the Store Choice I?urchased_;_sss DDD (over-all) 000 10.054 ‘ 0.173 0.085 |(5490) 7 (2265) (12251) 010 i DSD 1 SDS )0 271 0.355 ' 0 111 0.312 0.235 7(365) (93) (199) (256) (1292) i 001 I DDS ' SSD {0 270 '0 400 0 160 0.292 1 0 269 ‘(397) (140) (187) (295) (1359) 011 I : DSS SDD (0.553 {0.713 0.343 0 471 0 525 (217) 3(101) (70) (170) (737) 100 E i SDD DSS 0 _69 0.360 0.098 0.316 0 243 (390) (86) (234) (291) (1344) 110 E 1 SSD DDS £0-523 v0.645 0 234 0.497 0.492 i(218) 3(62) (94) (149) (725) 1 s 101 i ' SDS DSD 0 560 0 676 0 290 0.484 0.536 (209) (74) (62) (151) (662) 111 0.927 0 794 1 0.886 (1666) (564); (3383) 184 TABLE 3.24 PROBABILITY OF A HOUSEWIFE PURCHASING BRAND C2 GIVEN THE HISTORY OF HER PAST THREE BRAND PURCHASES AND THE CORRESPONDING STORES VISITED PRODUCT C C Coffee) 1-Purchased Brand 02 BRAND C2 0-Not Purchased Brand 02 IifiiStorical; “"‘” ' ‘7 ”—3 Sequence {PastHistory of Stores Visited Irrespective of of Brands :v— E the Store Choice £1urmhased LSSS DDD (over—a11)__ 000 i0.023 0.072 0.038 5(7596)! (3288) (17783) ! 010 ’ DSD SDS 1 0 273 0 328 0.081 1 0.258 0.226 (242) (61) (99) 3 (182) (826) 001 DDS SSD ' 0 270 0.377 0.098 0.18 0 231 '(237) (77) (102) (197) (828) 011 DSS SDD 0 482 0 605 0.185 0-268| 0 413 (11“) (38) (27) (71) ' (315) 100 , SDD DSS i 0 243 0 328 0 134 0.118? 0 186 (251) (58) (112) g (169)) (818) ‘ I 110 i SSD i DDS 1 3 0.459 0-594 3 0 206 1 0.355. 0 416 (122) (32) 1 (34) 5 (62) a (310) 7 101 . SDS I DSD f0 481 0 567 0 154 0 257 0.410 H108) (30.) (26) (70) (315) 111 $0.809 0 667 0.769 ,(282) (102) (558) Y,_—— 185 TABLE 3.25 PROBABILITY OF A HOUSEWIFE GIVEN THE HISTORY OF HER PAST AND THE CORRESPONDING PURCHASING BRAND C3 THREE BRAND PURCHAQES STORES VISITED :PRODUCT C (Coffee) l-Purchased Brand 05 BRAND C3 O-Not Purchased Brand C3 IiistcriEaIE“ -‘ )“"" Sequence L_§2§£-.§1§£2§Y_10f Stores Visiteilrrespective of of Brands 1 I the Store Choice Purchased_1'__S_S_S__L_' __ _D_DD (over-all) 000 30.022 7 1 0 052 g 0.033 g(7829)- 7 (3378): (18369) 010 E DSD ‘ SDS E ;0 145 ;0.2A2 0 033 0 136 ' 0.136 2(165) (62) (60) (154) g (617) 001 3 DDS SSD i 10 258 ‘0 348 0.071 0.230 g 0 227 1(186) (69) (56) (165) g (679) 011 DSS Q SDD I 0.449 . 0.559 g 0 214 0.306 ‘ 0.440 €(78) (34) (28) (49) . (243) 100 | SDD DSS , . l0.1.24 ,‘0.244 0.043 ; 0 129 .118 .(185) é(45) (70) i (163) 7 (688) f s 7 110 SSD 1 DOS 0.370 .0 618 ; 0 231 0.410 ; 0 395 '(81) ;(34) 1 (26) (61) i (248) 101 1 SDS DSD ; ;0.519 i0.741 . 0 083 0.405 3 0.497 3(52) f(27) (12) (42) g (181) 111 0 894 0 690 t 0.850 (376) (129) . (728) 186 TABLE 3.26 PROBABILITY OF A HOUSEWIFE PURCHASING BRAND Cu GIVEN THE HISTORY OF HER PAST THREE BRAND PURCHASES AND THE CORRESPONDING STORES VISITED PRODUCT C (Coffee) l-Purchased Brand C4 IBRAND C4 O-Not Purchased Brand 04 Iiistorical 7 Irrespective ESequence ) Past History of Stores Visited of the Store c>f Brands Choice I?urchased SSS DDD (over-all) 000 0.025 0.059 0.038 (7755) (3365) (17783) 010 DSD SDS 4 0 244 0.234 0.143 0.383 0.226 (246) (47) (21) (65) (826) 001 DDS SSD 0 203 0.455 0.108 0.235 0.231 (246) (88) (74) (179) (828) 011 DSS SDD 0 419 0.628 0.143 0.383 0.413 (74) (43) (21) (65) (315) 100 SDD DSS 0-170 0.315 0.112 0 140 0.189 (247) (54) (89) (172) (818) 110 SSD DDS . 0.293 0.500 0.069 ‘0.210 0.416 (82) (32) (29) (62) (310) 101 . SDS DSD 0 238 g 0 500 0.222 0.200 0.410 (84) 7 (24) . (18) ((35) (315) 111 0 821 § 0.578 0.769 (218) _(90) (558) 187 TABLE 3 . 