AER? ECONOMEC mam?» OF PQ’MJO YIELDS ON CERTAIN ONTAR10 MiNERAL 50:15 EN CQM‘RGLiED FERTILEZER EXPERIMEN‘FS. 1954 4156 Thesis Fe: fine Degree cf Ph. D. MSCHifiifid‘i STATE UNNERSE‘W Philip A W righ‘? €962 m if! U) ES iiiiiiiiiii: 3 This is to certify that the thesis entitled An Economic Analysis of Potato Yields on Certain Ontario Mineral Soils in Controlled Fertilizer Experiments, 1954-1956 presented by Philip A. Wright has been accepted towards fulfillment of the requirements for Doctoral degree inAgricultural Economics Major prEfes§or DateAugust 1, 1962 0-169 LIBRARY Michigan State University PLACE Ill RETURN BOX to remove this checkout from your record. TO AVOID FINES return on or betore dete due. DATE DUE DATE DUE DATE DUE MSU Is An Affirmative Action/Equal Opportunity lnetttwon WMt This response ‘ types of r all carrie lization a practices The s an imports. results to fertilizer varied; to reliabilit: reSponse i: experiments TWO t. 1 & Una Zlyaa In general 1 ABSTRACT AN ECONOMIC ANALYSIS OF POTATO YIELDS ON CERTAIN ONTARIO MINERAL SOILS IN CONTROLLED FERTILIZER EXPERIMENTS, 195h-1956 by Philip A. Wright This study reports on the economic analysis of late potato yield response to fertilizer in twelve controlled experiments on eight types of mineral soils in southwestern Ontario. The experiments were all carried out in farm fields of potatoes so that, except for ferti- lization and harvesting, they were subject to the same managerial practices as obtained for all potatoes grown on these private farms. The study was designed to initiate inter-departmental research in an important aSpect of agricultural production; to obtain useful results to serve as a basis for advising potato farmers as to Optimum fertilizer use as the price of potatoes and basic fertilizer nutrients varied; to deve10p and test a method of determining the statistical reliability of marginal physical product estimates; to obtain basic reSponse information useful to the design and analysis of further experiments in this area. Two types of production functions were fitted to the fertilizer- yield response data: . 2 2 = + + 1) Y a blN + b2? b3K + thP + bSNK + béPK + b7N + b2? + sBKZ 2) Y = a + blN + b2? + b3K + bAVN + bSVP + b6/K + b7VNP + b8VNK.+ b9VTK In general the first form of the polynomial yielded better results in terms of significant 9 values, consistent and useful high profit point Philip A. Wright solutions and significant marginal physical products at the mean treatment level. While several of the experiments did not yield high profit point estimates which could be relied upon, due to the extreme values obtained, in nine cases full sets of solutions for varying values of Py’ Pn’ Pp and Pk were obtained. These results were compared with extension recommendations issued in general form for the soil types included in this study. The amounts indicated by the economic analysis tended to be at the upper level or somewhat above general recommendations for P and K.where significant reSponse to these variables were observed. In those cases where the reSponse to N was significant, the analysis tended to suggest higher appli- cations at current prices than are generally recommended. However, the reSponse to N varied more widely than for the other two nutrients. In this analysis the functions were fitted to the individual plot yield observations rather than to the mean of replicated obser- vations, as is sometimes done. The R2 values obtained thus reflect all within treatment variation and tend to range rather widely from .2h287 to .92615. The variance in these data is consistent with data from small plot experiments and points out a need for a better way of decreasing eXperimental variation in this type of eXperiment. In those cases where more than one eXperimental location was used on the same soil type, the results raise serious questions as to the representativeness of data from one location in relation to a major soil universe. In only one case were the results reasonably consistent for two locations on the same soil type. VF; 3) i: 1111 L) l) 3) z.) 5) 6) Philip A. Wright In summary it may be stated that: a successful start on inter-departmental research was made in this study; the existence of functional relationships between potato yields and added amounts of N, P and K was demonstrated; valuable insights into the nature of these relationships, with implications for further studies, were obtained; uneXplained variance in the relationships observed, while limiting the potential for economic analysis, was not larger than obtained by research groups elsewhere, mainly in the U.S.A.; questions with regard to eXperimental design, plot size and universe sampling remain unanswered and should be objectives of further research, and, general fertilizer recommendations for extension purposes were demon— strated to be partially inconsistent with the agronomic-economic conclusions to be found in this analysis. AN ECONOMIC ANALYSIS OF POTATO YIELDS ON CERTAm ONTARIO I MINERAL SOILS IN CONTROLLED FERTILIZER EXPERIMENTS, l95h - 1956 by Philip A." oWright A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Agricultural Economics 1962 .91 Ix. ACKNOWLEDGEMENTS The author wishes to express his appreciation to Dr. Glenn L. Johnson for guidance, inspiration and enduring encouragement, not only in the work of the thesis but in many ways throughout the doctoral program. The Canada Council, by means of a pre-doctoral fellowship, enabled the author to complete the analytical work at Michigan State University. The Department of Agricultural Economics, Ontario Agricultural College, and the President, Dr. J.D. MacLachlan have been of continu- ing assistance throughout the author's professional career and have provided the impetus necessary to the completion of the thesis. Co-workers at the Ontario Agricultural College, in several depart- ments, have cooperated in the research work on which this thesis is based. Both the spirit and performance of their assistance is appre- ciated. ii TABLE OF CONTENTS CHAPTER PAGE I. - THE INITIATION OF THE RESEARCH PROJECT . . . . . . . . . Fertilizer Use in Ontario and Canada . . . . . . . . . Cost ASpects of Fertilizer Use . . . . . . . . . . . . «a to \o +4 Selection of a CrOp for the Experimental Project . . . II. SOME METHODOLOGICAL CONSIDERATIONS . . . . . . . . . . . 12 Functional Relationships as a Basis for Decision Making........................ 13 The Determination of Economic Optima . . . . . . . . . 1A Modification for Capital Restrictions . . . . . . . . 16 Modification to Include Harvesting Costs . . . . . . . 17 Statistical Significance of Marginal Physical Product ES timted O O O O O O O O O O O O O O O O O O O O O O 18 III. DISCUSSION OF THE EXPERIMENTS AND ANALYSIS OF THE DATA . 21 Tioga Silt Loam 195h, Location 1 . . . . . . . . . . 2h Tioga Silt Loam 1954, Location 2 . . . . . . . . . . 26 Honeywood Silt Loam l95h, Location 1 . . . . . . . . 28 Honeywood Silt Loam l95h, Location 2 . . . . . . ... 29 Brighton Fine Sandy Loam l95h . . . . . . . . . . . 31 Experimental Design 1955 and 1956 . . . . . . . . . . 32 Honeywood Silt Loam 1955 . . . . . . . . . . . . . . 33 Guelph Sandy Loam 1955 . . . . . . . . . . . . . . . 3h Fox Loamy Sand I955 . . . . . . . . . . . . . . . . 35 Analysis of Experimental Results for 1956 . . . . . . 36 Honeywood Silt Loam 1956 . . . . . . . . . . . . . . 37 iii CHAPTER Fox Sandy Loam 1956 . . . . . . . . . . . . . . . Bookton Loam 1956 . . . . . . . . . . . . . . . . Tioga Loam 1956 . . . . . . . . . . . . . . . . . General Conclusions . . . . . . . . . . . . . . . . IV. CONSIDERATION OF PROBLEMS ARISING FROM THE ANALYSIS . Comparison with Analysis of Variance . . . . . . . Negative High Profit Point Solutions to Square Root chtions 0 O O O O O O O O O O O O O O O O O O 0 Lack of Joint Product Relationships . . . . . . . . Low values 0 f i2 O O O O O O O O O O O O O O O C C Representativeness of Experimental Locations . . . Other FaCtOI‘S Needing StUdy e e e e e e e e e e e e v. SUIVfi'iARY [LND COT: CLUSIOINS . g g g g g e o e e e e e e e BIBLIOGRAPHY O O O O O O O O O O O O O O O O I O O O O O O 0 iv PAGE 38 39 to Al 43 #3 A6 A7 A8 A9 50 SI 60 TABLE I. II. III. IV. VI. VII. VIII. XI. XII. XIII. XIV. LIST OF TABLES PAGE Fertilizer Use Ontario and Canada, 1935-61 . . . . . . . Index.Numbers of Prices of Commodities and Services Used by Farmers, Canada, 1935-61 (base 1935-39 = 100) Some Nitrogen Fertilizer Materials and Prices, 1961 - ontariOeeeeeeee Comparison of Independent Variables with 5 Percent or Higher Level of Significance as Determined by Correlation Analysis and Analysis of Variance . . . . . Primary Observations of Potato Yield Response to N, P and K, l95h-l956 Per Acre Yields at Experimental Locationl-195l+ 0 e e e e e Per Acre Yields at Experimental Location 2-1954 e e e e e e Per Acre Yields at Experimental Loam, Location 1 - 1954 . . . Per Acre Yields at Experimental Loam, Location 2 - 195A . . . Per Acre Yields at Experimental sandy'ICaJn-lgBhe e e e e e Per Acre Yields at Experimental Loam - 1955 Per Acre Yields at Experimental Loam - 1955 Per Acre Yields at Experimental 1955 O O O O O O O O O O O 0 Per Acre Yields at EXperimental I—roa-In - 1956 e e e e e e e e e O O O O O O O O O O O O 0 Levels - Tioga Silt Loam, Levels - Tioga Silt Loam, 0 O O O O O O O O O O O 0 Levels - Honeywood Silt O O O O O O O O O C O O 0 Levels - Honeywood Silt O O O O O O O O O O O O 0 Levels - Brighton Fine 0 O O O O O O O O O O O 0 Levels - Honeywood Silt Levels - Guelph Sandy Levels - Fox Loamy Sand 0 O O O O O O O C O O O 0 Levels - Honeywood Silt O O O O O O O O O O O O O h 7 AS 55 62 63 6h 65 66 67 68 69. 7O i“? ‘7’..- in e-s.v '1. 45b; . er- 2. .L‘. e-.. f I . dug Omn? 1 . E H O a“; .M I 5']? ‘ML l. m :1. TABLE XV. XVI. XVII. XVIII. XIX. XXII. XXIII. XXIV. XXV. XXVI. XXVII. Per Acre Yields at Experimental Levels - Fox Sandy Loam-1956..................... Per Acre Yields at Experimental Levels - Bookton Loam 1956 Per Acre Yields at Experimental Levels - Tioga Loam - 1956 . . . . . . O O O O O O O O O l O O O O O O O 0 Regression Equations Derived from Experimental Location Yield Data - 195A, 1955, 1956 . . . . . . . . . . . . High on 26 High on 27 High on 28 High on 29 High on High on High on High on High on Profit Point Solutions for Fertilizer Applications Honeywood Silt Loam, 195A - Location 1 - Equation Profit Point Solutions for Fertilizer Applications Honeywood Silt Loam, l95h — Location 1 - Equation Profit Point Solutions for Fertilizer Applications Honeywood Silt Loam, 1954 - Location 2 - Equation Profit Point Solutions for Fertilizer Applications Honeywood Silt Loam, 195A - Location 2 — Equation Profit Point Solutions for Fertilizer Applications Brighton Fine Sandy Loam, 195A - Equation 30 . . . Profit Point Solutions for Fertilizer Applications Honeywood Silt Loam, 1955 - Equation 32 Profit Point Solutions for Fertilizer Applications Guelph Sandy Loam, 1955 - Equation 3A Profit Point Solutions for Fertilizer Applications Fox Loamy Sand, 1955 - Equation 36 . . . . . . . . Profit Point Solutions for Fertilizer Applications Fox Loamy Sand, 1955 - Equation 37 . . . . . . . . PAGE 71 72 73 75 88 9O 92 9h 96 98 100 102 10h TABLE PAGE. XXVIII. High Profit Point Solutions for Fertilizer Applications 106 on Honeywood Silt Loam, 1956 — Equation 38 . . . . . . XXIX. High Profit Point Solutions for Fertilizer Applications on Fox Sandy Loam, 1956 — Equation LO . . . . . . . . 108 XXX. High Profit Point Solutions for Fertilizer Applications on Fox Sandy Loam, 1956 - Equation Al . . . . . . . . 110 XXXI. High Profit Point Solutions for Fertilizer Applications on Tioga Loam, 1956 - Equation AA . . . . . . . . . . 112 XXXII. Summary of Analysis of Variance - Guelph Sandy Loam, 1955 O O O O O O O O O O O O O O O O O O O O C O O O O 115 XXXIII. Summary of Analysis of Variance - Honeywood Silt Loam, 1955 O O O O O O O O O O O O O O O O O O O O O C O O O ll6 XXXIV. Summary of Analysis of Variance - Fox Loamy Sand, 1955 . 117 XXXV. Summary of Analysis of Variance - Honeywood Silt Loam, 1956 O O O O O O O O O O l O O O O O O O O O O O O O O 118 XXXVI. Summary of Analysis of Variance - Fox Sandy Loam, 1956 . 119 XXXVII. Summary of Analysis of Variance - Bookton Loam, 1956 . 120 XXXVIII. Summary of Analysis of Variance - Tioga Loam, 1956 . . . 121 vii TH ES‘ 3 eeeeee OOOOOOOO ‘‘‘‘‘ eeeeeee FIGURE PAGE 1 Acreage and Production of Potatoes, Ontario 1930—1961 . 9 2 Counties in the Area of the Experiments and Acreage plan- ted to late Potatoes . . . . . . . . . . . . . . . . . ll 3 Derivative of a Polynomial with a Negative Coefficient for N2 and a Positive Coefficient for N, with Respect to N O O O O O O O O O O O O O O O O D O O O O O O O O 19 h Experimental Design - Cooperative Potato Experiments, Ontario, 195h O O O O O O O O O C O O O O C O O O C O 22 viii TH EST 5 APPENDIX PAGE A Co-operative Potato Fertility Trials - Experimental Field Observations — 195h, 1955, 1956 . . . . . . . . 61 B Regression Equations Derived from Experimental Location Yield Data, 1954, 1955, 1956 . . . . . . . . 7h C High Profit Point Solutions . . . . . . . . . . . . . 87 D Analysis of Variance of Data for 1955 and 1956 . . . . 11h E Revised Design for Fertilizer Response Experiments . . 