AN ECQNOMIC EVALUATION $1: IHREE $055.. NIYROGEN TESTS Thesis §or Ha: Degree of: M. S. MICHIGAN STATE UNIVERSETY Gordon R. Anderson 1958 THESQB L I B R A R Y Michigan State University O F A N E C O N O M I C E V A L U A T I O N T H R E E S O I L N I T R O G E N T E S T S by Gordon R. Anderson An Abstract Submitted to the College of Agriculture of Michigan State University of Agriculture and Applied Science in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Agricultural Economics 1958 This the standpoi: The bell wheat p research ven partnent and sits. 'I'Zce 6 1/62 acre 8: 501‘ 1955 an three diffe *9 Organic E EBWt. A U beliefs, ‘I) :91 {id ‘ in u “e I‘l.‘ ‘Ifno Gordon R. Anderson ABSTRACT This study evaluates three soil nitrogen tests from the standpoint of usefulness to farm managers. The evaluation is based on data taken from the Camp- bell wheat plots nhioh are a part of a Joint agro-economic research venture sponsored by the Agricultural Economics De- partment and the Soils Department of Michigan State Univer- sity. The data included 1956 wheat yields from 130 plots of 1/62 acre size in a homogeneous field, N application rates for 1955 and 1956, and soil samples from each plot tested by three different methods; i.e., Iowa N test, Truog N test, and the Organic Matter test. In order to establish the usefulness of N tests, it was necessary to eXplicate some relevant concepts of manage- ment. A problem occurs whenever there is a conflict between beliefs, between values, or between a belief and a value. A belief is defined as a concept of reality (what is), and a value is defined as a notion of the ideal (what ought to be). A farmer's main problem is that of securing satisfac— tion. A sub—problem is that of growing a particular crop for maximum profit. Within this sub-problem lie questions con- cerning the nitrogen level of the soil (belief—belief problem) and the nature of the production function from which Optimum profit points can be determined (belief-value problem). Gordon R. Anderson An examination of nitrogen fertilization information from technological researchers disclosed the fact that some doubt exists as to the true value of results obtained from any one of the three nitrogen soil tests; i.e., their value in resolving a belief-belief conflict. It was not clear Just how these results are or may be used objectively to determine fertilizer requirements of crOps; i.e., their value in re- solving a belief-value conflict. An attempt was then made to develOp a chain of ob- Jective relationships between test results and the determina- tion of Optimum fertilizer application rates. The first step was a calculation of correlations be— tween pairs of test results to determine an answer to the question, "Do these tests tell the same story?“ The correla— tion coefficients were quite low, so low in fact as to meas— ure degrees of association of no practical importance. Next, correlations were calculated between each test and previous known N applications, which ranged from zero#/ acre to 2hO#/acre, and which were consummated within the pre- vious 6 months. Once again the correlation coefficients were very low. So far, it was determined that the tests did not tell the same story, and that no one was superior to any other, based on the assumption that a test should distinguish a recently applied range of N. These results would tend to complicate the belief-belief conflict rather than resolve it. Then an attempt was made to determine the predictive value of sec lished form tion of the and N applic at determine was 3.83 bu, to be consis With wheat a 83# 01' rm. w It w Tate 0f Subs; residual nit 3‘35. for the 0” could b The My 01' ‘1, A 251. Manet curv 901mg I‘eve‘ ~12‘Vee were Jest regult 3r. Gordon R. Anderson value of each test by fitting its result into a well estab- lished form of prediction equation. A basic prediction equa— tion of the form Y = a 4 blNa + sza2 was fitted to the yield and N application data and it was found that the coefficient of determination was .3844 and the standard error of estimate was 3.83 bu. Optimum profit points were calculated and found to be consistent with reason and experience. For example, with wheat at $2.00/bu. and anhydrous ammonia at $.lO/lb., 83# of NH3 was determined to be the Optimum application rate. It was then assumed that there is a constant marginal rate of substitution (A) between applied nitrogen (Na) and residual nitrogen (Nr) as determined by test. .A was estima- ted for the Iowa and Truog tests, but no sensible estimate of A could be made for the O.M. test. The Iowa and Truog tests were then introduced into the same type of prediction equation, i.e. Y = a 4 b1(Na 4.fo) + b2(Na +.\Nr)2, to see if an improved prediction would result. The coefficients of determination were not materially improved, and the calculated Optimum ap- plication rates were such that a further check on the effi— cacy of the two tests was indicated. A graphic comparison of iso-product curves and iso- product curves constructed from actual equal production points revealed no apparent similarities. Further, when curves were constructed from production points with the O.M. test results plotted against application rates, they too proved to be erratic, and showed no reasonable relationships Gordon R. Anderson between N; and Nr. An inspection Of the graphs showed that no linear relationship between Na and Nr would fit the data very well. A variable rate of substitution arrived at by other computational procedures would not improve the fit without resulting in iso-product lines which cross each other in ways inconsistent with the law of diminishing returns. At this point no other ways Of incorporating a ni- trogen test result into a prediction equation were apparent. Techniques assuming non-continuous functions would Offer little chance of making N soil tests more useful, because solving the problem of determining the marginal rate of sub- stitution between NP and N3 is a necessary preliminary to