27 PROPORTION OF HOUSEWIVES CHANGING THE SIZE OF PURCHASE OF PRODUCT A VS. THE PURCHASE PATTERN PRODUCT A £;Paper Product) Increased No Change Decreased EDatern of Two the Size in the the Size Consecutive of Size of of Marginal Purchases Purchase Purchase Purchase" Total Same Store & 0.124 0.784 0.092 0.312 ESame Brand (152) (963) (113) (1228) ESame Store & 0.212 0.574 0.214 0.131 [Different (112) (303) (113) (528) Brand Different 0.184 0.630 0.186 0.333 EStore & (240) (820) (243) (1303) Same Brand Different 0.236 0.521 0.243 0.224 Store 8: IDifferent (208) (460) (214) (882) EBrand IVEarginal 0.181 0.646 0 173 zotal (712) ) @2546) (683) 3241 PI = 13 30 + BC x 7.00 + so x 4.20 PD = 10.80 + BC x 8.95 + 30 x 6.15 188 TABLE 3.28 PROPORTION OF HOUSEWIVES CHANGING THE SIZE OF PURCHASE OF PRODUCT B VS. THE PURCHASE PATTERN IDRODUCT B C Toothp§§.§§_l.=___ ..1 _ ’i ' ' Increased No Change? Decreased- Pattern of Two the Size in the the Size Consecutive of Size of ' of.“ Marginal Purchases . Purchase 1 Purchase L Purchase Total ' 1 Same Store & 0.188 0.687 I 0.125 0.324 Same Brand (575) (2143) 1 (400) g (3118) 1 : Shame Store & . 0 216 } 0.546 1 0.238 0.159 Different ; (331) i (835) (364) (1530) Brand 1 I 1 : : , Different 1 0,187 0.622 0,191 i 0.292 Store & 1 (527) (1757) (540) . (2824) Same Brand : I IZXifferent 0.253 0.473 ! 0.274 1 0.225 Store 8! 1 Different (549) (1025) (594) 7 (2168) .E337and i { ‘ : rv'larginal 7‘ 0.206 0.597 T 0.197 2 Total _3_ (1982) 1 _(5760) (1898) ' 9640 P1 = 17 85 + BC x 4.7 + 80 x 1.8 13 25 + BC X 9.8 + SC X 5.1 "U C II 189 TABLE 3.29 PROPORTION OF HOUSEWIVES CHANGING THE SIZE OF PURCHASE OF PRODUCT C VS. THE PURCHASE PATTERN PRODUCT C (Coffee) 1 Increased _ No Changeu' Decreased IPattern of Two f the Size f in the g the Size) (Zonsecutive of 1 Size of of ’Marginal Purchases Purchase ' Purchase Purchase) Total fSame Store & 0.081 0.841 0.078 0.429 ESame Brand (776) (8114) (755) (9645) Same Store 8: 0.150 0.691 0.159 0.199 IDifferent (672) (3087) (709) (4468) Brand IDifferent 0.144 0.716 0.140 0.136 Store & (424) (2103) (411) (2938) Same Brand Different 0.232 0.540 0.228 0.236 Store & Different (1264) (2937) (1244) (5445) Brand fqarginal 0 139 0.722 0.139 CPQtal (3136) (16241); (3119) 22496 7.62 + as x 7.85 + 30 x 7.25 7.62 + BS x 8-45 + SC x 6.55 iProduct A (Paper Product) 190 TABLE 3.30 SUMS OF PRODUCTS AND SUMS OF SQUARES No. No. No. of Brands 4 of Stores 10 of Periods 36 Yijk‘ Market Share of Brand 1 in Store 3 and Period k as determined by number of purchases. Xijk: Average Price of Brand 1 in Store J and Period k. =— "'“ Source of Degrees Sums of Sums of Sums of Regression \fariation of Squares Products Squares Coefficient _Freedom (yz) (xy) (x2) Between . £3rands 3 91.353 -0.261 0.033 -7.903 LBetween EStores 9 2.785 0.901 0.945 0.954 .Between IPeriods 35 l 309 0.562 0.573 O 981 Brand x Store IInteraction 27 9.135 0.073 0.107 0.683 Brand x Period :[nteraction 105 11 453 -0.1250 0.115 -1.086- EStore x Period :Eiiteraction 315 7.879 35333 5.156 0.646 lEizéror 945 82 518 0.252 1.082 0.233 CI7<:>tal 1439 206.433 4.736 8.012 0.591 R 191 wmo.o om: mm :20 poppm smo.o om:.mw 22m Locum coauom coam **om.m m:m.o mmo m mm upoucH smo.o mmo.o wmo.o H Imohwom mLOpm on cam x Unchm Eopoopm Eopmonm ofipmmlm mopmsvm moumzum mo coapmflhm> oapmm mmpmzdm mmpmsvm mo coauwapm> cams mo mssm moopwmo wo mozsom um 2mm: mo mezm mmmpwoa mo condom onBo ompmzwp< mompwom noum3np< :oammopmmm mo wesm mo mESm wo m83m7mmmpwma mo condom