122 TH ES ' ‘ , \ Q CHAPTER I THE INITIATION OF THE RESEARCH PROJECT Research devoted to the consideration of the economics of fertie lizer use is of relatively recent origin in Canada. This is not to say that economic considerations have been entirely lacking in earlier research work in this area, but, rather, that the growing body of know- ledge and techniques for applying economic theory to practical research problems has only recently received formal consideration. The eXperi- mental project which this thesis reports is the first recorded instance of joint work by agricultural economists and soil scientists on econo- mic problems in the use of fertilizer in a specific crop experiment in Canada. This experiment represents, of course, only a small part of the overall research in fertilizer use. Numerous other experiments carried out by soil scientists provide important information in their technical field of interest. In addition, such eXperiments permit the standardi- zation of certain techniques which enter into either implicit or eXpli- cit assumptions of economic analysis. Examples of these would be (1) the placement of fertilizer in relation to the efficiency of its utili- zation by the crop, (2) the effects of foliar application versus dry application, and (3) the resoonse of a crop to a Specific form of a fertilizer nutrient. Generally Speaking, it is expected that the level of technology used in experiments designed for economic analysis will be as advanced or more advanced than that practiced by successful farmers. In addition to the joint considerations already mentioned the inclusion of other subject matter specialists in economic studies is often.desirable. The experiment to be described in this thesis was also used by the field crops specialists of the Canada Department of Agriculture to study potato quality in relation to fertilizer treat- ment. Their findings may indicate the necessity of including other variables in the model used for economic analysis. Beyond any doubt, a salient feature in the initiation of this experiment was encouragement of inter-disciplinary c00peration in the experimental determination of solutions to farm.problems. All too frequently agricultural scientists have disregarded the obvious fact that the farmer'is vitally interested in knowing whether or not recom- mended practices, techniques or machinery will or will not increase his net income. While there may be certain technical areas in which it is difficult to determine economic feasibility there are still many unexplored areas Open to joint research which could readily be investi- gated. In Canada this work has been slow to develop due, in large part, to the very few agricultural economists centred at the universi- ties, where Opportunities for interhdisciplinary research projects are the greatest. Due to several very practical considerations, a controlled experi- ment in the use of fertilizer presented Opportunities to initiate a joint research project. Firstly, only minor modifications in research already considered by the soils scientists were required to meet mini- mum specifications fer economic analysis. Neither did the preposed changes involve the allocation of appreciable additional funds, labor and.machinery, nor did the changes in proposed experimental design in any way impair the particular objectives of the soil scientists. TH 55‘s 3 Secondly, the use of fertilizer as an input in the farm business has increased rapidly in the past twenty-five years. Thirdly, competitive forces within the agricultural sector of the economy require increa- singly complex managerial decisions with reSpect to the use and pro- ductivity of all inputs. Fertilizer Use in Ontario and Canada The increase in the use of fertilizer from 1955 to 1961 in both Ontario and Canada is shown in Table I. The tonnages in each case are given in terms of (1) mixed fertilizers, and (2) materials, while the percentage use figure is based on total fertilizer sales. It will be noted that current use figures indicate that over h6 percent of all fertilizer used in Canada is used in Ontario. The proportion of mixed fertilizer is 52.2 percent for Ontario while for materials it is 30.7 percent. This difference in the proportions is largely due to the fact that the Prairie Provinces are using increasing amounts of ferti- lizer, primarily ammonium phOSphate (ll-hB-O or 16-20—0), which is classified as a material. Cost ASpects of Fertilizer Use During the 1935-61 period, the increase in use of all fertilizer was 533 percent in Ontario while for Canada as a whole it was 328 per- cent. With reference to mixed fertilizers, the increase was 728 per- cent in Ontario and 5&1 percent in Canada. The change in the use of fertilizer materials was considerably less, being 196 percent for Ontario and 133 percent for Canada. In addition to the actual tonnages reported, it is also certain that content analysis would reveal THES‘ES h * TABLE I - FERTILIZER USE ONTARIO AND CANADA, 1935-61. Ontario Canada Percent Year Used Mixed Materials* Mixed Materials* in Ontario -------- tons - - - - - - - - percent 1935 h7,686 2h,533 107,768 10h,7ll 33.8 1936 60,261 23,688 137,361 96,L79 36.0 1937 92,770 31,330 191,283 106,993 h1.8 1938 105,101 28,812 216,602 106,77h L1.h 1939 llh,097 28,072 232,926 101,077 h2.5 19h0 119,08h 28,886 261,083 85,638 h5.2 1911 105,593 21,310 219,667 7L,53h 39.1 1912 161,559 22,251 319,111 72,136 11.6 19h3 159,713 16,768 h17,669 72,162 35.h 19hh 175,380 17,638 455,875 79,233 36.1 19h5 190,279 21,217 £83,081 92,026 36.7 19h6 220,196 16,911 5&2,h97 90,hL6 37.6 19h? 252,137 20,399 564,851 95,870 h1-3 19h8 251,918 22,558 564,872 107,299 40.8 19h9 275,897 26,779 611,758 129,968 h0.h 1950 317,03h 29,534 618,609 1&5,972 h5.3 1951 33h,16l 3h,135 616,57h 153,933 A7.8 1952 337,731 11,218 612,196 156,019 19.2 1953 351,569 h7,811 6h0,203 179,600 h8.8 1951 375,673 50,938 651,160 160,181 52.6 1955 380,235 18,517 651,173 139,301 51.0 1956 375,185 5h,26h 652,6L3 lh8,037 53.5 1957 36h,502 51,h8h 651,75h 156,497 55.8 1958 385,626 65,690 688,566 181,973 51.8 1959 395,173 72,111 689,553 218,661 51.5 1960 363,33h 73,798 691,708 243,720 L6.7 1961 #07,250 91,h55 779,682 297,730 h6.2 Source: The Fertilizer Trade in Canada, 1935-19 yearly, Dominion Bureau of Statistics, Ottawa. The Fertilizer Trade, l9h9-59 yearly, Dominion Bureau of Statistics, Ottawa. * Includes, Nitrate of Soda, Sulphate of Ammonia, Calcium Cyanamide, Ammonium Nitrate, Ammonium PhOSphate: 11-h8-O and 16-20-0, Super- phosphate (20 percent), Natural Phosphate Rock, Basic Slag, Bone Meal and Flour, Muriate of Potash: 50 percent and 60 percent, Sulphate of Potash, Tankage, Sheep Manure, Dried Blood and other Materials. 5 significantly higher plant nutrient content in current mixed fertili- zer sales. While there are no price series which relate value terms to this input, the physical figures are ample indication of the increasing importance of fertilizer in agricultural production. An idea of the relative change in the cost of fertilizer as com- pared with other inputs may be obtained by reference to the index numbers series shown in Table II. While the over-all cost of inputs used in this series has increased from an index value of 95.4 in 1935 to 282.2 in 1961, the change for the fertilizer input is from a value of 97.0 to 19h.6, or roughly 97 percent less. In this regard, the relatively small increase in the price of fertilizer is only slightly higher than that of gasoline, oil and grease which together show the smallest relative change. Among those items for which fertilizer is a substitutel/, machinery and farm labor costs have increased propor- tionately more than most other inputs. Accordingly, an increased use of fertilizer is warranted on this basis alone. Apart from the general situation of low relative prices for fer- tilizers as a group, the price of nitrogen in particular has been moving downward in recent years. Some recent prices for nitrogen are indicated in Table III. As might be eXpected the more eXpensive sources of nitrogen have declined in usage, with ammonium nitrate, anhydrous ammonia and aqua ammonia as cheaper sources comprising the bulk of current sales. ‘l/ The discussion of fertilizer use as a substitute for other inputs is included in E.L. Baum and Earl O. Heady in "Over-A11 Economic Considerations in Fertilizer Use", Economic and Technical Analysis of Fertilizer Innovations and Resource Use, ed. E.L. Baum et a1. (Ames: Iowa State Press, 19571, pp. 125-135. 114 ESE 1 E 6 TABLE II - INDEX NUMBERS 0F PRICES 0F COMMODITIES AND SERVICES USED BY FARMERS, CANADA, 1935-61.* (base 1935-39 = 100) 1 Farm Wage Building Gasoline Year Composite-/ Fertilizer Rates Machinery Materials Oil & Grease 1935 95.h 97.0 87.6 95.5 87.1. 105.1 1936 98.1 98.2 91.7 97.8 97.3 101.7 1937 105.3 101.h 102.6 97.2 108.7 99.7 1938 101.7 103.3 105.0 10h.1 98.7 97.h 1939 99.3 100.2 110.3 103.6 108.1 96.2 1910 106.8 106.3 131.7 105.8 117.2 97.0 l9h1 116.1 116.7 163.5 109.1 137.2 112.1 19A2 131.6 121.8 211.7 11h.h 1h9.h 11L.6 19h3 1L3.h 112.9 267.9 117.1 156.2 llh.7 19th 118.0 112.9 275.3 118.7 176.2 11h.7 19h5 152.1 112.9 298.1 115.1 l7h.2 11h.h 19h6 157.0 115.8 31h.6 121.6 176.0 117.h 1917 170.1 120.8 311.1 125.1 201.0 123.6 19h8 197.6 132.2 371.2 1L7.2 23h.0 139.7 19h9 20h.1 1h1.3 388.1 158.6 236.5 139.h 1950 210.L 167.7 h01.2 166.h 279.9 1A6.h 1951 230.0 168.3 h57.3 189.2 301.8 1A9.2 1952 2h3.1 18h.9 55h.2 19h.0 303.9 1&9.6 1953 239.8 182.0 hh9.1 198.0 309.7 153.h 195A 237.2 182.7 hh1.2 198.0 307.7 152.6 1955 238.3 180.6 139.7 199.8 311.1 151.7 1956 2A7.6 180.5 A70.3 209.7 321.2 152.8 1957 255.9 185.6 501.h 226.5 303.b 156.1 1958 259.9 181.h 53h.0 237.2 320.0 156.2 1959 269.5 188.1 538.2 268.4 325.6 155.9 1960 276.7 191.8 555.3 251.2 327.7 155.0 1961 282.2 19h.6 566.0 261.h 324.3 156.5 * Source: Dominion Bureau of Statistics, Ottawa. ,1/ Includes farm implements, building materials, gasoline, oil and grease, feed, fertilizer, bindertwine, seed, hardware, tax rates, farm wage rates and rates of interest. 6 TABLE II - INDEX NUMBERS 0F PRICES 0F COMMODITIES AND SERVICES USED BY FARMERS, CANADA, 1935-61.* (base 1935-39 = 100) 1 Farm Wage Building Gasoline Year Composite-/ Fertilizer Rates Machinery Materials Oil & Grease 1935 95.h 97.0 87.6 95.5 87.1. 105.1 1936 98.1 98.2 9A.7 97.8 97.3 101.7 1937 105.3 101.h 102.6 97.2 108.7 99.7 1938 101.7 103.3 105.0 10h.l 98.7 97.L 1939 99.3 100.2 110.3 103.6 108.1 96.2 1910 106.8 106.3 131.7 105.8 117.2 97.0 1961 116.1 11A.7 163.5 109.1 137.2 112.1 19A2 131.6 121.8 211.7 11h.h 1h9.h 11h.6 19h3 lb3.h 112.9 267.9 117.1 156.2 11h.7 19AL 1L8.0 112.9 275.3 118.7 174.2 116.7 1965 152.1 112.9 298.1 115.1 17h.2 11L.h 19h6 157.0 115.8 31h.6 121.6 176.0 117.h 19h7 170.h 120.8 3h1.h 125.h 20h.0 123.6 19h8 197.6 132.2 371.2 1L7.2 23h.0 139.7 19h9 20h.1 1h1.3 388.1 158.6 236.5 139.h 1950 210.h 1h7.7 #01.2 166.h 279.9 1A6.h 1951 230.0 168.3 h57.3 189.2 301.8 149.2 1952 2L3.1 18h.9 55h.2 19h.0 303.9 1h9.6 1953 239.8 182.0 hh9.1 198.0 309.7 153.h 195h 237.2 182.7 hh1.2 198.0 307.7 152.6 1955 238.3 180.6 h39.7 199.8 311.h 151.7 1956 247.6 180.5 h70.3 209.7 321.2 152.8 1957 255.9 185.6 501.1 22h.5 303.h 156.1 1958 259.9 18h.h 534.0 237.2 320.0 156.2 1959 269.5 188.1 538.2 218.1 325.6 155.9 1960 276.7 191.8 555.3 25h.2 327.7 155.0 1961 282.2 l9h.6 566.0 261.h 32h.3 156.5 * Source: Dominion Bureau of Statistics, Ottawa. 1/ Includes farm implements, grease, feed, fertilizer, farm.wage rates and rates building materials, gasoline, oil and bindertwine, seed, hardware, tax rates, of interest. 1HESW 7 TABLE III - SOME NITROGEN FERTILIZER MATERIALS AND PRICES, 1961 - ONTARIO. Material N Price per Lb. N percent cents Solid: Ammonium Nitrate 33 13.3 Calcium Cyanamide 21 18.2 Sulphate of Ammonia 20 15.9 Nitrate of Soda 16 25.h Urea A5 12.8 Gas: Anhydrous Ammonia 82 10.0 Solution: Aqua Ammonia 20 11.6 Ammonium Nitrate-Urea 32 12.8 However, several forms of urea are currently increasing in importance and give indications of offering certain price and technical advan- tages for the future. No significant price variations are observable for the two other major plant nutrients, P205 and K20, in the Ontario market. However, as farmers increase their usage of fertilizer materials, source and price information for individual nutrients becomes increasingly important. Selection of a Crop for the Experimental Project While it was recognized that farmers require information with reapect to the use of fertilizer for most of the cr0ps grown in Ontario, introductory research experiments of this type could not be set up to cover all crOps. Since the concept was new and the possible applica- bility of the results highly uncertain, a decision as to the specific THES‘S 8 crOp to be studied was necessary. Soil scientists and agronomists consider certain crops to be reSponsive to incremental additions of plant nutrients while certain other crops are considered to be rela- tively unresponsive under good farm fertility conditions. Further, a cash crOp, which was both reSponsive to fertilizer increments and sub- ject to fairly wide fluctuations in market price was deemed most suitable for economic analysis. Accordingly, the late potato crop was selected as potentially fulfilling these conditions. In addition, this crop is generally produced in commercial quantities on fairly well identified soil types over most of the important late potato producing counties. It is quite clearly indicated in Figure 1 that Ontario potato acreage has decreased rapidly in recent decades. The highest level of planting since 1930 was 171,000 acres in 1931. By 19AO, plantings had dropped irregularly to 116,000 acres and following that, dropped steadily to a level of about 55,000 acres in 1951. Since then plant- ings have varied annually but appear to have stabilized in the range between 55,000 and 65,000 acres. Actual Potato production has not changed nearly so much as acre- age planted. While total Production was estimated at 20 million bushels in the peak planting year, 1931, it was 20.1 million bushels in 1961 when only 37.h percent of the 1931 acreage was planted. This indicates quite clearly the change which has occurred in production per acre. Crop reports indicate an average yield of 117 bushels per acre in 1930 while in 1961 an average yield of 31A bushels per acre was reported, an all time high. While there are several factors which influence per acre yield, there is little doubt that increasing use of THREE“; .oucoaoe .opsuasowpm< mo pcoEppmdoo owpmpco .Homa .owumpco pom moaumwumpm Metapasofipw< "oopsom \w .deH I Omda cappuco .mooumpom mo cowpospopm paw swamp"; I g )1” Ho 00 mm 0m 4m mm Om we we 44 N4 04 mm on an Nm 0mma m 1 o v o b. o h + u a .61 u d. u u 11 Om 0 at b .. .