fitting either continuous or discontinuous functions which include Nf and Na as the independent variables. In conclusion, it was found that the evaluation of the three soil N tests, with reapect to their usefulness to farm managers, produced evidence to support the contention that the problem concerning the nature of the N fertility of a specific soil sample is complicated rather than resolved by present tests. The problem concerning optimum N fertil- izer application rates was also not resolved by test results, as no objective method of introducing the test results into a prediction equation giving sensible results could be dis- covered. Approvedfl M Major Pr fessor O A N E C O N O M I C E V A L U A T I O N til 51 :1 ti] E S O I L N I T R O G E N T E S T S by Gordon R. Anderson A Thesis Submitted to the College of Agriculture of Michigan State University of Agriculture and Applied Science in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department Of Agricultural Economics 1958 Approved by 74%“ b gUgi “El ACKNOWLEDGEMENTS The author wishes to express his sincere apprecia- tion to Professor Glenn L. Johnson for his valuable direc- tion and encouragement throughout the develOpment of this thesis. Professor A. R. Wolcott, N. Burt Sundquist, and Clark Edwards gave generously of their time in helping to solve sub«problems and in reading and criticizing the thesis. Mrs. Iantha Perfect and other members of the computing staff carried out a major portion of the computations. Hjordis Anderson, the author's wife, provided the typing and much encouragement. The author wishes to take this Opportunity to thank them all. The author is also grateful to Professor L. L. Boger who has provided the opportunity to carry on the studies connected with this thesis. 11 TABLE OF A CKETOT‘IIJEIJGEE‘IE\:T o o o o o o 0 LIST LIST OF LIST OF Chapter I. II. III. IV. v. OF TA BL its . O O O O O C O €7qu PH S o o o O o o o 0 hr! CT IRS? 13‘] THE PROBLEM IN P PRODUCTION PROCESS . Summary . . . . . NITROGEN FERTILIZATION TECHNOLOGICAL ESEARCH The O.N. Test . . The Truog Test . . The Iowa Tee . . Use of Test Results Janagement Process Summary . . . . . INFOEEIATION AND THE ISA CONTENTS 0 O O O O O O O O O O O O O O O O O I O O O O O O I O O O O O O O O O O O O O O O O O . IV? -'--I o o o o o o o o 0 NA GER IAL o o o o o o a o o o o o o o o o o a o o o o INFORHATION FR M ‘ in Accelerating the AN EVALUATION OF THE TESTS . . . . . . . . . Erperimental Data )- A. Plan of Procedure The Findings . . . SUMHARE AND CONCLUSIONS BIBLIOGRAPHY . . . . . . . . . 111 Page ii iv 10 ll 12 11+ 15 17 18 18 19 21 36 39 same 1. 2. LIST OF TABLES Correlation Between Pairs of Tests . . . . . . . Correlation Between Tests and Prior N Applica- tion 0 O O O O C O O O I O O O O O O O O O O O 0 Data Used for Estimates of Lambda . . . . . Estimates of Air. ‘1 _ Nigger) . . . . . . . . . Optimum Application Rates of N Fertilizer Based on Y = f(I\:a) o o o o o o o o o o o O o o o o o 0 Optimum Application Rates of N Fertilizer Based on Y ; f(Na,Nr) Incorporating Iowa Test . . . . Optimum Application Rates of N Fertilizer Based on Y = f(Na,Nr) Incorporating Truog Test . . . . iv 33 LIST OF GRAPES Graph I. Relationship Between Wheat Yields and Nitrc~ gen Application Rates . . . . . . . . . . . . II. A Comparison Of Iso-Yield Curves Estimated from Iowa Test, and Iso-Yield Curves Esti- mated from Equal Production Points . . . . . III. A Comparison of ISO-Yield Curves Estimated from Truog Test, and Tao-Yield Curves Esti- mated from Equal Production Points . . . . . IV. Iso-Yield Curves Estimated from qual Produc- T?! tion Points Located by Plotting O.M. Test Re— sults Against Na Rates . . . . . . . . . . . ‘1' LIST OF FIGURES Figure Page 1 Amount of Information to Get in the Learn— ins Situation 0 o o o o o o o o o O o O o O 9 vi ............... CHAPTER I THE PROBLEM IN PERSP CTIVE Fl Farmers' replies to the question, “Why do you farm?“ encompass a gamut of reasons from enjoyment of fresh air, through love of relative independence, to the necessity for earning a living. Pointed questioning, however, usually elicits admissions that profit is a necessary adjunct to all such pertinent belief-value sub-structures. Publicly employed professional agriculturists engaged in technological research frequently justify such eXpendi- tures of public money on th general principle that research results will contribute either directly or indirectly, sooner or later, to the assurance of an efficiently produced and adequate national food and fiber supply. The farmers' interest in profit, the researchers' interest in technological discoveries, and the public's in- terest in an adequate and efficiently produced food and fiber supply, when considered simultaneously within the framework of the “democratic process," form the component parts of an enormously complex dynamic model of social and/or individual choice and action. Agricultural production economists have accepted the responsibility of analyzing this model and the multitudinous 1 2 sub—models within it for the purpose of educing or extract- ing information which can promote the interests of the appo- site groups and/or individuals. A high value has come to be placed upon Objectivity in such analyses. The following chapters describe an attempt to fit objectively a fragment of technological research results into a simple economic model, such that the farmers' inter- est in profit, and the public's interest in an adequate and reasonably priced food supply may be directly or indirectly forwarded.l The research results of this thesis concern soil, the importance of which, as a factor in farm production, is obvious. Soils and agronomy scientists have, to date, learned much about its nature. Many studies have provided us with information concerning the relationships between soil elements and plant growth. One outcome of these studies has been the deveIOpment of specific tests for the quantitative determination of various soil elements important to