Apczwopm podmmv Ammmmnohsm mo LQQESZV < Hosaomm mom mozOo mo mHqu mm mLOpm I- I x pcfiwm Eonompm 1 Eopmmpm oapmm mmpmsvm mmpmsqm mo coapmfimmxw oapmm mmpmddm mmpwzvm mo coapmfinmuz 1m saw: no wasm moopwmm mo condom IIIHMII 2mm: mo mesm woopmoa mo condom ZOHBo pmpmzm©< mmohmmm popmzmp< coammmpwom mo wasm Co.mE:mlmo mesm mmopmoa mo wohzom lAuddUdHMlHdemq Ammamm co essao>v < eoaaomm mom mozaHm<>oo mo mHmmaaza mm.m mqm Between Brands 3 13.379 0.352 0.030 11 646 Between Stores 9 0.847 -0.020 2 199 -0.009 Between Periods 35 1 031 -0-140 0.156 -0.902 Brand X Store Interaction 27 4 395 0.081 0.154 0 528 Brand x Period Interaction 105 9.050 —0.388 0.330 -1 176 Store x Period Interaction 315 3 543 —0:617 1.189_-__ -0 519 Error 945 27.977 -0.778 1.932 -0.403 Total 1439 60.221 -1 510 5 989 —0.252 195 mmo.o moo mm :20 Lonpm **mm.oa :Hm.o :Hm.o H coflm Imohwmm on mom Eoooopm OHpmm mopw5dm mopmsum mo coapwasm> um :60: mo meow moopwoa mo mocsom ZOHmmmmomm mmB UzHBmMB mmo o mow.~m 22m ._ Loppm cofipom ..He,m Boa.o mmm.a on -eooee oLOpm x ocmpm l Eowmwum oapmm mopmsvm mopmsvm Mo coapmfipm> um 2mm: mo mmmm moopmoplmo mofimmm 23 9.113335 .. ‘ mmoem a ozamm mo weHm>m Ixxm (Ill m>m Eopoopm oapmmum zoo: mo m ucofiofiwgooo monmzvm muozoopm mothUm mo :ofiumapm> Umpmdm©< moopwoo 66pm3no< coammopwom mo mEzm mo mesm do mE:mlMomeoQ mo mopsom Aopmmdzpooev Ammwmcohdm mo thESZV m Boaaomm mOh mozOo mo mHmwQ_- (x2) Between Brands 3 13.902 0.300 0.030 9 924 Between Stores 9 0 817 -0.246 2.199 -0.122 Between Periods 35 l 062 -0 142 0 156 -0 910 Brand x Store Interaction 27 3.845 —0.098 0 154 —0 635 Brand x Period Interaction 105 10.391 -0.612 0 330 -1857 Store x Period Interacfion 315 3;21...:9..-.1§2__. 4189* -0 641 Error 945 31.917 -2.429' 1.932 -14257 Total 1439 65 873 -3.989 5.989 —0 666 197 II I . .l .In'i Hmo o mom.mm aam totem Hmm o mom mm 33m totem :oHpcm - coflm **mm : mzfl o mmm.m om upop:H **mH mm mmo m mmo,m H (mocmom ocoom O .H mg I -...III .-|l.| III--.) IIIIIIIIII .. x. UCMhm Eooooum . . . Eoooopm oflcmmlm moLmzom mohmsqm Ho coHpmHLm> oHHmmum moumzdm moumsvm mo mocmapm> 2mm: Ho mEDm moopwoc mo mowwmm 2mm: Pm mESMImmmhmwmIWo mWWdom I- onHoammazH onmmmmomm mmB mzHEmME mmoem x Q2 cmpmzm©< mmogwmm woum3mo< :onmmmem mo mE3m -MmlmmwaMQImmqm-mmWWMoQ Ho oomsom - .II _IIIIIe Hopmmdnpooev HmoHom Ho oeaHo>v m Boeooma mom mozoo mo mHquqzq m:.m mqm<8 198 TABLE 3.46 SUMS OF PRODUCTS AND SUMS OF SQUARES Product C No. of Brands 4 (Coffee) No- of Stores 10 No. of Periods 36 Yijk: Market Share of Brand i in Store 3 and Period k as determined by number of purchases. Xijkz Average Price of Brand 1 in Store 3 and Period k- . _v- ...—. :- ~W—r-— ___-2:11. =: 1—_—--.——--- __- _. .-- _— -—-'—~ ~-——- Source of Degrees Sums of Sums'6f Sums of Regression Variation of Squares Products Squares Coefficient _ -_1_- Freedom (yz) (xy) (X‘) Between ' Brands 3 24 957 2 054 0*339 6 065 Between Stores 9 8 002 2 312 5 135 -0 450 Between Periods 35 0 517 0.116 0 829 0.140 Brand x Store Interaction 27 6.834 -0.259 0.399 -0 648 Brand x Period Interaction 105 3,540 -0.587 0 341 -l.724 Store x Period In+e3agglon _ 315 5 594 _2~3§21_.5r501 0 433 Error 945 21 608 -1 406 2 988 -0 471 Total 1439 71 053 —0-013 15.532 -0-001 H . .. _g, ___. ._ __9! w‘ - . _— 199 8.8!]! 'I'r'lllll“; II ‘ I," mmo 0 BBQ on :30 totem mmo o mso on Hem Lotta COHHN COflm IL®HCH *aoo om 666,0 moo o H Iaoemom **BB_HH omm o ©o©.