€ 00 m .1 o as .: Ob .5 > OH .fi \ / s. .3” I. a \ . > 5. NH .. \I s (\ — > a / \\-|)z \II/I 0m 7 \ IK — a s /\ (\ J MH av ~ /( a 5 I h a ’ ll 00 ea .. . . \>’ a . x 1.. . 303 I 1 . 3 .. . c .2 1. . x . .. 8H 0H s. as ass .. \) NaH 1r \s < a \\ a ll OHH r a ma 1 a ”x a .. 0H .. a . a 1. ON a: 5‘ < (\ ONH HN .. ommouoa. 1. end [t 3H 1. OmH l 00H 1. ova maozmsm mo m:6fiaaaz naked 000. :oapoSUOLm ogmuom ammouo< oamvom THESIS fl lO fertilizers is one of the more important ones. DeSpite the fact that the acreage devoted to potato growing has declined in recent decades, it is still an important cash crop in certain areas of the provinces. The counties which include conditions common to the eXperimental project, Figure 2, produce approximately L0 percent of the total late potato crOp in Ontario. In this area, which is as yet climatically unsuited to other types of cash crOps, potatoes are the only major cash crop. For the province as a whole, tobacco, shelled corn and winter wheat rank considerably more important in terms of total value as cash crOps. However, it has been estimatedl/ that at $1.20 per bushel potatoes will return 25 cents per bushel net to cover risk and management. If these figures are reliable it would appear that potato production can be a profitable enterprise on many Ontario farms. For the several reasons discussed and illustrated above, the late potato crop was selected as being suitable for analysis in a c00pe— rative eXperiment. The eXperimental design and the results of the analysis will be considered in detail in later chapters. ‘1/ H.L. Patterson, "Can Potatoes Compete", American Potato Journal, 1958, Vol. 35, pp. 679-686. 11 .Opcouoa .ougasowamd. mo pcoafimaoa oEwpco 3“de .owampco pom 3333.5 3.335033 «ooh—3m \w .8338 SS 3 eosfiahmmafioa es. 38.82888. 65 .8 no: 65 5 83566 u N Emma O..>O*CO 6.71M 6x61. an. :dm..:0..£ 1:02.31 A 6:64 masns CHAPTER II SOME METHODOLOGICAL CONSIDERATIONS The underlying motives for this study were to improve either directly through its results, or indirectly through further studies using knowledge gained from it, our knowledge of scientific phenomena and make it available for the advancement of agricultural science. Much of the research of this type is, appropriately, an integral part of the program of agricultural eXperiment stations where a major part of the research effort is directed toward the solving of problems important to farmers. 'Nith particular reference to the use of fertilizer, the farmer seeks Specific information as follows: 1. whether or not to use commercial fertilizer for a specific crop, 2. if so, what kind of fertilizer to use, 3. what amount of fertilizer to use given certain price infor- mation, a) without capital restrictions on the use of fertilizer, and b) with capital restrictions on the use of fertilizer, and c) given knowledge of certain functional relationships between crop value and harvesting costs. While the present study does not provide for sufficient information to answer all of the questions noted above, the general framework of analysis is such that flexibility is provided to permit the intro- duction of additional information as it becomes available. 12 13 Functional Relationships as a Basis for Decision Making The economic analysis used in this study as well as some of the possible modifications of it may be found in many publications. Never- theless, it is desirable to present a brief synOpsis of these ideas before considering their Specific application. A concept shared by both economists and agronomists is that a functional relationship exists between crOp yields and the application of plant nutrients. A typical expression of such a relationship is shown in equation (I). (1) ’f = f(N,P,K/Xh...xn)+U where Y is yield in bushels per acre, N, P and K are the three plant nutrients studied as independent variables, and XL . . . X.n include variables fixed at certain levels (cultural practices, varieties, soil uniformity, etc.).;/ The variations in yield not explained by the studied independent variables are represented by U. In other words U is an error term indicating how much I. (predicted yield) differs from Y (the observed yield). This functional relationship which, in equation (I), is indicated in very generalized form may be further refined in numerous more Specific forms as Shown in equation (2) the quadratic form, and in equation (3) the square root form. 2 2 (2) ’f = a + b2N 4- b3? + th + bSNP + b6NK + b7PK + b8N + b9P + me2 (3) Y a a + b2N + b3P + th + bsm + b6“? + 1.7.4 + b81/NP + 13ng + bid/PK ;/ G.L. Johnson, "Planning Agronomic-Economic Research in View of Results to Date", Fertilizer Innovations and Resource Use, ed. E.L. Baum et a1. (Ames: Iowa State Press, 1957), pp. 217-225. TEES“ v0 '- 1h 04/ One group of researchers has foun that these two forms have been the most satisfactory of the various regression equations considered for the regression analysis of functional relationships in fertilizer experiments. Further and more detailed treatment on the use of pro- duction functions in estimating fertilizer - crop yield relationships . . 2/ y2/ may be found in articles by Redman and Allen- and Head . It must be stated, however, that lacking a precise theory as to any required functional form, it is usually necessary to compare several equations, subject to restrictions in the eXperimental design, to see which best describes the observed relationships. This subject has been raised in the literature with regard to problems of research in applied production economics and it has been suggested by Johnson£/, that this is one of the most important problem areas in this type of research. The Determination of Economic Optima After obtaining an estimate of any given production relationship between crop and plant nutrients, various optimal combinations of plant ‘l/ John P. Doll, Earl O. Heady, and John T. Pesek, Fertilizer Production Functions for Corn and Oats; Includinggan Analysis of Irrigated and Residual Response, Iowa Agricultural Experiment Station Research Bulletin #63, 1958. ‘g/ John C. Redman and Stephen Q. Allen, "Some Interrelationships of Economic and Agronomic Concepts", Journal of Farm Economics, Vol. XXXVI (August 1951.), pp. 1.53-1.65. Earl O. Heady, "Methodological Problems in Fertilizer Use", Methodological Procedure in the Economic Analysis of Fertilizer Use Data, ed. E.L. Baum et al.(Ames: Iowa State Press, 1956), pp. 1-21. 5/ Glenn L. Johnson, "Discussion: Economic Implications of Agri- cultural Exneriments", Journal of Farm Economics, Vol. XXXIX, No. 2, May 1957, pp. 390-397. 15 nutrients may be obtained. We will assume for the present the case in which there is no capital restriction on the use of fertilizer. Then, if for example, equation (2) describes the relationship between crop yield and the three plant nutrients N, P205 and K20, the following procedure is used to determine the optimum combination of nutrients and the optimum yield. The partial derivatives of yield with respect to each of the three nutrients are: .951. ._. (1.) ON b2+b5P+b6K+2b8N a? _ (5) 7;; - b3 + bSN + b7K + 2b9P a? __ (6) 5K - bh+b6N+b7P+2blOK Equations (A), (5) and (6) are then set equal to the respective price ratios, i.e. P _ .2 (7) b2 + 2b8N + bSP + b6K — P y z ._2 (8) b3 + bSN + 2b9P + b7K P y Pk (9) bu + b6N + b7P + 2bloK = ‘5; and solved Simultaneously for the values for N, P and K which represent both the Optimum combination and optimum level of application. The ability to determine economic optima is contingent on securing evidence of the law of diminishing returns in eXperimental results. In the functional relationship this is observed in the minus coefficients of N2, P2 and K2. If the experiment has not adequately identified this relationship, the calculated optima may be logically inconsistent by virtue of their magnitude, or may be impossible to determine. TH 5818 15 nutrients may be obtained. We will assume for the present the case in which there is no capital restriction on the use of fertilizer. Then, if for example, equation (2) describes the relationship between crop yield and the three plant nutrients N, P and K O the following 205 2 ’ procedure is used to determine the optimum combination of nutrients and the optimum yield. The partial derivatives of yield with respect to each of the three nutrients are: (A) = b + b P + b6K + 2b N 2 5 8 (5) = b + b N + b K + 2b P 3 5 7 9 In» 01o.1»r> r4)‘U*<>Zf-<> (6) = b + b N + b P + 2b K h 6 7 lO O! 7? Equations (h), (5) and (6) are then set equal to the respective price ratios, i.e. P _ .2 (7) b2 + 2b8N + b5? + b6K — P y = ._2 (8) b3 + bSN + 2b9P + b7K P y Pk (9) bh + b6N + b7? + 2b10K = F; and solved simultaneously for the values for N, P and K which represent both the optimum combination and optimum level of application. The ability to determine economic Optima is contingent on securing evidence of the law of diminishing returns in experimental results. In the functional relationship this is observed in the minus coefficients of N2, P2 and K2. If the experiment has not adequately identified this relationship, the calculated optima may be logically inconsistent by virtue of their magnitude, or may be impossible to determine. Tapas 16 It is readily observed that any change in the prices of the plant nutrients or in the price of the product will result in different values for N, P and K being obtained in the solution. Modification for Capital Restrictions While it may be convenient to assume that the farmer has unlimited capital and will thus employ each resource up to the point where it returns exactly its cost in value of output as indicated in the prece- ding solution, it is realized that in the real world this is not usually the case. At least two costs other than the actual resource unit cost may be of some importance, (1) the cost of using borrowed money to obtain the resource and/or (2) the opportunity cost of not using the resource, the capital used to purchase it, in some other productive capacity. It is highly probable that many farmers do use borrowed funds to purchase fertilizer, thus adding to its cost. The only reference found to be a Specific study to determine the extent of the use of credit to purchase fertilizer was in a report by Yeager and Belcherl/. They found that, depending on the area studied, from 3A percent to 92 percent of the farmers borrowed money to buy fertilizer. The second point under consideration involves the desire of farmers to limit the use of capital to purchase fertilizer in order to use some of that capital for inputs in other productive activities. He will do l/ J.R. Yeager and O.D. Belcher, "Farm Characteristics and the Use of Credit as Related to Fertilizer Use in Alabama", Report of Con- ference for COOperatorS in the TVA Agricultural Economics Research Activities, TVA Division of Agricultural Relations, March 1959. 17 this because he believes that the earning power of the last dollar invested in fertilizer should not be less than it could earn in the other activities and vice-versa.‘ In either or both of the cases indicated above, it is possible to ascertain the fertilizer rate and combination for a Specified return on the marginal dollar investment in fertilizer by modifying equations (7), (8) and (9) t0, Pn(l+r) (10) b2 + 2b8N + b5? + b6K = —P—;——— P (1+r) (11) b +bN+2bP+bK - —E——- P 3 5 9 7 y Pk(l+r) (12) bA + b6N + b7? + 2b101< = —§;—— where r is the percentage cost of borrowing money for fertilizer and/or the Specified rate of return set by the farmer as a necessary restrict- ion on his use of fertilizer, this Specified rate being determined by his. or other, analysis of the rate of return to be realized by capital outlay for productive resources in other parts of the farm business. Modification to Include Harvesting Costs The per acre non—fertilization costs of producing some farm crops may not be appreciably affected by the rates of fertilization while others may be quite strongly affected. In the case of the present study, there may be Significant increases in harvesting costs asso- ciated with higher yields due to fertilization. If this is the case and the nature of the relationship can be determined, adjustment can be made in equations (7), (8) and (9), or (10), (11) and (12) as, 1Hti‘fi'i'3 18 Pn(l+r) Py - CH (13) b2 + 2b8N + bSP + béK P (1+r) (11.) b3 + bSN + 2139? + b7K —B——-—-Py _ CH Pk(l+r) (15) b4 + b6N + b7P + 2b10K = P;-:_C; where C is the cost of harvesting per unit of product. The relation- H ship of CH to Y may be of linear or non-linear form. The adjustment Shown above is applicable to the linear or "piece-work" cost relation- ship. In general these relationships have not been studied as an adjunct to controlled fertilizer input-output studies and will not be examined herein. Statistical Significance of Marginal Physical Product Estimates The foregoing theoretical construction depends in its application on our‘ability to determine the estimating equations which "satisfacto- rily" express the fertilizer-yield relationship. This is commonly attempted by following familiar linear least squares methods for deter- mining correlation and regression coefficients from experimental data.l/ Assuming that "satisfactory" results are obtained in this process the above procedure indicates optimal combinations and amounts of plant nutrients. If we consider, for purposes of illustration, the effects on yield of changes in the amount of one of the nutrients, N, we can graph this *— l/ See for example, M. Ezekiel, Methods of Correlation Analysis, 2nd ed., (New York: John Wiley & Sons, Inc., 1953), Appendix 1, or other modifications of this method. THEsE; l9 relationship as in Figure 3. Generally, the resulting line will have a negative or downward slope since we are measuring the effects of N applied over and above that already in the soil. The exact nature of the line will depend in part on the levels at which the other nutrients are held when the derivative is taken and on the Sign of the b coeffi- cients of N and N2. The value of the derivative decreases as the amount of N increases and eventually becomes negative at higher levels of application of N. J .,. 