plant nutrition. Three such tests are the Iowa, Truog, and O.M. tests for soil nitrogen. This thesis is specifically concerned with an evalu- ation of these three soil nitrogen tests from the standpoint of farm management. Such an evaluation may be in the form of an eXposition of a simple model of sequential relationships, 1The more complex problem of measuring change in general welfare is not under consideration herein. between the soil nitrogen test results and the farmers' profit interest. I If, for instance, a farmer wants to make a decision concerning the most profitable amount of N fertilizer to ap- ply on a wheat field, and intends to use a soil N test re- sult as a factor in that decision, then he should eXpect a relationship between the test result and the high profit application rate. The succeeding chapters will consider in order: (1) the farmers' use of production information for profit maxi- mization within the managerial process; (2) the soil re- searchers' potential contribution of production information to farm managers with particular respect to soil nitrogen, its tests and fortification; (3) an evaluation of the use- fulness of the information discussed in 2. to farm managers, and (4) a summary and conclusions of the evaluation. CHAPTER II PRODUCTION INFORNATION AND THE MANAGERIAL Psccsssl The farm Operator who is engaged in the constant and continuous duty of decision making is said to be managing the farm. Decision making is the core of the managerial process and distinguishes it from all other human procedures in the conduct of the farm business. Obviously decisions, and hence management, are necessary only when problems exist. A brief excursus into the nature of problems in re— lation to farm management is in order at this point. If we accept farmers' reasons for farming as being included essen— tially within the general concept of "satisfaction seeking," we can then say that farmers are seeking full appeasement of desires, longings, needs and requirements.2 The manager's main problem can then be defined as any perplexing question, _—-—‘ 1The management theory concepts presented in this chapter are drawn from the following sources: G. L. Johnson and C. B. Haver, Decision—Naking_Principles in Farm Management, Kentucky Bulletin 593 (Lexington: Kentucky Agricultural EXperiment Station, 1953). G. L. Johnson, {anagerial Concepts for Agriculturists, Kentucky Bulletin 619 (Lexington: Kentucky Agricultural Echriment Station, 1954). 2Websterjs Dictionary of Synonyms, (Springfield, Nass.: G. and C. Merriam Co., 1951). s situation, or the like, which demands a solution in order that satisfaction be obtained. Some farm management re- search workers, realizing that such definitions are too gen— eral to be useful, delved deeper into problem—decision con- cepts, and synthesized somewhat more Specific management models.3 These, however, are still too general, but from them we can extract the following salient points: A belief is defined as a concept of reality (what is). A value is defined as a notion of the ideal (what ought to be). A problem then occurs whenever there is a conflict between beliefs, between values, or between a belief and a value. Such conflicts are ever present because change is normal, and partial ignorance is universal. Change and imperfect knowledge then eXplain the need for management, and learning and deciding are, there- fore, fundamental tasks of management. The five functions that a manager, Operating in the presence of continuous change, and only partly informed, must perform if he is to chart successfully the course of his business over a period of time, are as follows: a. observation b. analysis 0. decision making d. action taking 3Johnson and Haver, op. cit. 6. acceptance of responsibility for action taken Five broad subject-matter areas which managers must study as a basis for adjustment, can be distinguished: may price structures and changes. production methods and reSponses. prOSpective technological develOpments. the behavior and capacities of people associated with farm businesses including changes therein. the economic, political and social situations in which a farm business operates including changes therein. Five different knowledge situations in which managers find themselves are tentatively conceived: 8. Perfect knowledge - knowledge is nearly enough perfect to permit action without the protection of formal or informal insurance. Risk action - present knowledge is good enough for action, because the risks involved are as- sessable and insurable, and additional knowledge is not worth the cost of acquisition, so action is taken. .Learning — the value of what can be learned is worth more than the cost of learning it, so action is postponed. Inaction - present knowledge concerning the prob- lem is insufficient for positive action, and the cost of learning exceeds the value of what would be learned, so no action is taken. e. Forced action — the existing state of knowledge is inadequate, and if time were available more knowledge could be acquired. However, some out- side influence forces action, so time is not available. The classification of degrees of knowledge was intro- duced as being "tentatively conceived." Recent information presented by G. L. Johnsonl‘L indicates that these five degrees of knowledge, while clearly relevant, are still inadequate. Originally the classification provided the basis for six questions to be used in the Interstate Managerial Survey, and designed to determine whether farmers do, in fact, en- counter, and are able to comprehend and know when they en- counter, these situations. A high prOportion of the ques- tioned farmers were able to understand and give verified ex- amples of situations in which they had encountered these varying degrees of knowledge. However, close examination of the answers indicates that the classification is valuable mainly at the time of decision. Ex posts, it appears diffi— cult for farmers to distinguish among the various negative Idecisions. For instance, it is difficult for a farmer to tell, after a decision, whether he decided not to act because circumstances forced him not to act or because he decided on “Glenn L. Johnson, “Methodology for Studying Decision Iaking," Address to The American Farm Economic Association, Junaluska, North Carolina, August 1957. 