© mm otoom Op QED x UCMLQ 88...... I 886.5 I oHpmmIm motmsvm mmumsvm Ho COHomHLm> oHme mqpmsvm motmswm Ho coHumHLm> cam: Ho mESm moohwoo Ho mcLsom Im II cmoz Ho mmmmI mooLwca Ho motsom 20H9c ocpmzme¢ momtwmg oopm3n©< :onmoLmqm Lo mESm II. III-Ill- .Ilslll’I-l I801?!" Ill... 0' Amommgopsm Ho pooEzzL o 5:.m mamOo mo mHme oHme moszvm mcLBSUm Lo :oHpmHLm> 1111 1 2mm: H) m53m1mNmmmmm1mw1wmwmmm 111um11.1mmwaa1mm mean-m-wqum Lo mmczom 11- zoLLoammLzH onmmmmamm mze quemme mmoem x Qz IL ocpmsmo< moomeQ oatquod rI-u. 4|-lltliu1llll‘lll1lll ill--||."'l.'lll dlll'l' 511'" ||l Ho MESm mo mEHm mooLwaQ mo QLLSO) I’Llll' conmoLwom Lo mEdm IIIII I'll ....III'IIYIOII .alllil lfiiii It! rmmflmm ..HO mESrO>V D Ammcuooc Hcsaomm mom mozaHm<>oo mo mHmLuaza Hm,m mamag APPENDIX IV ANALYSIS OF TOOTHPASTE DATA As mentioned earlier, only the data for product B, D1, include families with one or more weekly diaries missing For products A and C, only during the period of study. families who reported continuously without missing any single diary have been included for the purpose of analysis. IIn order to insure that the general results are not sig— 11 ificantly affected by the inclusion of data on families VJ ith missing diaries, the screened data of product B, D2, (3 (Dnsisting only of families who reported continuously for t? 11 ree years have been-re—analyzed. The results of the I) :V’potheses tested against both the samples of D1 and D2 E1 ‘F‘e tabulated side by side for comparison. Only hypotheses El 1; micro level have implications in terms of a disconnected Some t3 I? and or store sequence due-to a missing observation. C) if these hypotheses are tested for both the samples and pre— 53 eE‘nted in the following tables. No significant differences i~t1 the estimates of conditional probabilities of brand ‘3t10ice are observed between the two samples D1 and D2. However, this does not assure the reader that any type of brand and store analysis can be done on panel data with 202 203 sets of families having missing diaries, though in my analysis the results are not significantly affected. A possible explanation could be that a missing weekly diary for a family in the panel does not always imply a missing purchase observation, especially when the time between two consecutive purchases is longer than a week, as in the case of product B (toothpaste). STORE CHANGE VSo BRAND CHANGE 2014 TABLE “.1 IN TWO CONSECUTIVE PURCHASES 0F PRODUCT B COMPARED BETWEEN THE TWO SAMPLES D1 AND D2. Product: B (Toothpaste) Store { Change Data Different Marginal Brand 'Base Same Store Store Total Change D1 10 662(3078) 0.557(2780) 0.607(5858) Same Brand D2 0.684(1670) 0.637(1405) O 612(3075) j i ; D1 0.338(1572)’0.uu3(2212) o 393(378u) Different { Brand D2 t0.316(771) 0.363(1177) 0.388(19u8) D1 'o.u82(u650) 0.518(u992) 96u2 Marginal Total D2 0.A86(2uul) 0.514(2582) 5023 TABLE 4.2 205 PROBABILITIES OF A HOUSEWIFE PURCHASING BRAND Bl GIVEN THE HISTORY OF HER PAST TWO BRAND PURCHASES AND THE CORRESPONDING STORES VISITED COMPARED BETWEEN THE SAMPLES D1 AND D2. PRODUCT: B (Toothpaste) l-Purchased Brand Bl BRAND: Bl 0-Not Purchased Brand 51 Historical Sequence Data Past History of Stores Visited of Brands Base DD Purchased 33 SD D3 010] 0l02 D1 0.050 0.060 0.082 0.083 1 0.097 (1858) (765) (1012) (1008) (1310) 00 D2 0.040 0.061 0.075 0.077 0.104 (985) (411) (535) (534) (721) D1 0.352 0.279 0.254 0.266 0.321 (165) (86) (114) (94) (196) 10 D2 0.354 0.256 0.200 0.213 0.287 (82) (43) (55) (47) (101) 01 0.409 0.333 0.558 0.359 0.382 (159) (78) (111) (92) (202) 01 D2 0.481 0.310 0.581 0.375 0.298 (79) (42) (62) (40) (104) 01 0.899 €0.843 0.864 0.765 0.798 (711) 1(191) (242) (260) (302) 11 D2 0.887 0.859 0.855 0.773 0.777 (389) 1(85) 1(124) (141) (121) TABLE 4.3 206 PROBABILITIES OF A HOUSEWIFE PURCHASING BRAND Bu PAST Two BRAND PURCHASES AND THE CORRESPONDING STORES VISITED COMPARED BETWEEN THE SAMPLES D1 AND D2. GIVEN THE HISTORY OF HER PRODUCT: B (Toothpaste) l-Purchased Brand Bu BRAND: Bu 0-Not Purchased Brand Bu Historical Sequence AData Past History of Stores Visited of Brands 'Base L‘i DD Purchased A 58 SD DS 1 DlDl D1D2 1 D1 0.075 0.072 0.058 . 0.098 0.101 1 (2023) (759) (1005) 1 (1009) (1276) 00 . 02 7 0.080 0.058 0.082 ‘ 0.097 0.116 2 1 (1023) (520) (390) (538) (666) . IL L 1 D1 1 0.397 0.442 0.292 0.329 0.376 I (179) (77) (113) (79) (157) l O 1 ; 1 D2 ’ 0.365 0.232 0 386 0.405 0 368 3 (104) .(69) (44) (42) (77) D1 ? 0.436 10.488 0.596 0.548 0.487 I (202) (84) 1 (114) (104) (193) 01 : ' D2 . 0 414 .0.619 g 0 449 0 531 0.459 1 (116) 1(631 <49) <49) (111) D1 : 0.857 0.825 0.830 0 763 0 818 i (489) (200) (247) (262) (384) 11 D2 7 0 887 0.791 0.767 0 797 0.825 I (292) (134) (93) (133) (183) 207 TABLE 4.4 PROBABILITIES OF A HOUSEWIFE PURCHASING BRAND Bl GIVEN THE HISTORY OF HER PAST Two BRAND PURCHASES AND THE CORRESPONDING STORES VISITED COMPARED BETWEEN THE TWO SAMPLES D1 AND D2. PRODUCT: B (Toothpaste) l-Purchased Brand B1 BRAND: B1 O-Not Purchased Brand Bl Historical, Sequence éData Past History of Stores Visited of Brands (Base Purchased i_ SSS 1 DDD ? 1 000 : D1 0 041(1184) 0.0w87(121) ' D210 036(635) ; 0.0087 (8 8) 1 DSD T” SDS 010 . D1.0 219(64) {0.212(33)§0.158(19) 0.270(126) . D210 222(27) 0.056(18)$0.100(10)10.217(69) T f T “DDS } “SSD ' 001 A Dl 0295(61) :0.580(50)10.250(20) 0.2 92(1 4) A 0510.346(26) .0.680(25):0.286(14),0.2 86(7 - .:_..L_-.__,.._.- 1‘. 1 ' A ; DSS 1 SDD 011 *0 468(47) ~0.692(26).0.619(23);0.524(82) %A0. 469(32) ;0.706(17)!0.667(9) :0 460(37) l 23 ' SDD I DSS 1 100 Dl'O 164(73) 0.219(32) 0.175(40)§0 204(147) ' D2 0 143(35) 10.182(22)>0.118(17)10.158(82) 5 SSD ' DDS - 110 D1 0 511(45) g0 615(13) 0.314(35) 0 430(86) D2 0 555(27) 0 667(9) 10.353(17) 0 391(46) . ’ —“_’—SDS'" DSD T‘ 101 D1 0 683(41) 0 727(11) 0-333(18);0.418(55) 7 D2'0 783(23) 10.571(7) 0 167(6) 0.440(25) 111 D1 0.952(505) : f0.842(355) D .0.945(274) '0 842(177) PROBABILITIES OF A HOUSEWIFE PURCHASING GIVEN THE HISTORY OF HER PAST THREE BRAND PURCHASES 208 TABLE 4.5 BRAND Bu THE CORRESPONDING STORES VISITED COMPARED BETWEEN THE SAMPLES D1 AND D2. PRODUCT: B (Toothpaste) l-Purchased Brand Bu BRAND: Bu O-Not Purchased Brand Bu Historical “—_ — Sequence Data ‘__Past History of Stores Visited of Brands Base Purchased '— 000 D1 0. 059(1338) 0.07811589) D9 0 064(669) 0 087(849) ‘5' ’ ' DSD SDS 010 D1 0.338(80) 0. 462(13) 0.261(23) 0.302(96) D2 0.292(48) .0 333(9) 0.267(15) 0.345(55) f—' DDS‘"—* SSD 00l D1 0.361(97) 50.569(51) 0 324(34) 0.4 3 (158) D2 0 345(55) 10 607(28) 0.211(19) 0 417(84) 1 5 DSS SDD 011 D1 ,0 750(60) 0.806(36) 0.810(21) 0 664(116) D2 10 781(32) 0 818(11) 0.864(21)i0.646(63) 7 ‘5 SDD DSS T 100 01 10.324(74) 0.290(31) 0.281 32) 0.262’126) D2 {0.341(47) 0.?86(14 ) 0.294(17T¢0-260(77) 7’ —'“”"“ SSD ' DDS §”" - 110 D '0 490(51) 500(22) 0 300(30) 0.353(85) D2 0 500(22) 0 636(11) 0 363(11) 0 467(45) —*w.T.