2%) Figure Q - Derivative of a Polynomial with a Negative Coefficient for N2 and a Positive Coefficient for N, with Respect to N. A feature of the present study is the application of a test to determine the statistical reliability of such derivatives (marginal physical products in economic jargon). This may be done for each of the partial derivatives at any determined level of application of each of the three nutrients. The procedure involves the concept of the variance of the sum of the variances of the regression coefficients in the partial derivative. aY dY aY dN’ dP’ 6K Given the equations for as in (A), (5) and (6) the variance 20 of each is determined as follows: (16) 52 (.339 -= 52b + 1.st + P282b + K282b + ANK Sb + ANP Sb b 2 8 5 6 6b8 5 8 + LN Sb2b8 + 2px 86566 + 2K Sb2b6 + 2P 56265 (17) 52 (g) = 82b3 + NZSZbS + 1.195269 + K252b7 + hPK Sb7b9 + LNP Sbsbg + LP Sb3b9 + 2NK Sb5b7 + 2K Sb3b6 + 2N Sb3b5 (18) s ("3316) = 82b,+ + N252b6 + P282b7 + 1.1352610 + APK 567610 + + ' + + ANK Sbéb10 AK Sbhb10 + 2NP Sbéb7 2P Sbhb7 2N Sbhbé Having obtained the S values for each of the partial derivatives they can be tested for reliability by: A H \0 U c" A 0’ +-< V I 0! 2 6K It is recognized, however, that both the decision to accept certain values of the bi's and determination of required levels of significance of the partial derivatives is a normative matter. The procedure is similar for the square root form of the polynomial. Modifications of this procedure could be carried out for certain other functional forms. However, since this study is limited to the quadratic and square-root forms of the polynomial, others are not con- sidered here. In general the method can be used where the marginal physical product functions are linear combinations of estimated regression coefficients. 0‘: 1‘“" 5‘ 1:823:13 CHAPTER III DISCUSSION OF THE EXPERIMENTS AND ANALYSIS OF THE DATA The experimental projects for which the analysis is reported here were carried out over three production seasons, l95h, 1955 and 1956. In the first year, the eXperimental design consisted of a single repli- cate factorial with three treatment levels, N at O, 25 and 50 lbs., P and K at O, 50 and 100 lbs., plus an increment study with six treatment levels, replicated twice. The increment study was as follows: N P K N P K N P K - lbs. per acre - - lbs. per acre - - lbs. per acre - O 200 200 100 O 200 100 200 O 25 200 200 100 25 200 100 200 25 50 200 200 100 50 200 100 200 50 75 200 200 100 75 200 100 200 75 100 200 200 100 100 200 100 200 100 200 200 200 100 200 200 100 200 200 The design is illustrated graphically in Figure A. The experiments were carried out on three soil types. with two locations for each of two types and one location for the third. A second location had been planned for the third soil type but was can- celled due to delays in seeding. The soils were chosen by agronomists, who also supervised the seeding and harvesting. The author partici- pated in preparation of fertilizer, checking plant pepulations during the growing season and assisted in harvesting the crop. The plots were four rows wide and 25 feet long. The two centre rows in each plot were harvested. Prior to harvesting the border effect at the end of each plot was removed by hand digging. At the same time, 21 K lbs. 22 H 200 175 ‘ ——--!(-d----- 71‘ l 150 .190 , I ._.... A... 'y I / I 100 ’ l ._.:9’ -_-f’ l 75 A7 / / 50 ’\ p + 25 i . «p <9. X = l observation 0 «y 0 = 2 observations . 1 I I O 25 50 75 100 125 150 175 200 lbs. P Figure 5 - Experimental Design - COOperative Potato Experiments, Ontario, 195h. 23 as far as possible, all hills next to misses were removed. The number of hills left for harvesting was then counted and these stand counts were used in converting yields in lbs./plot to bus./acre. That is, the bus./acre yields used in this analysis are calculated on the basis of a perfect stand. A perfect stand was figured at forty-four hills per plot and 15,378 per acre. Accordingly, the results are in terms of approximately l/BSOth of an acre. All field results are shown in Appendix A. In 1955 and 1956 some changes in soil types and locations were made and the eXperimental design was changed. These changes are indi- cated, as they occur, in the discussion of the results. The analysis is similar for each soil type and location. It includes least squares estimation of two polynomial forms, as previously noted, tests of significance of the bi's, tests of significance of the marginal physical products at the mean treatment levels and the deter- mination, where possible, of the high-profit level of application of the reSpective soil nutrients for Specified price relationships. For computing convenience the fertilizer inputs were coded in 25 lb. units. Prices were selected with regard to observed price fluctuations in the price of potatoes, and with regard to recent and probable future prices of the basic fertilizer nutrients. The price combinations con- sidered are as follows: ESIS Price of Potatoes Price of N Price of P 0 Price of K20 2 5 per bus. per lb. per lb. per lb. Py = $1.00 Pn -- 8,! Pp = 8;! Pk = a)! 1.20 10,! 10;! 5;! 1.1.0 12,! 2.00 11.)! The solutions of high profit point levels of treatment were pro- grammed on Michigan State University's MISTIC Computer. After several false starts series of high—profit solutions for all combinations of P , P , P and P ynp k for each soil type for which reasonable results were obtained are indicated above were computed. The specific results arrayed in Appendix C. In this section only the main findings are indicated, with common price levels of Py = $1.20 per bu., Pn = 12¢ per 1b., Pp = 10¢ per lb. and Pk = 5; per 1b., used for illustrative purposes. Further, the marginal physical product of each nutrient at the mean treatment level was tested for significance in each case using the technique outlined in Chapter II. It would be desirable to comp puts this test for a range of marginal physical products at various levels of N, P and K including the indicated economic optima. However, this is a very arduous and painstaking manual operation which must eventually be programmed for computers as a part of the general solu- tion to estimating equations of the type used here. Tioga Silt Loam 1954,,Location_l (22) f a 11.3.36 + 31.36»: - 4.16P + 83.25K + 1.33sz + 3.38 NK + 2.35 PK - 8. 90112 - 1. bOP2 - 5.52K2 H2 = .925818 R = .962l9h S = 54.86079 THESIS (23) 25 The bi's were significant at 10 percent level or above the coef- ficients of N, K, PK, N2, K2. Marginal physical products of N, P and K were all significant at the 5 percent level or higher for the mean treatment application. This equation yielded the high profit solution N = L15 lbs., P = 976 lbs., K = 521 lbs. for the common price relationship, in amounts considerably in excess of the levels of observation. Nevertheless, the function indicates significant relation- ships between yield and applications of N, P and K. In this case additional yields of P alone are indicated as having the effect of depressing yields. However, the marginal physical product of P at the mean level of treatment is still positive due to the NP and PK interaction terms. The high profit levels of application estimated may indicate too narrow a range of treatment and/or a unique location which may not represent the universe intended in the selection of this location. Further, the indicated optima are considerably in excess of recommendations currently being made for extension purposes. ? = 219.61 - 23.83N - 10.39P + 18.88K + 5.56m - 1.0.091/1D + 1.6.651“ + 35.501/NP + 20.9mm + 20.851/PK 82 E .92615 . 96237 E = 511. 88958 The bi's were significant at 10 percent level or above for K, VK, VNP, VNK,-VPK. Marginal physical products of N, P and K were all significant at the 5 percent level of higher for the mean treat- ment level. The attempt to determine the high-profit solution using this THEE E» 26 equation proved to be unsuccessful. Solution in ordinary matrix form of the partial derivatives of the main soil nutrients yielded solutions for VN and VP in terms of minus quantities. Discussion with Dr. R.L. GustafSon, Department of Agricultural Economics, Michigan State Univer- sity, has led to the realization that while such results are mathema- tically consistent they must be interpreted as are negative values obtained in the quadratic form of the polynomial. That is, the actual optimum in such cases is zero, since negative values are inadmissable. This situation occurs a number of times in this project and may be due to the relatively low levels of treatment, or in some cases the exis- tence of large within treatment variation, resulting in unreliable and/or inconsistent 2 values. Further discussion of this problem is included in Chapter IV. The indicated optima of 0 lbs. N, 0 lbs. P and 24 lbs. of K varies amazingly from.that indicated by equation (22). This writer has not yet been able to offer a satisfactory reason for this difference. Tioga Silt Loam 1954..Location 2 (2h) ? = 275.42 - 1.21m + 36.78P + 33.91K + 7.69NP + 1.38NK + 2.85PK - 3.98N2 - 6.LSP2 - 4.60K? 22 = .16425 E = .68136 s = 95.67229 The bi's were significant at the 10 percent level or above for P, K, NP, PK, P2, K2. Marginal physical products of N, P, K, were not signi- ficant at the mean treatment level. This equation yielded solutions at the high-profit point, N = 3&8 lbs., P 8 329 lbs. and K - 244 lbs., which were in excess of the main treatment levels. This fact along with the non-significance of the MPP's limits the value of the solutions for m 1 4 27 direct application. An interesting observation in this case is that P, which on the first Tioga location had an individually depressing effect on yields, has a strong positive relationship with yield. The reverse is true for N in this location. This may be due to one or a combination of factors such as soil identification, high or low soil test values for particular nutrients, or a large amount of within treatment variance. Certainly, one must raise the general Question of the relevance to the Tioga silt loam soil universe of the two locations represented here, where basically different responses are observed. Indeed, this Opens up an area for consideration with reSpect to the validity of small controlled eXperiments for broad soil classifications. (25) T = 361.25 - 8. 68N - 22.2213 - 27.8w - 6.16m + 1935/P + 33.03vK + A2.1LVNP + 26.00%NK + 23.h5VPK R2 R .hh562 .66755 S = 97.32226 The bi's were significant at the 10 percent level or above K, VNP, VPK. Marginal physical products of P and K were significant at the 5 percent level for the mean treatment. The high profit solutions for this equa- tion yielded minus values for-VN and VP, while only a very small amount of K, less than a pound, was indicated. As yet there does not seem to be an explanation of why these results differ so much from those obtained from equation (2h). 28 Honeywood Silt Loam 195A, Location 1 (26) i = 318.53 + 23.65N + 20.65? + 23.75K + 3.35NP - 2.09NK + 3.13PK - 3.67M2 - 1.5582 - 3.62K2 82 = .39931 R = .63193 S = 52.62539 The b 's were significant at the 10 percent level for P, K, PK, P2, K2. 1 Of the marginal physical products only K yielded a significant value at the mean treatment level. High-profit solutions within the range of treatment levels were found for 6h combinations of PY’ PN’ PP’ PK' The full list is shown in Appendix C. In the common price situation, the solution calls for the application of 99 lbs. of N, 123 lbs. of P and 103 lbs. of K. This would be approximated by the application of 1000 lbs. of a 10-12-10 formula fertilizer. While the series of high-profit solutions indicates some minor changes in the level of nutrients required these are not considered to be as significant in this case as the pro- portions indicated. The amounts of fertilizer suggested are quite close to the general recommendations for P and K, but higher for N. (27) ?‘= 378 - 17.01N - 23.19? - 26.6OK + 37.99VN + 31.01v2 + 15.13% + 13.931/NP - 1.5mm + 23.1mm R2 . 