8 a risk action basis that he was willing to refuse to act and take the consequences of being wrong. It was also difficult to distinguish, ex poste, between negative forced actions and plain inactions. While it appears that the classifica- tion is inadequate, it is also apparent that Wald's5 contri- bution prevents researchers from returning to Knight's6 risk, uncertainty and certainty classification. The five knowledge situations are used in the ex- ante sense in this thesis. We are now able to see how soil nitrogen tests fit into the managerial process. The act of sending a sample of soil to a testing laboratory for the nitrogen analysis evi- dences on the one hand the awareness of a belief-value con- flict - ("I think I ought to be getting more wheat per acre"); and on the other hand an entreaty to solve a belief- belief conflict - ("Just what is the nature of the fertility of said soil?“). The act also tells us that the farmer is performing the first task of management (observation) and is in the "learning" situation. Marginality concepts applied to the foregoing situation might appear graphically as in Fig. 1. W a— V— fi ~v — wfi-v vw w i—vv—v 5Abraham Wald, Sequential Analysis, (New York: John Wiley and Sons, Inc., 1957). Sequential analysis provided the basis for dividing imperfect knowledge situations into subjective risk situations, on one hand, and into three sub- Jective uncertainty situations, on the other hand. The dis— tinction depends on the subjective standards of accuracy elected by the analyst. 6Frank Knight, figsk,_Uncertainty and Profit, (New York: Houghton—Mifflin 00., 19211 I In!" 9 The observing farmer in the learning situation is at A, where MUJ>NI. He feels that the cost of more informa- tion will not exceed its value, so wants to move to the right; hence he sends in his soil sample to be tested. If analyses of the test results make him feel that he has arrived at point B, where MU = KC, he will then act with no further consideration (the decision is made), having subjectively moved from the "learning“ to a "risk" or "perfect knowledge" situation; and having satisfac- torily completed the observation, analysis, and decision tasks of management. Fig. 1. - Amount Of Information to Get in the Learning Situation A 5' Accuracy The MU of soil test data is a function of the man- ~ager's ability to analyze these data. The question then arises, "Is it possible for anyone to analyze said data?“ Very likely, if the professional agriculturist cannot, then the farmer does not stand a chance. The question asked in this paragraph is actually another way of presenting the purpose of the study. 10 Summary The farmer's main problem is that of securing satis- faction. A sub—problem is that of growing a particular crop for maximum profit. Within this sub-problem lie questions concerning the nitrogen level of the soil, and the nature of the production function from which optimum profit points can be determined. Three nitrogen soil tests giving three dif- ferent measurements of fertility would seem to complicate rather than to clarify part of the problem. The complica— tion occurs in the sense that incompatible test data add a belief-belief conflict to the belief—value conflict which defined the problem. If both the main and sub—problem are not subject to resolution, the usefulness of soil test data would be zero, and their marginal utility could not be equated with the marginal cost. If, on the other hand, they could be resolved, the soil test data would be useful to farm man— agers. CHAPTER III NITROGEN FERTILIZATION INFORMATION FROM ECHNOLOGICAL RESEARCH c. E. Millarl said in 1955, "With the recognition of the fact that plants obtain their mineral nutrients from th soil came the demand for methods to determine the quantities of available nutrients in soils. It is interesting to note that, although the search for such methods has been under way for over a century, it still continues. Much progress has been made, but a method which works satisfactorily under all conditions has not yet been devised. When, to the inquiry concerning the quantities of available nutrients present in a given soil, is added the query, 'how much of each nutrient should be added to give a large yield of a given crop,‘ the problem becomes more complicated. Because of the dynamic nature of the soil system and the fact that one is dealing with a living organism, the plant, which is sensitive to all environmental conditions, a method of obtaining a definite answer to the above questions may never be develOped. Never- theless, information has been obtained which is helpful in giving approximate answers to these questions." 10. E. Millar, 3011 Fertility, (New York: John Wiley & Sons, Inc., 1955), Chap. 13. ll 12 Because of the apparent orderliness of natural rela- tionships which have so far been brought to light by research, the author tends toward a more Optimistic faith in the even~ tual resolution of all pragmatic questions concerning com— mercial fertilization on farms. So long as the variables in a soil system, in a plant system, and in natural environment are not definitely proven to be infinite in number or reac- r tion, their eventual appraisal and evaluation seem theoretic— ally possible. In the case of nitrogen, one of three different soil L tests is being used at the present time by one or more of the upper midwest land-grant college soils research depart- ments in attempting to answer the above stated queries. The tests considered here included the 0.x. test, the Truog test, and the Iowa test. The O.H. Test2 In the O.M., or organic matter test, an attempt is made to measure the total