-— —Ims‘"“"mm “ 101 D1 ;0,652(46) 0 8651 15) 0 636(11‘ 0.620(71) 02 0 545(22) 0 889(9) 0 571(7) 0.600(40) 1_ _”_, n__-__fl_”_fl_T_, ‘ 111 D_ A0.887(274 ' 10 844(385> D? ?0-908(184) A 0 876(186) 1L" —-- _v‘_——————-—o-—v om x m s + an a 3,0H + mL «L n ma on x m a + on a m a + 03 mL u Ha mo mmwm dime om x L m + om a m.m + mm.mH n ma cm x m H + om x H.s + mm La 1 a Ho 0mmm mtmm Ammomc coo H Lsmmc mmH,o m Ammmmv Bmm.o Ammon-mom-o we 1 1 1 1 111-1mm1mm Acqomc goo L Aromas HHL.O “ Looamv Lam.o AmmmLc mom 0 Lo . meHwamz LHHLHI mmm.o ,mev Hmm.o Amsmc mm: o memc mmm_o ma 1 ecmam acmamauHa Lmonc mmm o Loamv sum.o AmmoHc ms: 0 Amsmv mmm.o Le a madam uzmamecHo Amosac mam.o Ammmv :HL.O Ammmc Hmm.o Ammmc HRH 0 mg ecmam mamm w Lsasmc amm,o Loamv LHL,O LLHLHV mmo,o Asmmv HmH 0 Ho ” a madam tamamamao ILLHLV mmfl.o LsBLV mmm.o LNHBV msm.o mmmmw1mmm a- MQI. _.1e:mtn Lcdadmnmm Lemmas de.o Asomv mmm.o _ mewc msm.o Asmmv BLm 0 La w radam team AOHBHV mmm.o1 AaHmc mma o AsmLHV Law.o memv maL1m mm1.1,1 1 1111wQMMM1mamw AmHHmV 3mm.o Loos, mmH o Amsamv Law 0 Amsmv me m1 Hc a mcotm qsmm Hmpoe camchzm ommgoLzm . owmchzml -mmMml l 1-11111mdmmLMMBL HmcHMLmz Lo mNHm on; no mNHm 051 . Lo mNHm opp mtmo m>Hu200mcoo pmmmmLomm CH mmcmno oz Ummmmmmmwl 11 11111 1-1039 LolmLONme 1111111-1 111.1.1111dmmmmmmmmmmw m Hoaaoma .ma aza Ha mmaazam oze mme ZBBszm ammaazoo Zenaeaa mmamomaa mza .m> m Hoaaoma ao mmamomaa mo mNHm mes ozHozamo mm>H3mmaom ao onHoama m,: mqmde APPENDIX V ANALYSIS OF COVARIANCE The technique of Analysis of Covariance is the combina- ‘t i.on of the methods of regre851on and AnalySIS of Variance. Vitiile making observations on a variable "Y", if some other Eiciditional factor 'X' varies, any dependence of "Y" on 'X' vv:ill tend to obscure and possibly invalidate the results of Ikxialysis of Variance performed on 'Y'. A brief explanation C>f: the technique of Analysis of Variance follows: If a set <>.f’ observations can be claSSIfied according to one or more C11?.iteria, then the total variation between the members of the 53 ea 1 can be broken up into components which can be attributed t3<=> the different criteria of claSSIfication. With the kncw ‘L-€Er' the criteria and their contributions to the over-all varia— tion. h) l:-—“<'ands, in addition to the variation due to the factors under L In our present study of analyZIng the market shares of ‘71 qustigation, the results are affected by the relative pri _~___“_ i:t><#<:erpts of this material are taken in part from the follOW‘ <3><3ksz 1‘ ~ Jogabratha Roy, 1. Chakravorti, and R. Laha, Handbook for Practical Work in Statistics, (Calcutta: Indian Statisti- cal Institute, 1959), pp. 278-283. :2 ~ Bennett C. Allan and Norman L. Franklin, StatIStical AnalySIS in Chemistry and the Chemical IndustryJ New York: Wiley Publications, 1959), pp. 441-461. 2ll 1.63V815 of the brands in the market. The factors under in- v'ezstigation are brand, store and the period of purchase de- TIC) ted by A, B and C respectively. In performing the Analysis cszf: Covariance, we assume a relationship between the average p>xnice of the brand and its market share, and the analySIS c>fF variance on market share data is performed by adjusting ttkie market shares to some standard condition of price level. T‘tie regression relationship for adjustment of 'Y' due to varia— t:5.on in 'X' 18 normally sought within the data by a suitable Eirialysis, unless a relationship based on previous experience i 5 available . It is assumed in the model that the distribution of 'Y' i-ES approximately Normal, though moderate departures from