56216 E The bi's were significant at the 10 percent level or above for P, K, VPK. Marginal physical products significant at 5 percent level for P only when tested at the mean level of treatments. This equation also yielded a full set of high-profit solutions. However, a much lower level of application was indicated, at the same price combinations, than by 29 equation (26). At the same price levels as noted above the high-profit solution calls for the application of 18 lbs. N, 66 lbs. P and 18 lbs. of K. The proportions indicated are, however, quite similar and the recommended application would be approximated by the application of 500 lbs. of a 10-13-10 formula fertilizer. Again in this case minor changes in the levels of application are indicated at various price levels with the range being proportionately greater than for equation (26). The high profit level amounts are lower than general recommendations for P and K, but very much in line for N. There are no firm grounds for expressing greater confidence in the results of one eouation as compared to the other. However, the square root polynomial does have a much larger Hz value and would appear to more fully explain the relationship between yield and applied nutrients. Honeywood Silt Loam 1955. Location 2 (28) T = 115.51 + 5.12m + 31.67P + 69.93K + 1.38Np - 1.89NK + 1.53PK - 1.97N2 - 5.57P2 - MW2 82 = .56216 R = .71918 S = 66.91608 The bi's were significant at the 10 percent level or above for P, K, P2, K2. The marginal physical product of K was the only one significant at the 5 percent level or above for the mean treatment level. Analysis of this function yielded a full set of high-profit point solutions all within the range of observed treatment levels. At the common prices noted previously an application of 91 lbs. N, 130 lbs. P and 1L3 lbs. K was indicated. A full set of the solutions may be found in Appendix C. At this location quite large changes in the requirements THESIS 30 of N are indicated in response to price changes, while the other two nutrients vary within narrower limits. These findings are consistent with the general recommendations for applications of N, P and K, depending on past crOpping history and soil test values. (29) T’ - 175.39 - 9.78N - 35.25P - 32.12K - 5.19/N + 66.1OVP + 127.00/K + 23.67VNP - 1.57VNK + 17.69/PK 82 = .61162 R = .78206 S = 62.98658 The bi's were significant at the 10 percent level or above for P, K, VP, MK,'¢NP,-VPK. The marginal physical product for K only was significant at the 5 percent level or above for the mean treatment level. This equation yielded a full set of high profit solutions which indicated considerably lower requirements of N and P than equation (28), but indicated virtually the same application of K. The application at the common prices used for illustrative purposes was determined to be 56 lbs. N, 93 lbs. P and 112 lbs. K. It should be noted that in addition to some differences in the amounts indicated the proportions are quite different. Here again it is difficult to indicate which equation provides a more reliable solution. The square root polynomial includes more significant variables and has a slightly higher R2 value. Also, the marginal physical products are more likely to be significant for the lower levels of application determined by the square root equation. However, both fall within the rather broad limits of general recommend- ations. TH E518 31 Brighton Fine Sandy Loam 1954 (30) ? = 316.12 + 23.21N + 21.71P + 52.51K + 6.17NP - 6.86NK + 1.33PK - 0.68N2 - 5.10132 — 1.63K2 82 = .75882 a = .87110 e a 51.09312 The bi's were significant at the 10 percent level or above for N, P, K, NP, NK, PK, P2. The marginal physical product of N and K are sig- nificant at the 5 percent level or above at the mean treatment level. This equation also yielded high-profit solutions for the prices used, which were within the range of observation. At the common prices used previously the indicated application is 131 lbs. N, 159 lbs. P and 185 lbs. K. The variations in indicated applications are quite small over the price changes, which again stresses the importance of proportions relative to variations in quantity. The amounts are near the upper limit or above the general recommendation levels for unma- nured soils, and above those for cropping histories other than conse- cutive potato crops. (31). f = 332.17 - 2.28N - 25.70p + 1.39K + 37.197N + 11.21v2 + 61.ABVK + 25.87VNP - 23.65vNK + 15.01VPK 2 E .76933 .87112 5 = 19.96869 FUI I The bi's were significant at the 10 percent level or above for P, VP, VK,'VNP, VNK, VPK. The marginal physical products are significant at the mean treatment level for N, P and K. This equation yielded high-profit solutions for the prices noted earlier, which indicated applications of the nutrients far in excess of observed treatment levels. The common price solution was N = 1312 lbs., TH L‘S‘ J 32 P = 709 lbs. and K = 503 lbs. There seems to be no good reason for the very large difference in the solutions from equations (30) and (31), except that the square root transformation may possibly affect the slope of the regression line. Experimental Design 1955 and 1956 The form of the experimental design was changed for the continu- ation of the project in 1955 and 1956. The design was basically a 3 x.3 factorial, replicated three times, with treatment levels of 0, 50 and 100 lbs. of P and K, and 0, 25 and 50 lbs. of N. In addition six larger treatments (replicated three times) were used as follows: .11.. .13. .15.. 50 100 200 50 200 100 100 100 100 150 300 0 150 O 300 150 300 300 The change was made by researchers in the Department of Soil Science, Ontario Agricultural College, and their explanation of the additional observations was "to explore limit effects". Further, in 1955, only the Honeywood silt loam soil type was repeated, at a different location, while two different soil types, Guelph sandy loam and Fox loamy sand, in different counties were selected for experimental locations. In 1956 the same design was used on another Honeywood silt loam location as well as those on Fox sandy loam, Bookton loam and Tioga loam. The researchers in the Depart- ment of Soil Science, Ontario Agricultural College, prevailed in the selection of soils and the opinion that the 1!»! as?! S 33 nwst important mineral soils for the late potato crop had been covered by this selection. Hongywood Silt Loam 1955 (32) T = 311.21 + 13.30N + 1.56? + 5.23K - 0.88NP + 0.82NK + 0.21PK - 5.97N2 + 0.60?2 - 0.38K2 2 .175193 .689312 S = 15.35969 :0! ll :0! II The bi's were significant at the 10 percent level or above for N only. The marginal physical product of N was significant at the 5 percent level for the mean treatment. This equation yielded a full set of high-profit solutions. At the same price levels as used previously for illustrative purposes the high profit solution indicated the application of 10A lbs. N, minus 19 lbs. P and 219 lbs. K. This would have to be interpreted, in terms of prac- tical application, as requiring a fertilizer with only N and K present. The amount of N indicated is at the upper level of general recommen- dations while the amount of K is far in excess of recommendations. The full range of solutions is shown in Appendix C. (33) T’ = 322.06 - 2.75N + 6.15? - 1.63K + 11.79VN - 6.70v9 + 1.69/K - 2.36VNP + 3.LZVNK + 7.09vex 22 = .155899 E 2 .675203 8 = 16.185923 The bi's were significant at the 10 percent level or above for VN and ‘VPK. The marginal physical product of N was significant at the 5 per- cent level for the mean treatment. This equation yielded high-profit solutions for N and K while indi- cating minus values for 1/P. However, the value for N = 635 lbs. was far 5 T H v. -1“ BA in excess of treatment levels while those for K = 225 lbs. was approa- ching the upper limit of the additional treatments in the eXperiment. Accordingly, it was felt that no results useful for direct application were obtained in the analysis of this equation. Both equations indicate quite large amounts of unexplained vari- ance, a problem which appears to be a major one in most of the results reported here. The effect of this variance on the coefficients of the independent variables may in part explain the poor results using the square root polynomial which occurred in this instance and have been a recurring problem. Guelph Sandy Loam 1952 (31) i = 117.22 + 17.35N + 9.71p + 12.15K + 2.33NP + 1.27NK - 1.26PK - 6.82N2 — 0.11?2 - 0.01m2 R2 .130817 .656389 S = 35.73h96h A The bi's were significant at the 10 percent level or above for N, P, K, PK and N2. The marginal value product of K was significant at the 5 percent level for the mean treatment. This equation yielded solutions at the high-profit point for the prices used heretofore, which indicated 90 lbs. of N, 310 lbs. of P and 101 lbs. of K. The amount of P indicated is in excess of treatment jlevels and therefore limited in validity. However, the amounts for both.blenni K are within observed lindts and may be considered valid. Very little variation was found in amounts of N indicated over the various price levels used. The optima for P were quite stable, while those for K ranged as much as 25 percent from low to high price levels. General recommendations concur with the findings for N and K but are 35 mudilpwer than the amount of P indicated here. (35) i‘ = 160.19 - 16.06N + 1.88P + 6.20K + 15.175N + 15.25v? . 18.29/K + 0.16VNP - 5.20%NK - 2.16v9K E2 E .110658 .663815 S = 35.125892 The bi's were significant at the 10 percent level or above for VN and VNK. There were no marginal physical products significant at any reasonable level for this function. The coefficients of both P and K are positive in this case which would indicate that the law of dimi- nishing returns was not observed and, accordingly, optimum levels could not be determined. It would appear that the range of treatments was not high enough to furnish conclusive eXperimental evidence in this case. Fox Loamy Sand 1952 (36) 9 = 120.90 + 0.53N + 9.35? + 1.89K + 1.65NP + 1.56NK - 0.118K - 1.68N2 - 0.87P2 - 0.18K2 R2 = .211210 8 = .191162 S = 31.923977 The bi for P was the only one significant at 10 percent level or above. None of the marginal physical products were significant at the mean treatment level. While a full set of high-profit solutions were computed the results indicated applications of P only. Solutions for N and K20 were nega- tive under all price situations. The solution at the common price level Luuxi‘throughout was -8 lbs. N, 125 lbs. P and -117 lbs. K. This would be interpreted as indicating a requirement for P alone, with the Optima for N and K at the zero level. 36 A possible reason for the lack of reSponse observed here is that a number of areas in Ontario experienced very dry conditions from May through July. Such weather would have a marked effect on a very light soilimum as Fox Loamy Sand. General recommendations would be too high.fln'this type of soil, particularly in a dry year. 120.96 + 9.3111 - $th + 2.28K - 111.89s/N + 19.68%? - (37) Y = 0.61VK + 3.99VNP + .89VNK + .6BVPK 82 = .212871 E = .192819 3 = 31.889616 The only bi significant at the 10 percent level or above was for W. None of the marginal physical products were significant at any reason- able level, at the mean treatment application. Solution of this equation for high-profit applications yielded The level of treatment indicated at the positive results for N and_P. In previously used common price level was 12 lbs. N and 51. lbs. P. view of the problem of significant p values it may be that the recommen- dation for P is the only significant one, and it is only 1.3 percent of the amount indicated by equation (36). In this case it tends to confirm the findings of equation (36). Analysis of Experimental Results for 1956 The experimental design was not changed for the 1956 eXperiments. Since 1955 was considered to be a "dry year" during parts of the production season, the poor eXperimental results did not indicate a need for any change in the design or treatment level. However, different locations were used and only one soil type was repeated. 37 Honeywood Silt Loam 19L6 188.35 + 35.92N + 18.LOP + 38.62K + 3.03NP + 2.31NK - (38) ? == 2 - 1.95?2 - 2.66K2 82 .593119 .770337 8 = 62.026951 :0) l Thetfifs were significant at the 10 percent level or above for N, P andIL Marginal physical products were significant at the 10 percent level or above for N and K. A full set of high-profit solutions was computed for this equa- tion. In general the results tended to be above the factorial treat- ment levels but within the extended limit levels. The common price solution was 137 lbs. N, 195 lbs. P and 226 lbs. K. All of these amounts are in excess of general recommendations. A question exists as to the validity of a level of application of 195 lbs. P which is more than three times the mean treatment level based on a non-signifi- cant marginal physical product. Indeed, the marginal physical products should be tested for significance at any suggested level of fertilizer .application, but as noted earlier the computational problem was too great to permit this. 186.85 - 13.20N - 12.0hP - 2.15K + 51.79VN + 30.61%? + (39) ‘f = 59.1298 + 13.56VNP - 2.60vNK + 5.39/PK 52 = .591191 E - .769085 8 = 62.173810 The bi's were significant at the 10 percent level or above for N, ‘VK. Marginal physical products were significant at the 10 percent level or above for NandK. (I) 1Has1 38 While this equation yielded a full set of high—profit solutions, these solutions tended greatly to exceed the levels of eXperimental treatment. Only the indicated application of N fell near the upper limit of exnerimental observation and it tended to vary widely under differing price combinations to levels nearly double those in the eXperiment. Accordingly, it is considered that these results indicate the necessity for eXperimental results from higher levels of treatment before general recommendations can be given with confidence. However, the evidence indicates that higher than recommended rates were justi— fied in this instance. Fox Sandy Loam 1956 (10) f’ = 200.12 + 12.32N + 17.71? + 5.50K + 1.15NK - 0.19PK - 2.86N2 - 1.53122 - 0.57K2 R2 = .325078 R = .570156 3 = 38.012800 The bi's were significant at the 10 percent level or above for P and P2. Marginal physical products were significant at the 10 percent level for P only, at the mean treatment. This equation did yield a full set of High-profit solutions as given in Appendix C. At the common price used previously, the high- profit application would be 129 lbs. N, 178 lbs. P and 198 lbs. K. The indicated applications did not vary more than 5 - 10 percent over thef price ranges used. The amounts indicated at the high-profit point are all in excess of general recommendations. However, the low value of P2 indicates the need for experimental results in which the applied soil nutrients eXplain a much higher percentage of the variations. 