carbon in the sample. The result is converted to total organic matter by the use of an arbi— trary conversion factor. Then another conversion factor, the mineralization factor, is used to estimate the nitrogen 2"Soil Organic Matter Determination,“ (Soils Testing Laboratory, Michigan State University, East Lansing), (mimeo- graph . C. M. Woodruff, “Estimating the N Delivery of Soil from the OM Determination as Reflected by Sanborn Field," Soil Science Society of America Proceedings, Vol. in (1949), 2 08-212 0 13 in the sample which, by projection to the field on an acreage basis, will be released during the growing season in a form available to a Specific crop. Difficulty in achieving consistent results is due to several causes. There are several methods of determining carbon, ranging from the dry combustion method, to the highly subjective method based on the feel of the wet soil between the fingers of the lab technician. The conversion factor is based on the average rate of disappearance of soil nitrogen in long term field experiments, or on mathematical prepor- tionality constants calculated from soil tests and crop yields, using variations of Mitscherlich's equations for growth where one nutrient is limiting. The TruogTest3 The Truog test for available nitrogen is based on the solubility of various forms of nitrogen in a permanganate so- lution. It measures NH3 nitrogen, and the more labile forms of organic nitrogen. Difficulty in achieving accurately useful results from this test lies in the facts that the less labile forms of organic nitrogen are not measured, and that microbial 'suppression of N availability in presence of carbonaceous residues is not taken into account. 3Directions No. 697-18 for the Hellige-Truog_Combin— gtion Soil Tester, Technical Information Bulletin, Hellige, Inc., 877 Stewart Avenue, Garden City, New York. in L; The Iowa Test During the past decade much hepe for accurately de— termining a useful measure of the available nitrogen in soils has been pinned on incubation techniques, of which the Iowa test is representative. Soil scientists are in agreement on the fact that the rate of mineralization of soil nitrogen is more important to crOp growth than the amount of mineralized nitrogen in the soil at any given moment. Therefore, the technique of measuring said rate by artificial incubation has become popular. The soil sample with its indigenous organ- isms is incubated artificially for a specified time, usually two weeks, and the mineral nitrogen is measured. A conver- sion factor is applied, and an estimate is made of the miner~ alization rate of nitrogen under field conditions. The difficulties with the incubation test can best be summed up in the words of soil scientists Harmson and Van Schreven5 who say, "It should not be forgotten that the incu- bated soil samples are kept under entirely artificial condi— tions. The results of such experiments are in no way compar- able with the mineralization process under field conditions. So it must be considered worthless to try to imitate natural . “George Stanford and John Hanway, "Predicting Nitro— gen Fertilizer Needs of Iowa Soils: II. A Simplified Tech- nique for Determining Relative Nitrate Production in Soils,“ Soil Science Society of America Proceedings, Vol. 19, No. 1, (January 19557, 7D- 7. 5G. W Harmson and D. A. vanSchreven, "Mineraliza— NO tion of Organic Nitrogen in Soil," Advances in Agronomy, ed. A. G} Norman, Vol. VII. 15 conditions in incubation experiments, and we will have to accept mineralization eXperiments in the laboratory as pro- vidingus with an artificial magnitude which has great value but which must be interpreted with care. --- Reliable results can be eXpected only when the incubation technique is re~ stricted to one soil type, one climatic zone, and one farming system, and when all samples are collected within one season, preferably during early spring. -~— Xperimental evidence showing correlation between incubation results and crop pro- duction has varied from the one percent level of reliability to wholly negative results." Use of Test Results in Accelerating the Management Process The soil researcher's incorporation of test results into fertilizer recommendations to the farmer is an example of the socialization of the analysis task of management. The analysis, as performed by the professional, is based primar- ily upon the results from field experiments.6 Soil test re- sults, and agronomic knowledge, experience and judgment, are used in applying and interpreting the experimental results. In Michigan there are 300 recognized types of soil. The shape of the land surface and the height of the water ‘table cause additional soil differences. Experiments have been conducted on many soils, but not on all th~ recognized 6For example, see Fertilizer Recommendations for Michigan Crops, Extension Bulletin 159, (East Lansing, Michigan State College), pp. 7. 16 types. In addition there are areas not characteristic of any recognized type. Thus it is sometimes necessary to re- sort to experience and judgment in performing the analysis task. Other pertinent variables such as cultural practices, past and present rotations and soil tilth increase the diffi- culty of analysis because their values are often unknown. The place of soil test results in making analyses is seen in the following quotes from Michigan Extension Bulletin 159:7 “The use of soil testing results makes less essential as knowledge of how the soil has previously been managed. This does not hold true so much with reSpect to nitrogen as it does for phosphoric acid and potash." "The immediate ni- trogen needs of a crOp growing on a mineral soil depends more on the system of management than on the soil type or test at 'the time of planting." "In fact, the crops which immediately follow alfalfa or clover may obtain sufficient nitrogen from the decomposing plant residues." Michigan recommendations :for N fertilizer on wheat8 do not take into account soil ni- 'trogen