IqWCDtrmality are unimportant in the Analysis of Variance. As ‘t }1.e variable of proportional market share of a brand follows ‘t)-5L:nomial distribution, the following transf rmation has been ‘1'53 «ed to approximate the distribution to normality. Y ; 0(m) Arc Sin (Mm) Where m = Proportional market share of brand y : Transformed value of m : liliese transformations do not result in any substantial loss :3 . . - 5i? effic1ency for the estimates. T h e model of our study is: Yijk : “*a1+83+yk+6ljfe}k+elkfsxljkfnljk Vqlfiere Y. : Market share at Brand '1', in store '3', in ijk Period 'k' X_..k . Average pr-ce of Brand '1', .n store '3', J. . . J in period 'k' b . constant 8 4 Regression coeffiCIent of price on market share (assumed to be the same for all brands and Stores) 01 = Brand effect 83 = Store effect Yk Period effect 1] - Brand x Store interaction effect 63k ; Store x Periodinteraction effect eik : Brand x Period interaction effect le : Random effect (distributed normally with mean zero and variance 0‘) T‘Flee components of the variance are estimated by uSing the nléa‘thod of least squares, and Table 4.1 presents the corres- l 1 ' ‘ p Qnding algebraic equations. The subscripts i , 3', k IT‘LJ In from 1 to r, l to s, and l to t respectively in the corres- F>::> Inding summations. In our investigation, the data has teer C . : n - . ls éBSblfled aFCOPdng to 4 brands, 10 stores, and 36 (m:ntnlv) t:~1~ the periods. Thus: r z 4' s = 10; and t r 36. 9 T‘ ' . . 171 GB sums of squares and the sums of produzts are computed a 3 follows: T. t M130 2 E: yijk Nijo ‘ I{.lek k l k 1 q s M .: Z ‘ - iok y13K N;ok ' xljk jil 3 A r‘ - Mojk E: yljk NOJK X13k 1:1 1-1 213 ook ooo rst N —CF XY lOO .XX 'YY .xy .XX 53 [\C.yy S: £X(3.xy $3 1%.C.xx ~yy .xy .xx ~YY .xy .XX ails—1 (Db—J 214 B.yy C.yy-SAB.yy-SAC.yy BC.yy B.xy C.xy-SAB.xy-SAC.xy-SBC.xy “B.xx c.xx'SAB.xx'SAc.xx'SBc.xx Yijk: Yijk: 215 TABLE 4.1 SUMS OF PRODUCTS AND SUMS OF SQUARES No. of Brands 4(r) No. of Stores 10(5) No- of Periods 36(t) Market Share of Brand i in Store J and Period k- Average Price of Brand i in Store J and Period k. ..-,. -O—F—i——uv— — Source of- Dégrees Sums of.SJms of—TSUmS_Ofm Regression Variation . of Squares Products Squares Coefficient ___-.....- LIFE-929 sat-4m--.) $1311.19; 2 ) 1 1 ‘ 1 . l 0 Brands f 3 A 1 SA-xy/SA~xx : f 1 Stores 9 5 1 'SB°Xy/SB~XX Between (t—l) SC-yy SC~xy :SC XX Abook= Periods 35 ' 1 ASC-xy/sc xx Brand X (P-1)X ISABny ’ SAB-Xy :SAB‘XX Abijo= Store (s-l) f ESAB~xy/SAB-xx Inter- 27 . action Brand X (F-1)X SAC yy SAC xy ,SAC XX gblOk= Period (t—l) 1SAC-Xy/SAC xx Inter— 105 ‘ A action Store X (S-l)X SEC yy SBszy SEC-XX bojkz Period (t-l) - SEC—xy/SBC-XX Inter- 315 EPPAO” . _ -____-- (r-lIx -. Error (s-l)x 83- S - S - B=S~, ./Sw,. (t-l) L yy E xy E XX E X3 E xx __.-_.-____-._..9.£5 - -..-.. ..-..__-_-__._-.____-___-_.- 1839 ST-xy/ST-xx ‘ ---~ _ The covariance correction for the regression of brand ssales on price level increased the precision of the findings Ipeecause the results are then based on a standard condition c>:E price level. A brief description of the mathematical czcomputations follow. The computational procedure for obtaining sums of goiooducts and sums of squares (Refer to Table 4.1) is given j_r1 conventional text books (Bennett 6 Franklin, 1954; Lucas, .1 957). In computing the sums of products, correSponding \Iéalues of prices and market shares are multiplied instead of sscluared at each stage of the