39 192.1.0 - 11.37N — 6. 58P + 1th + 28.55141 + 37.761/P + 11.14% + 3.251/NP + 1.61.1/NK — 0,871/FK 82 - .312967 .585631 5 = 37.505675 FIJI l Thetfifs were significant at the 10 percent level or above for VP. The marghwfl.physical Product of P only was significant at the 10 percent levelcn'above for the mean treatment. This equation yielded positive solutions for high-profit levels At the common price used for illus- of application for N and P only. tration the indicated application was 27 lbs. N and 172 lbs. P. Appli- cations of N indicated were lower than for equation (10) and varied quite widely, while the indicated applications of P are very close to those derived by equation (10). Both equations have low HZ values, indicating a large amount of unexplained variance. Accordingly, high-profit point solutions may in reality be quite inaccurate estimates. Bookton Loam 1956 101.h7 - C.67N + 32.52P + 9.55K + 3 63NP + 2.A3NK - 0.1APK (121 ?= - 2.35N2 - 3.28P2 - 1.29K2 82 = .751688 a -- .866999 5 = 26-65'7 The bi's were significant at the 10 percent level or above for P, K, NP, NK, P2 and K2- The marginal physical products were significant at the 10 percent level or above for N and P. ‘This; equation yielded high-profit solutions indicating applications of the fertilizer elements far in excess of the treatment limits for all nutrients. The function does provide information that P and K are L0 posfidvahrassociated with increases in yield, while additonal amounts oflflnayrmye a depressing effect. These are significant observations 1michene reinforced by the high level of H2. Higher treatment levels couldtxaexplored in further eXperiments. (13) if = 102.78 + 1.2911 - 15.71? - 5.90K - 6.21m + 61.1.61/P + 15.llVK + 8.A9VNP + h.37VNK + 5.18vPK fiz .771530 E .880071 3 = 25.391501 The bi's were significant at the 10 percent level or above for P, VP, vK, VNP and VPK. The marginal physical products were significant at the 10 percent level or above for P only. The high profit point solutions gave minus values for VN, VP and VK. These are interpreted as indicating a 0 - 0 - 0 application which is directly opposite to the high levels indicated by equation (12). It is further evidence of probable limitations of the square root functions for certain types of data, for which no explanation has been found by the writer. Tioga Loam 1956 (1.1.) i? = 123.01 + 53.3111 + 27.0513 + 39. 98K + 5.05m» + 1.11118 - 0.09PK - 10.92112 - 3.12?2 - 3.62K2 82 = .661815 R = .815362 8 = 66.332803 The bi's were significant at the 10 percent level or above for N, P, 2 2 K, D) , F’ and K2. The marginal physical products were significant at the 10 percent level or above for N, P and K, at the mean level of treatment. 1.1 This equation yielded a full set of high-profit solutions. However, these solutions tended slightly to exceed the levels of the experiment. For the common price situation the application of 156 lbs. N, 233 lbs. P and 226 lbs. K was indicated. These do not appear to be unreasonable treatment levels, but since they are near the upper limits of any experi- mental treatments it would be reasonable to place more emphasis on the proportions than on the absolute amounts. That they exceed general recommendations may be an indication of the need to confirm these results as a base of future extension information. However, the levels of signi- ficance associated with the coefficients of the independent variables and the reasonably high value of E2 provide a strong indicationrof the importance of all three nutrients in this case. It appears here, as in several other cases, that a broader range of eXperimental treatments might have yielded very valuable information. (15) i = 139.06 - 7.00m - 19.88P - 19.211 + 11.59VN + 19.10v9 + 66.27% + 17.17%)? + 15.85/NK + 13.171/PK 82 - .685333 .827818 8 = 61.270189 :0) l The bi's were significant at the 10 percent level or above for P, K, W, A and WK. The marginal physical products were significant at the 10 percent level or above for N, P and K. This equ'tion was another of those which have yielded negative values for N, W and x/K. General Conclusions Throughout this section, which reports in detail the results of the analysis of the experimental data, several types of problems have 1H PICS-‘5 #2 endemiat one point or another. These include: low levels of signi- fumpamaof the coefficients of the independent variables; low values fin'fiz,vmich measures the percent of squared variability in the depen- dent*wndable that is explained by variations in the independent vari- ables;the inability to derive high—profit point solutions for some of the ammue root polynomial functions; the derivation of high-profit pohnLSOlutions far in excess of eXperiment treatment levels; the deter- nunation of very few significant interaction coefficients; vagueness as to the universes represented by the various sets of experimental data. These problems will be discussed in somewhat more detail in the follow— ing chapter. CHAPTER IV CONSIDERATION OF PROBLEMS ARISING FROM THE ANALYSIS The problems which are discussed in this chapter are not necessari- 1y unique for the project reported here. During the period since World War II the increased attention to the formal theory of production econo- mics in terms of its direct application to problems of agriculture has given rise to these problems in many cases. The purpose of this dis- cussion goes beyond this one experience in the h0pe that some broader insights may be gained which will benefit the work of others in this area. Comparison with Analysis of Variance The analysis of the data in this eXperiment was initially considered only in terms of the two types of production functions indicated so far. The disclosure of a relatively large number of,b values with very low levels of statistical significance as determined by the t test, raises the question of the desirability of using some method to pre-examine the variables which may be included in the functions fitted. While the level of significance considered to be necessary for inclusion of a variable is subject to arbitrary decision, some prior analysis could be carried out in a more simple form such as analysis of variance. While it is recognized that analysis of variance does not provide sufficient information of the kind necessary for economic decision- making, nor for deciding what variables to include, it does indicate whether or not significant differences exist in the response to various treatment levels. It does this for linear relationships, quadratic 1+3 THEE-‘53 1.1. relationships and joint products of any order, depending on the design of the eXperiment. At the same time it is recognized that the actual form of the production function is not indicated by this analysis. Also, the detection of significant differences for individual items does not assure the ultimate determination of a satisfactory production function or of significant derivatives of a function. After observingthe low levels of significance of several of the variables in most of the functions fitted, analysis of variance was carried out on the data for 1955 and 1956. This is shown in Appendix D. The levels of significance are indicated for the commonly used 5 percent and 1 percent levels, using the 3: test. Comparison between these results at the same levels of significance used in the quadratic polynomial are indicated in Table IV below. The quadratic form is used for compw arison, as it would be necessary to carry out an analysis of variance on the same transformation as the square root polynomial if any comparison with it were to be attempted. It must be made clear that Table IV does not imply that there should be an implicit coincidence of observed significant 1) values for data from these experiments have been forced into two Specific esti- mating equations. Rather, the suggestion is that strong evidence of significant statistical influence, which may be positive or negative, is suggested for certain terms by analysis of variance. The inclusion of a larger number of terms most probably results in a dilution of the measured effect of those most significant variables. This has been recognized by statistical writers such as Fox and Cooper/, who note, _]_../ Karl A. Fox and James F. Cooney, Jr. , "Effects of Intercorre- lation Upon Multiple Correlation and RegresSion Measures", mimeographed United States Department of Agriculture, 1951. Circular, TABLE IV - COMPARISON OF INDEPENDENT VARIABLES WITH 5 PERCENT OR HIGHER LEVEL OF SIGNIFICANCE AS DETERMINED BY CORRELATION AS ANALYSIS AND ANALYSIS OF VARIANCE EXperiment Analysis V a r i a b 1 e 8 1 K NP NK PK K2 Honeywood, silt loam, Quadr. 1955 Anal. Var. X Guelph, silt loam, Quadr. X 1955 Anal. Var. X Fox, loamy sand, Quadr. 1955 Anal. Var. X X Honeywood, silt loam, Quadr. K 1956 Anal. Var. X Fox, sandy loam, Quadr. 1956 Anal. Var. X Bookton, loam, 1956 Quadr. X X X Anal. Var. X X Tioga, loam, 1956 Quadr. K K Anal. Var. X X "Trained statisticians are also aware that increasing levels of inter- correlation are reflected in increasing standard errors of net regres- sion coefficients - that is, high intercorrelation tends to mean lowered :reliability for the individual regression constants". The introduction of intercorrelation influences not only the reliability of the _b_ values but may also lead to changes in sign. Since it was not the purpose of this thesis to pursue this subject in detail no attempt was made to reformulate functions offering more 16 gmsflfiyerelationships based on the clues provided by analysis of vari- anca. However, it is contended that this evidence leads to the con- clushxithat functions providing valid results for economic analysis coukinot be obtained from the experimental data used. The reason here nmy1flfll.be found in other areas such as the range of treatments, the sizecfiTplots or eXperimental techniques. The data for one location, Tioga silt loam - 1956, were recalcu- latedtxdpg the variables suggested by analysis of variance with the following results: (16) ’1’ = 161.60 + 25.67N + 36.92? + 10.6OK - 3.36P2 + 1. 21% All of the p values test significant at the 5 percent level or higher. It is interesting to note that the PK relationship indicated no discer- nible signficance in the quadratic function, as illustrated by equa- tion (AA). Further comparison indicates a marked change in the indivi- Certainly this new function, equation dual regression coefficients. 2 . . indicates (A6), is not adequate for economic analysis since now only P the effect of the law of diminishing returns. Whether there is any a priori basis for stating that this function more truly represents the .actual results obtained must be answered by someone with more statis- tical training than this writer. Negative High Profit Point Solutions to Square Root Functions A rnunber of the functions of the square root form yielded high- profit point solutions indicating minus values for W, VP and x/K. These have been interpreted here as being inadmissable solutions which should be regarded as zero level solutions for practical purposes. The reasoning 117 behind this as follows:-1-/ 1) I should be regarded as a quadratic function of the square ' _ 1 1 roots of N, P and K. That is, let N5 = X1, P?- = X2 and K5 = X3, then the function which is fitted is: A ' 2 2 2 Y - b0 + 61x, + b2X2 + b3X3 + bhxl + b5X2 + b6X3 + b7KlX2 + b8XlX3 + b9X2X3 Then it is the square roots (X1, X2, X3) with respect to which one is maximizing when solving the equations which determine the optimum treat- ments. 2) While mathematically the square roots (X1, X2, X3) can be posi- tive or negative, physically they must be non-negative. That is, the relationship one is actually fitting (the model) includes not only the above equation, but also the side relations X _>_ 0, X l 2 Or to put it another way, the X's are really defined as X1 = +N5, ZOandXBZO. X2 = +P‘:15 and X3 = +K2. This is clearly so, since it is always the posi- tive square roots of the observed data that one uses when fitting the equation. 