test results. The completed analysis is presented to the farmer in ‘the form of recommendations for specific quantities of N fertilizer to use, allowing him to move from the observation task directly to the decision task. 17 Summary It is clear that some doubt exists as to the true value of results obtained from any one of the three nitro- gen soil tests. It is not clear Just how these results are or may be used objectively to determine fertilizer require- ments of crOps. Considering the high value placed upon ob- jectivity in modern research, analyses performed mainly by use of eXperience and Judgment are not recognized as being highly desirable. CHAPTER IV AN EVALUATION OF THE TESTS In Chapters I and II an argument is deveIOped for the presentation to the farmer of production information in a form which both accommodates his profit interest, and facilitates his managerial tasks. Chapter III includes the background of and the form in which information is pre- sented to him by soil research personnel. This chapter describes an attempt to develOp a chain of objective relationships between soil N test results and the determination of Optimum N fertilizer application rates. The failure of the attempt provides some evidence to support the conclusion that soil nitrogen tests are of little Opera- tional value to farm managers, at least in the situation under consideration. Experimental Data The evaluation will be based on the results of man- ipulating data taken from the Campbell wheat plots which are part of a joint agro-economie research venture Sponsored by the Agricultural Economics Department and the Soils Depart— ment of Michigan State University. Pertinent information concerning these plots is listed as follows: 18 l9 1. Soil type is Kalamazoo silt loam. 2. Number of wheat plots of 1/62.5 acre size = 130. 3. The field on which plots are located is level, and was evenly fertile according to soil tests in 1954. 4. 1955 N application ranged from O to 240 lbs/acre on oats. I 5. 1956 N application ranged from O to 2M0 lbs/acre on wheat. 6. A soil sample (to plow depth) was taken from each plot in the fall of 1955, and tested for N content by each of the three methods. 7. 1956 wheat yields were calculated on a per-acre basis. Plan of Procedure The first step will be a calculation of correlations between results of the N tests to determine the answer to the first obvious question, "Do these tests tell the same i story?" In the licnt of managerial theory, the question 0 could be phrased, “Do these tests collectively support an identical concept of the nature of reality, or do they in- troduce a conflict between beliefs?" If the correlations are high and positive, any con— -venient one may be used in the search for objective relation— ships. If, however, the correlations are low and/or nega— tive, it will be necessary to tarry over the problem of effi- caciousness long enough to procure evidence from correlations between individual tests and previously applied nitrogen or yields. Should this evidence indicate the superiority of 20 one test, the others can be discarded and work concentrated on the superior test; but should the evidence be inconclu— sive,.the three must be considered further. At this point the assumptions would have to be made that soil tests measure residual soil nitrogen (Nr); that field test production functions are based on, and farmers p. . n“. are interested in, applied nitrogen (Na), and that the two , substitute for each other in some definite but as yet un- known preportion, e.g. N3 = Na 4.ANr. Therefore, the next step would be to estimate the marginal rate of substitutionl ;; of Nr for Na (A). This estimate would be necessary in order to introduce test results into well established production functions based on Na as the independent variable. If such introductions improve the existing yield pre- diction equations, and if resulting economic derivatives are compatible with reason and experience, then a farm manager would have a basis for using one or more of the soil N tests, at least within the limits of the emperimental data. By sim— ilar reasoning, should none of the test introductions improve presently workable production functions based n Na: then there would be evidence to support a similarly limited con- clusion that soil N tests have little value to farm managers, at least within the limits of the situation under investigation. 1For the sake of simplicity, and because of a lack of reasons for anything more complex, it will be assumed that there is a linear rate of suostitution between Na and Nr. However, by the same reasoning, there is a lack of reasons for anything less complex than a curvilinear rate of substi- tution. Further analysis will determine the necessity for resolving the problem. 21 The Findings The simple correlation coefficients among the three tests were quite low (see Table 1). Even though the correla— tions are significantly different from zero (statistically), they measure a degree of association between the tests which is not of practical importance. TABLE 1 CORRELATION BETWEEN TE”TS Level of r Sr Significance .M. and Truog .1850 .087 .03 O.M. and Iowa .4296 .080 .01 Truog and Iowa .1389 .087 .03 As these tests do not tell the same story, an attempt should be made to determine relative superiorities. This can be done by correlating each one with previous N applications. This appears to be a rational move in that 1955 N applica- tions ranged from zero to 240 lbs/acre, and were consummated within the previous 6 months. 1955 cat yields did not vary enough to even out the N: range. Oat yields varied 20 bushels between plots. To even out the range, 12 lbs/acre Na would 2 be required for each bushel increase. Sundquist's analysis indicated that the Na requirement per bushel was more nearly 2W. Burt Sundquist, "An Economic Analysis of Some Con- trolled Fertilizer Input-Output EXperiments in Michigan" (un— published Ph.D. thesis, Michigan State University, 1957). 