computation. In Table 4.2 the effect of the regression of price (X) c3‘r1 brand sales (Y) is removed from the sums of squares for €3:r‘ror, and sums of squares for store x brand interaction + £3 1?:ror, by using the corresponding sums of squares for x and 57 «and sums of products (xy) and the formula: 8 — (s )25 yy Ky XX One degree of freedom associated with the regreSSion is :S‘JJEDtracted from degrees of freedom for error, and interaction + . . . - €Elrror. The sums of squares due to the interaction effect is; (7 obtained by subtracting the adjusted sum of squares f r etbr‘cor from the adjusted sum of squares for interaction + error. ‘D . . . . e"Egr‘ees of freedom for interaction are obtained in a Similar meiInner by subtraction. Eiitggmetrics (Cochran, 1957). The F-tesr was used taking the Detailed descriptions are given in r‘El‘tio of mean squares (the sums of squares diVided by the 2l7 mzng mmm< 13m _ popmm _wawz< a wwm¢ :am bosom x.m< m i %% Ohfi @mnw COHuom aamwwum ssmzaum_ x a: H: unmch mm mx.mmm mx.mmm H conmopwmm znmzm mm\>>mm mm.m ofiummum mmumzom mommzom no _COHpmem> 2mm: no mean mmopwmo _ mo mopsom coma lmo meow mmmuwom_ho oopsom ZOHBoe< uxxe usme name x ncmpm m Anzmw ax m Amqm- WWII» an an» . mm: xx.m . Hipvx m< xAHnmv as.mm “alumna xx mm sx mm ss.mm Aaumox gonna as xA up us» x.mm up mza H V n ma ha c um n mm . I coauom A» I mxm >>m Eoomopm ofipmmlm coo: mo KCam ucofioammmoo mommsom muozoopm mmnmzdm mo coHpmHnm> oopmzno< mmopwoo ompmSwo< coammmawmm mo mszm. mo mazm mo mezm mmpwoo no oopsom mozoo mo mHqu¢z< N.: mqmdB 2l8 corresponding degrees of freedom) of interaction and error to test the Significance of store-brand interaction at both 5% and 1% levels. In Table 4.3, the sums of squares corresponding to error and interaction are adjusted for regression of price in a similar manner as described above, this time by using the corresponding class regression coefficients obtained in the last column of Table u.l. The ratio of mean squares for inter- action and error is compared with percentage values of the F-distribution to test the null hypotheSis that the observed interaction between brand and store can be explained by the class effect on regression coefficients. The estimates of regression coefficients in Table u.l are obtained by dividing the respective sums of squares of price of brand (x), the independent variable, into the sums of products of prices and market Shares. In Table u.u, the regreSSion sums of squares with one degree of freedom, the part of total variation in market Shares explained by the price levels (regression) is com- puted by the formula BBxy’ where B iS the regression coeffi- cient and Ex 18 the error sum of products. The ratio of mean squares corresponding to regreSSion and adjusted error, is compared with percentage points of the F-diStribation to test the null hypotheSis that price has no Significant effect on the market Share of a brand. 219 SELECTED BIBLIOGRAPHY Books Allen, Bennett C. and Norman L. Franklin, Statistical Analysis in Chemistry and the Chemical Industry. New York: Wiley Publications. 1959. Boyd, W. H., Jr. and Ralph L. Westfall, Marketing Research (Text and Cases), Richard D. Irwin, Inc., l9bu. Day, Ralph L. Marketing Models. International Text Book Company, 1964. Roy, Jogabratha, I. Chakravorti and R. Laha, Handbook f:r Practical Work in Statistics. Calcutta: Indian Statistical Institute, 1959. 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