3) Hence, having fitted the eouat ion and solved for the optimum, if the optimal square roots (Xi's) turn out mathematically to be nega- tive, the interpretation is the same as it is with other types of funct- ions: the actual Optimum is zero, since negative values are impossible. Lack of Joint Product Relationships Most studies by economists of agronomic data are replete with iso- product diagrams for various combinations of the basic fertilizer ;/ The author is indebted to Dr. R. L. Gustafson, Department of Agricultural Economics, Michigan State University, for this eXplanation. 1 L: 1:; ‘5‘- £3 1.8 In general these indicate that varying degrees of substi- nutrients. The functions tutability 0r complementarity exist among the nutrients. fitted to the eXperimental data in this thesis do not give strong evid- ence of statistically significant interaction relationships. Whether or not this is due to the small ranges of treatments in the particular experimental locations remains to be demonstrated by further eXperi- mental work. Consultation with the research staff of the Department of Soil Science, Ontario Agricultural College, reveals that their research has not yet disclosed significant interaction terms to any major degree. However, despite the relatively small number of statis- tically significant interaction coefficients the apparent effects of interaction were noted in at least two cases. In both equations (22) and (21.) where individual nutrients appeared to have an effect of de- pressing yields, the interaction terms were of sufficient magnitude to. yield positive marginal physical products for increments of the parti- cular nutrients. If these findings are valid then one must conclude that some interaction effects are present, if not adequately measured. Low Values of 82 The problem of low values of R2, indicating large amounts of unex- plained variation, may be strongly related to all of the problems dis- cussed above. This particular problem has been a characteristic of results from agronomic-economic eXperiments for a number of years in work carried out at Michigan State University, as reported by Hoffnar Since agronomic—economic eXperiments and Johnson-1], and elsewhere. l/ B. Hoffnar and Glenn L. Johnson, "Agronomic-Economic Experi- mentation at Michigan State University - A Summary Emphasizing the Cooperative Research with T. V. A. ", Agricultural Economics Mimeographed Report 888, 1962. THEQE‘; L9 were started at Michigan State University in l95h, a succession of experimental designs used with various cr0ps on several classes of soil have characteristically yielded low values of E2 and relatively few significant coefficients. At times the lack of homogeneity in soil types has appeared to be a problem, but the best efforts of the groups of researchers involved were not rewarded in terms of appreci- ably improved results. More recent exoeriments reported by Hoffnar and Johnson have indi- cated that the size of plot used in experimental work may be of major importance in reducing the unexnlained variance. Larger plot size, 1 acre for example, may tend to eoualize minor variations in soil type, a condition which apparently contributed to large amounts of within treatment variation when small plots, e.g. l/lOO of an acre, were used. This observation was supported by survey data collected directly from farmers and analyzed in the same manner as controlled eXperiments. In addition the larger plot size seemed to more clearly establish larger between treatment variation. In the Ontario experiments high fiz values were obtained for several locations. At the same time, however, it is apparent from the analysis that the range of treatments limited the applicability of the results, and may have been a contributing factor to the small amount of unex- plained variance. Representativeness of EXperimental Locations The selection of experimental locations has involved much time and effort devoted to the identification of small areas homogeneous with resnect to soil type. The heterogeneous results found in this 1g};$2:fi3 50 analysis, in those cases where more than one location was selected for a Specific soil type, raise questions with regard to their relation- ship to the universe of that soil type. Indeed, the low §2 values dis- cussed above may be partially eXplained by soil variation in even those carefull selected plots. One of the important aSpects of experimental work, its adaptabi- lity to farm eXperience, suggests that larger eXperimental plots, chosen as samples of a more clearly defined universe be considered in future research of this type. Farmers' decisions are almost always based on fairly large acreages which include and average out the variations which have become so evident in small plot experimentation. Larger plots on more locations, plus the inclusion of more of the causes of variability, e.g. soil test data, cropping history or rotation, weather variables, etc., in our models may contribute to more valuable results in terms of both applicability and lower unexplained variation. Other Factors Needing Study Other factors whidh may also contribute to reduced accuracy in experimental work are machine error, and the failure to consider cropping history and soil test values. On small plots machine error can grossly increase within treatment variation. While the role played by crOpping history and soil test values are not as yet fully resolved, logic dictates that there must be some significant relationship. It has been demonstrated by Hildreth and Rublel/ that soil test and applied K substitute in a ratio of 1:1. Clearly, there is need for more closely coordinated research if these problems are to be solved. ;/ See Hoffnar and Johnson, on. cit. 18193.5 CHAPTER V SUMMARY AND CONCLUSIONS As emphasized in the introductory chapter a major objective of this study was the encouragement of inter-disciplinary research in this area. This particular aspect of the study has been most success- ful in at least two ways. Firstly, the type of analysis carried out here and the reasons for it were not familiar to the soils scientists prior to this project. Detailed review of the methods and results of this analysis has resulted in both appreciation of and enthusiasm for its objectives. Secondly, the necessity of closer co-ordination in planning research and its associated problem of eXperimental design has resulted in close collaboration with soils scientists, economists and statisticians participating. In addition there has been recogni- tion that the need for changing the experimental design could result in superior results for the individual as well as joint interests of the researchers. The foregoing does not mean that practical results from exneri— mental co-Operation have yet been achieved. Although this situation is unlikely to obtain until more conclusive contributions to the general field of exnerimental designs are forthcoming significant progress is being made at Ontario Agricultural College and Michigan State University. All participants recognize that the statistician is not yet prepared to offer methods assuring entirely satisfactory results to research groups with diverse interests. However, in the present case it is possible to point directly to the eXperimental design currently being used for 51 1H iii-3'25 52 fertilizer resnonse studies and its increased potential for economic analysis. This design is given in detail in Appendix E. Its essen- tial features are directly influenced by the findings of the research reported in this thesis in two major ways. Firstly, the treatment levels have been increased in an attempt to establish definitely Upper reSponses. Secondly, a central composite rotatable design is included in the main eXperiments in an attempt to determine more accurately quadratic resnonse surfaces. While there is a mutual feeling that we are still doing exploratory work there is nevertheless a strong senti- ment of achievement in the joint understanding of the research to be undertaken. The size of plot in these experiments is still of the small plot pattern of conventional practice. The findings of the 1961 experi- ments at Michigan State University and their further experiments in progress in 1962 may provide positive guides to our future work in this area. As a contribution to scientific knowledge in the area of economic analysis, the method of determining the statistical reliability of marginal physical productivity estimates was develOped and tested in this study. While the applicability of the results for general ex- tension purposes is in this case limited by the nature of the data, due in part to the unexplained variance as well as to questions of repre- sentativeness of the results, the method is clear and its application in other types of studies as well as further studies in the same area should contribute to the potential value of all such work. Problems which arose in some of the analysis pose questions which should receive the attention of statisticians interested in the derivation of quadratic polynomial relationships from experimental evidence. Further, since 1H V i” 53 the S g; must be determined for each marginal productivity estimate, i an exceedingly tedious task by manual computation methods, attention should be given to computer programming of a more detailed nature for these kinds of estimates. The optimum use of eXperimental data can not be made until more adequate computer services are available. Another feature of this study is the inclusion of sets of high- profit point solutions for common ranges of product and factor prices. Previous studies have been limited to a small number of illustrative solutions of this type, again largely due to computational difficulties. In this instance the general formulation of such calculations was pre- pared for programming on Michigan State University's MISTIC computer and the full results as illustrated in Appendix C, were obtained. Here again a number of problems relative to the adequacy of the data were raised. Such problems must, however, be considered as a positive contribution to the sum total of knowledge in this type of research. Despite the inadeouacy of the results for general public distribution, informal use of the information obtained, has produced satisfying results as a basis for further experimental work. To place any credence in high-profit point solutions, two charac- teristics seem required, statistical significance and representativeness of the results. In most cases only minor changes in the quantities of nutrients Specified were obtained when either prices of the product or prices of the factors were varied. Even in the two cases where fairly large changes were indicated, the dollar cost of such changes are rela- tively small and if one considers the variability due to such non- measured variables as weather the importance of such differences seems rather small. However, an indication of optimum levels of application SA is important information. Probably more important in this study is the indication of the proportions in which the fertilizer elements should be applied. It is the opinion of this writer that this latter finding is relatively more important than the small changes indicated in Optimal amounts. Despite the limitations ascribed to the data for purposes of eco- nomic analysis, it would be unrealistic to overlook certain relevant findings which have bearing on further agronomic-economic experiments and, as well, on the validity of current recommendations to potato growers. A summary of the primary observations of yield response to applications of N, P and K for all experimental locations is concisely indicated in Table V. As is readily seen in Table V the nature of the treatment reSponse varies from soil type to soil type and from year to year. Only one soil type, Fox sandy loam, shows a consistent relationship for the two years in which it appears. That these two years include a dry year, 1955, and a normal year, 1956, further emphasizes this one consistent relation- ship. Relationships such as those indicated for the two Tioga silt loam locations in l95h pose some questions as to what universe is being sampled. It is not logical to discover directly opposite results to applicationsof N and P on soils selected from the same universe. Indeed the whole puestion of the ability of small sample areas to provide data representative of a Specific soil type for large area plantings of any crop merits serious eXperimental investigation. In particular, the mineral soil areas of Ontario where most of the late potatoes are grown are characterized by a wide range of soil types with very small irregu- lar patterns of distribution. Past history of research on this crop 55 mNN I o I m3 an uncommon announce uncommon pcwowMflcmflm acmoHMficmwm o>wuamoo Emoa saw I o I moa .a on 0: swan aaam voozemco: mama new I och I mama A9 uncommou uncommon oncoommp o>apwmoo o>fipwmoa o>wpwwoo Emoa hogan mma I oma I HmH .a x2 .az sea: am“: new; scam copzmacm amoa Ned I mo I on an omcoomog oncoamop omcoommg N cowpmooa o>wpflmoo o>wpwmoa endowmwcuwm .Emoa sea I OMH I as .a new; new; 0: saam coozsoco: awed we I we I me An omcoomou omcoommp omcoommp H gowpmooa xm o>fipfimoa o>wpwmoa pcmowmwcuwm .stH moa I mma I so Am new: swag o: pawn coozsmco: smoa o I o I 0 AD oncoamoh uncommon mm omcoomou o> amoa pcwofimwGMwm N :oappooa saw I man I mam is .