22 one pound. There appears to be no other documentary evidence available to refute that estimate. If it is argued that leaching would level out such an application rate differen- tial in such a short period of time, it can also be argued that annual N soil tests for practical purposes are futile.3 Soil samples are taken as sections of the soil profile to plow depth. Most of the nitrogen used by the plant is gath- ered from this stratum. If leaching moves so much nitrogen to a deeper level that soil sample tests cannot distinguish a 2&0 lb. range of N applications made within the previous 'V six months, then the farm decision maker must be justified in deciding to eliminate the costs of sampling and testing when the results would contribute nothing which was not al- ready known. Results of said correlations produce r values which are very low, and significance levels which are very low for two of the three correlations (see Table 2 on following page). The Iowa test, although statistically significantly correlated with previous Na, has a low correlation value. In attempting to determine the predictive value of the three N tests, one may first set up a production function of the type V - f(Ng), and then attempt to improve the pre- diction of Y by incorporating N in the function as 3Note: A. R. Welcott of the Michigan State Univer— sity Soils Department, points out that since there were no significant effects of previous fertilizer treatment on the soil test results, sufficient time has not elapsed in this experiment for the experimental fertilizer treatments to im- pose an adequate range of variability in the soil. TABLE 2 CORRELATIONS BETVEEN TESTS AND PRIOR N APPLICATIONS Level of r Sr Significance 0.M. Test .0638 .088 .25 Truog Test .0133 .088 .25 . Iowa Test .lh84 .087 .05 r; '3 = f(Né,Nr). The Nr, of course, will be that residual N which is determined by test. The problem here is to incor— i porate Nr in a meaningf‘ull‘L way. As it is assumed that plant use of N is divided between Na and Nr, some marginal rate of substitution must be estimated. The estimate (,4) will be based on the following system. First it is assumed that the linderlying relationship between yield and total nitrogen (Nt) can be satisfactorily approximated by a quadratic func- tion such as: (l) :«r = .(O 4 Ath 4 421th 4 u or (2) y a 40 4 4131a 4 .(lmr 4 .(gNaZ 4 .(2 A2211? 242Awanr. 'which.may be written: (3) Y a. ,40 4 #1Na 4 flgNr 4 #3Na2 4 #4er 4 ,IENaNr Comparing equations (3) and (2), it is seen that the coeffic- ients in (3) are subject to the three restrictions: #2 _ //’LL It; A #1 " 2’3 " 2/3 ' “Meaningful is to be understood as testable. 24 Equation (3) can then be fitted by ordinary least- squares using 18 observations of plot yields with Na ranging from zero lbs/acre to 2&0 lbs acre and with P205 constant at zero lbs/acre.5 K20 was not considered as Sundquist's N,P205,K20 equations based on the same data produced coeffi- cients for K20 which were not significant. Actual Na rates and yields are listed in Table 3. TABLE 3 DATA USED FOR ESTIMATES OF LAMBDA (A) ww ~v~—— — T—v—v 1... w Yield ( Na Rate Nr(Te§FS) 2 iii: Iowa Truog 0.M. lbs/acre lbs/acre % 32.3 0 70 125 2.12 28.5 0 61 200 1.75 25.2 o 48 100 1.23 26.3 g o #3 100 1.23 28.2 0 47 75 1 1.23 26.8 0 48 12 1.52 22.5 o #6 1 75 1.23 30.5 0 58 t 300 1.52 28.1 0 68 225 1.61 28.6 o 51 75 1.34 31.8 o 67 225 1.52 30.b 80 49 75 1.34 32.0 0 56 75 1.42 32.2 20 46 75 .98 28.5 80 54 75 1.23 39.1 80 so 100 1.06 34.1 220 5a 100 ' l.u2 36.2 240 71 300 1.15 Obvious data limitations appear in Table 3. There are not enough observations, and too great a concentration 5The coefficient for P205 was significant, so P20g- was held constant at zero lbs/acre. Only 18 of the 130 o servations fitted that restriction. (Sundquist, op. cit.) of observations at the zero level of the Na rate to expect highly significant estimates of the /’ coefficients to ensue. Actually, most of the /5 coefficients fell between the .25 and the .10 levels of significance. The lack of significance of these estimates is not encouraging with reapect to answer— ing the question, "Which of the tests has the best predictive value?" However, one is Justified in continuing the analysis, because an answer, either negative or positive, to the related question, "Do any of these tests contribute objectively to managerial decisions?" is highly desirable. It is worth know- ing whether further analysis provides more definite conclu- alone. The alternative of designing and conducting an eXper- iment to test these relationships would take too much time and eXpense, and is beyond the intent of this evaluation. Table h shows the calculations of ,A for each of the three tests. TABLE 4 Restriction Iowa Test Truog Test 0.M. Test 12. 1‘ = 4.05 A = .52 1‘: -133.27 ”1 /£IZ‘L = 2.78 r: .57 =F§l,211.75 /’3 13.5. -.-.- .58 .-_- -.o35 = 227.38 2,63 _ A = 2.147 A = .352 A = ? 26 At this point the 0.M. test can be ruled out of fur- ther consideration for the following reasons: 1. It is not significantly correlated (.25 level of significance) with previous N applications (ranging from 0 to 2&0 lbs/acre). 2. Nr as determined by the 0.M. test cannot be incor- porated into a prediction equation when..A is esti- f? mated as above, because .A cannot be determined. Lambda = 2.47 will be used in incorporating the Iowa test in a prediction equation. Lambda = . 52 will be used in i incorporating the Truog test in a prediction equation. The basic production function will be Y a f(Na) where Na = Nt for the following reasons: (1) such functions from several upper—midwest soils research departments have proven useful over a period of years, and (2) this function based on field trials is basic to most nitrogen fertilizer recom— mendations. A polynomial will be used to eXpress the func— tion for the following reasons: (1) it should be compatible with the law of diminishing returns within the limits of the data, (2) it is fairly simple to work with, eSpecially in computing derivatives, (3) Sundquist's6 results on the same data with polynomials and emponentials indicate the possi- bility of acceptable results, and (A) data plotted on Graph I suggest its feasibility. 6Ibid. 2? mama ”no“: .coaascasm macaw passe Hacnasso mszmn + «zap + a u w .mmaem 20Hs¢0Hgama zmeomsaz nze aaaun seams zanasmm mammzoaaaasm 28 Results of fitting a polynomial of the form Y 2 a 4 blNa 4 bZNaZ 4 u to the eXperimental data are as follows: Y — 30.09 4 .0999 N8 -.0003 Na2 2 ..3auu ml SUI II : 3.83 Sundquist obtained the following coefficients in an NPK polynomial? of the form Y z a 4 bNa 4 cwa2 fitted to more data from the same experiment: .0859 Na 4.000w N82 Optimum rates of N fertilizer application were cal— culated from the above equation as follows: Y = a 4 blNa 4 nga2 ‘- hPPna(y) = bl + 2b2Na Optimum point z b1 4 2b2Na = £1 Plugging in the values for b1, b2, the price of N, and the price of Y, results as tabulated in Table 5 are obtained. These results are quite compatible with recommenda- tions based on soils research and actual farm use. 7First and second degree terms for individual nutri- ents, first degree cross-product terms, all nutrients taken two at a time. TABLE 5 OPTIMUM APPLICATION RATES OF N FERTILIZERS (IN LBS/ACRE) BASED ON Y = f(Na) 29 vj—T v wheat NH3 NH4N03 (NHu)ZSOQI' Price @.10/1b. @.lO/lb. 8.13/lb. 1.90 79 7O 52 2.00 83 75 58 2.10 87 79 63 When the Iowa test is incorporated into the same type of equation, the results for fitt Y = a 4 bth 4 bZNtZ where Nt : Na 4 A NP and A = 2.b7 are Y = l6.64 4 .1331 Nt a2 : .3920 s a 3.81 Optimum application rates rived from the above equation are TABLE 6 OPTIMUM AP BASED ON'Y P ing 4 u —OCOOZ Nt of N fertilizer (NH3) de- tabulated in Table 6. LICATION RATES OF N FERTILIZER f(NaNr) INCORPORATING IOWA TEST Test Result Low 35# Medium 60# High 80# 121 60 10 Optimum N application Rate Wheat 2.00/bu. mg Joht. 30 The incorporation of the Iowa test into the predic- tion equation produces a range of optimum N application rates adjusted for NP (by test) which, at first glance, has intui— tive appeal. However, when it is remembered that the correla- tion between the Iowa test results and previous N applica~ tions is very low, and the coefficient of determination and the standard error of estimate of the original equation are ET not materially improved by incorporation of the test, a fur- _ A ther check on the efficacy of the prediction equation includ- ing the Iowa test is appropriate. The form of the function Lg" is not suspect if the assumption of substitutability of Nr for Na is valid, but the measure of that substitutability based on soil N test results is suspect. One check of the validity of the marginal rate of substitution of Nr for Na can be accomplished by setting up a graph of actual yield levels plotted against expected yield levels based on iso—product curves drawn between Nr and Na (see Graph II). An examination of this graph reveals that there are no apparent similarities between estimated iso-product curves and iso-product points. The range of 0p— timum application rates of N fertilizer, based on the test result differential, predicts an Optimum yield of 35.6 bushels. The 35.6 bu. iso-yield curve does not correSpond in any way to a similar iso-yield curve constructed from actual production points. Further, it would appear that al- most any other estimate of‘A would be no "better" or "worse“ than the one used. 31 Lam VIQN o\J\ Pt -- -- 1Q TO. U 4Q N‘ 3‘ bn. 50 N0 3% NN 3V NN )<«-- I 433.2%; .(oi obnotK mama .scaz .ccssssass macaw passe aacnasso .mazHom 20Haonaomm games some assaaHamm mmsmpo nquwuomH nze .Bmme «aOH 20mm nmaazHama nm>mno nquwuonH so zomHmamzoo « a n I: “(do no O. Q. L , «q: 3‘ VN i .5 .6 nan: -_-,.‘ 32 Conclusions regarding Iowa test; 1. It is significantly (statistically) correlated with pre— vious N applications, but the correlation is so low (r : .lb) as to be of little practical importance. 2. When incorporated into a prediction equation, the fig and g are not significantly improved over those obtained in h the basic equation where Y = f(Na). l’i Although Optimum application rates of N fertilizer calculated from the original prediction equation are con~ r“ sistent with reason and emperience, when Nr is incorporated L; into the equation, the optimum application rates fall on an iso-yield curve which in no way corresponds to curves con~ structed from the original data. Truog_Test When the Truog test is incorporated into the equation, the results for fitting Y : a 4 bth 4 bZNtZ where Nt = Na 4 A NI. and ,A = .352 are Y a 27.25 i .0999 Nt —.0002 Ntz 32 = .3521 g = b.b8 Optimum application rates of N fertilizer (NH3) de- rived from the above equation are tabulated in Table 7 on the following page. A chart of actual yield levels plotted against ex- Dected yield levels based on iso-product lines between Na TABLE 7 OPTIMUM APPLICATION RATES OF N FERTILIZE BASED ON Y 3 f(NaNr) INCORPORATING TRUOG TEST . Optimum N Application Rate Test Result Wheat 2.00/bu. NH3 .lO/lb. Low 75# 181 Medium 150# 155 High 300# 102 and NI. (Truog) again indicates no apparent significant simi— larities (see Graph III). The conclusions are the same as for the Iowa test. O.M. Test There is no estimate for.A in the case of the O.M. test, but test results can be plotted against application rates with reapect to yield levels (see Graph IV). The iso— product lines in this case are erratic, so the conclusion for this test also is that there are no apparent objective relationships between Na and Nr. U. 3 13w. .. egg. ~3\ v.3 - n“ r.’ . xxxirauvaumwfl. _-.. - .3. a I .6 a. .- SQ an: O xQ ”N Q 80 NN ) 9.3“th gang; . ... . . . o 1 mmma .nodx .oouaaoauu upoam page: Haonnaao .mazunom ZOHBobnomm «Haydn 205” $92.53 Ego ghionH 92¢ .Bmaaéobmm. Souk Began“ Margo EHHIomH ho zoggo 4 ‘>. .00.. . HIM. . . a”. . lwmw” . [:3\ wwtvw}... .92....ka »o\u 5.: .oW ‘MN NV \< EQTQG 3% Qn/ 3% “In, 3% wN 3% MN \I ‘0- » quntxg >3: uh Qoo‘nux \. .Ail - . - mama .goaz .oonameM mpoam passe Hampssmu an .nmeam a2 BnZH