>asamoa as. as .saoa saw. .moaa awed am I o I 0 an uncommon oncoammh omcoommu mm o>wuwmoa pcmofimwcmfim o>fipflmoa H coepmooa Hmm I see I was Ami swag 0: swan .aaoa saam amoae awed I I I.mDH I I I a a z mpcdose mcowpompouCH x a 2 meme Hfiom has» Ismaseapao vapcaoaaacmam somoHIamoH .x 22¢ a .2 ca mmzoammm mamH» oeaeoa ac mzoae<>mmmmo emasza I > mamae C 1H}: ‘IJE: K II .um xa a n h HofiSOChHoo goon oposoo one kn pondEpouoo mo An A I A I A o I o sea I m uma I m om as I m ooownd 205500 on» now A Howaonhaoo owuouposc on» an pocwanopop mo Ao *** .o>ono no Ho>oH pnoopoo 0H one up ucoofimwnmwo ** .oocoaoon o>pwmoo nuwn o poponmwoop ofl o>ono no Ho>oH acooooa m one no unoowmwcmwo ono onnz .o>wpflooa no poponmwmop ow Ho>oa anoouoo OH on» no pcoowMHnwwo oonoooou o a o I o I 0 An oonooooh oncoomou oonoamoo o>HpHooo o>wpwooo o>wpfiooo saw I mmm I oma .a swan swan swan eaoa amoae omma o I o I O AD oocoooop oncoooou oncocooh n2 .az asapamoa m>asamoa pcmoaaacmam Hmo I amp I mmo «a swan .nmac 0: saoa copxoom omoa o I mod I pm An oncoooop oonoomog oonoaoou a» scaoaaacmam o>aaamoa pcaoaaa:Mam mma I mad I mma Am 0: swan 0: eaoa macaw woe omoa mmoMI mom I ova An oonoaoon oncoooop o>fipwmoa oncoomoo o>fipwooa Eooa omm I mad I ema nm swan m>apamoa swan saam noozemcom omaa o I Ho I NH an oonoomop oozedoop oonoaoou pnoowmwcmflo o>wpfiooa anoowuflcwwo o I mma I 0 na on can; on scam sewed won mmoa how I mmNoI mm «D oonoaoop omnoaoop ooCOQoou mm o>wufimoa o>fipfioon o>wufiooa sooa Hoa I can I om Am now; swan swan magma sedans mama oosnfiunoo I > mqm >m wOp mm mm Ooaloowlooa pmm m.m> pm OOanoatooa pm; so am and m.oo em ms IOQNIooH own me my ooauo new mom m: an 55m Mm pm Om IOONIOOa mmN m.>N Om Om IO IO mam pm mm pbm Np mm mm IOONIOOa awn m.mp Om Om IOm Iooa uma ma mm bqa mm Oq O loomlooa mpm m.N¢ Om Om IooaIOm >45 m.4m mm 5mm mm mm OONIOONIOOa mda ma pm O IO IOOa Nmp m .pm pm Nmm m .mp 4N oomlooaIOOa Oma pa pm 0 IooaIO mpp m.Oo mm amp om mm OONImb IOOa mam m4 mm ooaIOm IO pmp pm pm app pm NN OONIOm Iooa Nmm 4p mm OOaIOOaIO NNp mp mm bmp mm mm OONImN IOOa mam mm mm Om IO IOm N54 m.4p mm mam 4b mm OONIO IOOa mpm pp Nm Om IooaIOOa bmp mm mm man mm mm OONIOONIOON use m.mm mm ooaIOm IOm >45 NOa mm mmp m.op pN oowloomlooa mpm m.4m mm Om IOm IO 4mm m.pm mm aOp m5 mm OONIOONImb map mm mm OOaIO IOOa amp mo mm Opp mm mm OONIOONIOm ppm m.Om mm O IOm Iooa 0mm m.mv mm Nam up om OONIOONImN ham mm mm O IOOaIOm NOm m.mp mm umq mm mm OONIOONIO NmN m.Nm mm O IO IO whom\.mpa mpom\.mna .om\.m:p poaa\.mna 9:500 .om\.m59 poaa\.mpa mpcsoo x m z .oM\.m:p poaa\.mna pnsoo x m z mmopmpoa mo sauna acmsm mmosmsoa so mamas ecmsm semapampe weepmsoa mo cama» ucmsm semapmmpe .dmma I a 2023604 .58 Human «OOHB I magma A mam: 63 ppm m.m< mm ooaIOm IOm Omm pm pm. Om IooaIOm bpa ma mm 0 IO IOm mam am mm O IOOaIO .om\.msn u mamma. x wmmmw.MMMpm smm mm am om Io Iooa pmm me am ooan Io mmm mm mm O IOm IOOa pOm m.a4 am ooanoanoa aOm m.mm ON Om IOm IO map Om am pmp m .Np 4N OONIOONIooa aOm m .Np mm OOHIOm Iooa 0mm mm. mm Ohm ON. am ooaloomlooa ova m .ba mN O IO Iooa pap Np pm bmq pp mm mm IOONIOOa mp4 >4 pm ooaIO IOm 44m me mm 0pm am am On IoomIOOH son m.ps mm em IooanoH aom mm am Nnm up on mm IOONIOOa mp4 m.ap «N O IOm IO Nmm mm Om ooa ON hm O IOONIooa pam m.0m mm Om IO IO up; m.bm mm aap am pm OONIOONIOOa ppq m.mp pm Om IOm IOm Ohm mp am Nwm mm mm OONIooaIOOa own 54 am ooaIOOaIO pmm mp am pmq mm mm OONImb IOOa Owe m.>< mm O IooaIOm mpm m.>m mm Opp m.mp hm OONIOm IOOa pmm mm mm ooaIOm IO N>N mm mm mmq 4m mm OONImN IOOa omq mp 4N O IooaIOOa mma ma pm mmm mm mm OONIO Iooa Oaa m.ma om I Om IOm Iooa amp pp pm bmp m.mu am OONIOONIOON mam mm pa OOaIOOaIOm 40p mp 4N bmp Om Om OONIOONIOOa Omm a4 Om Om IO IOm mam om OJ pmm mtpq Nm OONIOONImNI NNm am am ooaIO IOOa pm; mm mm amm mm , mm OONIOONIOm aaa m.p4 mm Om IOOaIO pmm m.Op mm mam Nm pm OONIOONImN 04m 4m mm O IO IO Nam pm um pom mm mm OONIOONIO mmm m.04 om O IOm IOm whom\.mna opom\.mna .oM\.m:p poaa\.mpa #2900 .om\.m:p poaa\.mna assoc x m z .om\.m:n poaQ\.mna pcsoo m m z mmOpmpom mo papa». vcmpm mmOQmpom mo papa». pampm pcgpwopa mmofiwuom mo Gamay. pampm acmefimmpe .san I m zoaeaooq .xaog aqu auoHe I mau>mu.q mgmma a mamma a<92m2ammmxm e< OOQMH» mmo< mam I xa mamma aI>\»\pcnc>c>I>xo\o 218.6 73 TABLE XVII - PER ACRE YIELDS AT EXPERIMENTAL LEVELS - TICGA LCAM - 1956. Treatment Yéeldsper acre eplications N P K 1 2 3 1bs./acre busg/acre 0 0 - 0 129.3 255.8 149.9 0 0 - 50 178.8 191.1 262.6 0 — C - 100 189.8 163.6 195.3 0 - 50 - 0 187.0 203.5 143.0 0 - 5C - 50 184.3 182.9 148.5 0 - 50 - 100 162.3 259 9 303.9 C - 100 - 0 145.8 192.5 159.5 0 - ICC - SC 405.6 279.1 275.0 C - 1C0 - ICC 192.5 368.5 191.1 25 ~ 0 — C 193.9 162.3 162.3 25 - 0 - 50 125.1 167.8 176.0 25 - 0 - 100 173.3 397.4 347.9 25 7 50 - 0 143.0 203.5 275.0 25 - 50 - 50 303.9 376.8 365.8 25 50 - 100 254.4 446.9 374.0 25 - lCO - 0 147.1 204.9 184.3 25 - 100 - 50 358.9 398.8 319.0 25 - 100 - 100 407.0 279.1 413.9 50 - 0 - 0 239.3 242.0 140.3 50 - 0 - 50 254.4 390.5 145.8 50 - 0 100 253.0 431.8 170.5 50 - 50 - 0 276.4 214.5 262.6 50 - 50 - 50 374.0 356.1 313.5 50 — 50 - 100 500.5 451.0 423.5 50 - 100 - 0 269.5 218.6 233.8 50 — 100 - 50 391.9 343.8 379.5 50 — 100 — 100 409.8 336.9 397.4 50 - 10C - 200 426.3 500.5 468.9 50 - 200 - 100 418.0 386.4 453.8 100 - 100 - 100 462.0 372.6 523.9 150 - 300 — 0 265.4 365.8 265.4 150 - 300 - 0 270.9 358.9 357.5 150 - 300 - 300 519.8 518.4 589.9 TH I28“- 5 74 A P P E N D I X B Regression Equations Derived from Experimental Location Yield Data - 1954 - 1955 - 1956 c! 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Oaa. pr. 5mm.m pmm.a me.N a mump.~ I mamO.H I ~2~H.> I aamm.o I eZHm.~ + asz.m + emp.mm + mop.OH + zmm.mm + mm.OOH I w Hmmv pmma I adoa paam u003hmco: Omchpcoo I. aHst mHmpe. —’ THE‘S‘S 84 mmmmm. I m OOmmp. I a SmOm m I m Sam. I «W HOmmop. I we K K K K Om. K Oa. x mo. K aO. mHm. Nam. Hap. mam. m-.m mNm.H mpm. 06H.H mao.H n» mm\&m.o I mZ\pp.a + m2\mm.m + x\Np.p + m\pm.mm + ZXmm.mN + MppIa + mmm.p I zmm.aa I Op.Nma I w Aapv 6 2.42m I ”Wm mOOOHm I %m 38.38 I m.mm mHoam. I m_ IHNNO. I a OONHO Om I m OOmNm. I mm 88m. I am K K K. K K K K Om. K K Oa. K mo. 6. HO. ppm. mm®.a Nwm. ppm. mpm. pmm. pmm.a amp.p 0am.a nu Nxbm.o I Nmmm.a I Nme.N I mmma.0 I mZma.a + mzmp.a + MOm.m + mpb.ma + zmm.Na + Na.OON I w AOpV OmmH I 56H .838 68a 82:28 I HHHBH EOE _ .\—L. 85 888 .O. 2.8. I O OmHOm.mm I .m mmpg . I «W pwmmb. I mm K K K K K K K Om . K K K K K Oa . K K mO . K K aO . mpm .a Opm . ppm .a m.mm .a amp .N. pmp . mpp .a mom . m N: . 9» animpm + m§>m.p + mimm + x\pa.a.ma + Spap + z\aN.p I moom I mahma I zoma + mafimoa I w Ampv Q Q Gamma I Hm I 8S3 I Km m 88m... I Mm m OOOOO. I m. mmOOO. I O 8% ON I m $5. I NO $3. I NO K K K K K K K Om. K K K K K K Oa. K K K K K mo. K K K aO. me.O pOH.m OHO.H Omm. OOO.H mOm.~ HOp.m mmO.HH OHH. ma NORA I NOOOm I mama I 535 I O29...” + Ozmmm + Ommm I Ommam + OS. I 342 I m 3.: pmma I awoa copxoom Omschcoo I HHHOO OHOOH 86 pa.aa I m. OOomm. I Om OOHN.H + mOmm.m I OOO.OH + ONO.Om + zam.mm + OO.HOH I w Hmpp mmmmm. I m NHmpm. I O macaw pm I m. mmmOO. I Om mOpHO. I NO K K K K K K K K Om. K K K K K oa. K K mo. N HO. HOO.H Ham.H HHm.H Oom.m mmp.~ OON.H OOO.H mmO.H mOm. up OEXOama + xZXmmma + mgpéa + MXNINpp + m\.Op.mp + zxam .ap + gamma I mmm.ma I 200.5 I pomma I w“ Ampv . On . OO . ca mmbom m I Nd. m ppboo m I NW m Nmmmm Ha I a m mmmHO. I m mome. I O OOmmm pm I m. OOOOO. I mm. Ommmm. I NO K K K K K K K K Om. K K K K K K Oa. K K K K K m0. K K K K a0. mam.~ Omm.m ONO.H ama. NmN.H ~m4.H mma.m OOO.m msa.m ma ~O~O.m I NOmHm I O2~O.OH I OOOO.O I OOHp.p I O2mO.m + OOO.Om + OmO.OO I 2pm.mm I HO.m~H I m Asap OmOH I_EI6H Imoma pozzavcoo I HHHPN m.aa; —— THE?“ 87 A P P‘E N D I X. C High Profit Point Solutions 88 TABLE XIX - HIGH PROFIT POINT SOLUTIONS FOR FERTILIZER APPLICATIONS 0N HONEYMOOD SILT LOAM, 1954 - LOCATION 1 - EQUATION 26. P P P P N P X y n p k Dollars/bu. - - - Cents/1b. - - - - - 1bs./acre - - 1. 00 8 8 4 100 124 103 1.00 8 8 5 101 123 102 1.00 8 10 4 100 122 102 1.00 8 10 5 100 122 101 1.00 10 8 4 99 123 103 1.00 10 8 5 99 123 102 1.00 10 10 4 98 121 103 1.00 10 10 5 98 121 102 1.00 12 8 4 97 122 104 1.00 12 8 5 97 122 103 1.00 12 10 4 96 121 103 1.00 12 10 5 97 120 102 1.00 14 8 4 95 122 104 1.00 14 8 5 95 122 103 1.00 14 10 4 94 120 103 1.00 14 10 5 94 120 102 1.20 8 8 4 103 126 104 1.20 8 8 5 103 125 103 1.20 8 10 4 102 124 103 1.20 8 10 5 102 123 102 1.20 10 8 4 101 125 104 1.20 10 8 5 101 125 103 1.20 10 10 4 100 124 104 1.20 10 10 5 101 123 103 1.20 12 8 4 99 125 104 1. 2O 12 8 5 99 124 103 1.20 12 10 4 99 123 104 1.20 12 10 5 99 123 103 1.20 14 8 4 97 124 105 1.20 14 8 5 98 124 104 1.20 14 10 4 97 123 104 1. 20 14 10 5 97 122 103 1.40 8 8 4 104 127 104 1.40 8 8 5 104 127 104 1.40 8 10 4 103 126 104 1.40 8 10 5 104 126 103 1.40 10 8 4 102 127 105 1.40 10 8 5 103 126 104 1.40 10 10 4 102 125 104 1.40 10 10 5 102 125 103 89 TABLE XIX - continued 1.40 12 8 4 101 126 105 1.40 12 8 5 101 126 104 1.40 12 10 4 101 126 104 1.40 12 10 5 101 125 104 1.40 14 8 4 99 126 105 1. 40 14 8 5 100 125 104 1.40 14 10 4 99 124 105 1.40 14 10 5 99 124 104 2.00 8 8 4 106 129 106 2.00 8 8 5 106 129 105 2.00 8 10 4 106 128 105 2.00 8 10 5 106 128 105 2.00 10 8 4 105 129 105 2.00 10 8 5 105 129 105 2.00 10 10 4 105 128 105 2.00 10 10 5 105 128 105 2.00 12 8 4 104 129 106 2.00 12 8 5 104 129 105 2.00 12 10 4 104 128 106 2.00 12 10 5 104 128 105 2.00 14 8 4 103 128 106 2.00 14 8 5 103 128 106 2.00 14 _ 10 4 103 127 106 2.00 14 10 5 103 127 105 “2515 90 TABLE XX - HIGH PROFIT POINT SOLUTIONS FOR FERTILIZER APPLICATIONS ON HONEYWOOD SILT LOAN, 1954 - LOCATION 1 - EQUATION 27. P. P P P N P X y n p k Dollars/bu. - - - Cents/1b. - - - - .. 1bs./acre - - 1.00 8 8 4 51 67 49 1.00 8 8 5 51 67 48 1.00 8 10 4 50 64 48 1.00 8 10 5 50 63 47 1.00 10 8 4 48 67 49 1.00 10 8 5 48 66 48 1.00 10 10 4 47 63 48 1.00 10 10 5 47 62 47 1.00 12 8 4 46 66 49 1.00 12 8 5 46 65 48 1.00 12 10 4 45 62 48 1.00 12 10 5 45 62 46 1.00 14 8 4 43 65 48 1.00 14 8 5 43 64 47 1.00 14 10 4 42 61 47 1.00 14 10 5 42 61 46 1.20 8 8 4 54 71 51 1.20 8 8 5 54 70 49 1.20 8 10 4 53 68 49 1.20 8 10 5 52 67 48 1.20 10 8 4 51 70 50 1.20 10 8 5 51 7O 49 1.20 10 10 4 51 67 49 1.20 10 10 5 51 67 48 1.20 12 8 4 49 69 50 1.20 12 8 5 49 69 49 1.20 12 10 4 48 66 49 1.20 12 10 5 48 66 48 1.20 14 8 4 47 69 50 1.20 14 8 5 47 68 49 1.20 14 10 4 46 66 49 1.20 14 10 5 46 65 48 1.40 8 8 4 56 74 52 1.40 8 8 5 56 73 51 1.40 8 10 4 55 71 51 1.40 8 10 5 55 71 50 1.40 10 8 4 54 73 52 1.40 10 8 5 54 73 51 1.40 10 10 4 53 70 51 1.40 10 10 5 53 70 50 ESIE 91 TABLE XX - continued 1.40 12 8 4 51 72 52 1.40 12 8 5 51 72 51 1.40 12 10 4 51 70 51 1.40 12 10 5 51 69 50 1.40 14 8 4 49 72 51 1.40 14 8 5 49 71 51 1.40 14 10 4 49 69 51 1.40 14 10 5 49 68 50 2.00 8 8 4 60 79 54 2.00 8 8 5 6O 79 54 2.00 8 10 4 60 77 53 2.00 8 10 5 6O 77 53 2.00 10 8 4 58 79 54 2.00 10 8 5 58 78 53 2.00 10 10 4 58 76 53 2.00 10 10 5 58 76 53 2.00 12 8 4 57 78 54 2.00 12 8 5 57 78 53 2. 00 12 10 4 56 75 53 2.00 12 10 5 55 77 54 2.00 14 8 4 55 77 53 2.00 14 8 5 55 75 53 2.00 14 10 4 54 75 53 2. 00 14 10 5 54 75 53 92 TABLE XXI - HIGH PROFIT POINT SOLUTIONS FOR FERTILIZER APPLICATIONS ON HONEYWOOD SILT LOAM, 1954 - LOCATION 2 - EQUATION 28. P P P P N P K y n p k Dollars/bu. - - - - Cents/1b. - - - - - - lbs./acre - - - 1.00 8 8 4 100 132 143 1.00 8 8 5 101 132 142 1.00 8 IO 4 98 130 143 1. 00 8 10 5 98 130 143 1.00 10 8 4 94 130 144 1.00 10 8 5 95 130 143 1.00 10 10 4 92 128 144 1.00 10 10 5 92 128 143 1.00 12 8 4 88 128 144 1.00 12 8 5 89 128 144 1.00 12 10 4 86 126 144 1.00 12 10 5 86 126 144 1.00 14 8 4 82 126 145 1.00 14 8 5 83 126 144 1.00 14 10 4 80 124 145 1.00 14 10 5 80 124 145 1.20 8 8 4 105 135 142 1.20 8 8 5 106 135 142 1. 2O 8 10 4 104 134 143 1.20 8 10 5 104 134 143 1. 20 10 8 4 101 133 143 1.20 10 8 5 101 133 143 1.20 10 10 4 99 132 143 1.20 10 10 5 99 132 143 1. 20 12 8 4 95 131 144 1.20 12 8 5 96 131 143 1.20 12 10 4 94 130 144 1.20 12 10 5 94 130 144 1.20 14 8 4 90 129 145 1.20 14 8 5 91 129 144 1.20 14 10 4 89 128 145 1.20 14 10 5 89 128 144 1.40 8 8 4 109 137 143 1.40 8 8 5 110 137 142 1.40 8 10 4 108 136 143 1.40 8 10 5 108 136 142 1.40 10 8 4 105 136 143 1.40 10 8 5 105 136 143 1.40 10 10 4 104 134 143 1.40 10 10 5 104 134 143 ESIS 92 TABLE XXI - HIGH PROFIT POINT SOLUTIONS FOR FERTILIZER APPLICATIONS ON HONEYWOOD SILT LOAN, 1954 - LOCATION 2 - EQUATION 28. P P P P N P K y n p k Dollars/bu. - - - - Cents/1b. - - - - 4 - 1bs./acre - - - 1.00 8 8 4 100 132 143 1.00 8 8 5 101 132 142 1.00 8 10 4 98 130 143 1.00 8 10 5 98 130 143 1.00 10 8 4 94 130 144 1.00 10 8 5 95 130 143 1.00 10 10 4 92 128 144 1.00 10 10 5 92 128 143 1.00 12 8 4 88 128 144 1.00 12 8 5 89 128 144 1.00 12 10 4 86 126 144 1.00 12 10 5 86 126 144 1.00 14 8 4 82 126 145 1.00 14 8 5 83 126 144 1.00 14 10 4 80 124 145 1.00 14 10 5 80 124 145 1.20 8 8 4 105 135 142 1.20 8 8 5 106 135 142 1.20 8 10 4 104 134 143 1.20 8 10 5 104 134 143 1.20 10 8 4 101 133 143 1.20 10 8 5 101 133 143 1.20 10 10 4 99 132 143 1.20 10 10 5 99 132 143 1.20 12 8 4 95 131 144 1.20 12 8 5 96 131 143 1.20 12 10 4 94 130 144 1.20 12 10 5 94 130 144 1.20 14 8 4 90 129 145 1.20 14 8 5 91 129 144 1.20 14 10 4 89 128 145 1.20 14 10 5 89 128 144 1.40 8 8 4 109 137 143 1.40 8 8 5 110 137 142 1.40 8 10 4 108 136 143 1.40 8 10 5 108 136 142 1.40 10 8 4 105 136 143 1.40 10 8 5 105 136 143 1.40 10 10 4 104 134 143 1.40 10 10 5 104 134 143 3 IS 93 TABLE XXI - continued 1.40 12 -8 4 101 134 144 1.40 12 8 5 101 134 143 1.40 12 10 4 99 133 144 1.40 12 10 5 99 133 143 1.40 14 8 4 96 132 144 1.40 14 8 5 97 132 144 1.40 14 10 4 95 131 144 1.40 14 10 5 95 131 144 2.00 8 8 4 116 141 143 2.00 8 8 5 116 141 142 2.00 8 10 4 115 140 143 2.00 8 10 5 115 140 142 2.00 10 8 4 113 140 143 2.00 10 8 5 113 140 143 2.00 10 10 4 112 139 143 2.00 10 10 5 112 139 143 2.00 12 8 4 110 139 143 2.00 12 8 5 110 139 143 2.00 12 10 4 109 138 143 2.00 12 10 5 109 138 143 2.00 14 8 4 107 137 144 2.00 14 8 5 107 137 143 2.00 14 10 4 106 136 144 2.00 14 10 5 106 136 143 93 TABLE XXI - continued 1.40 12 -8 4 101 134 144 1.40 12 8 5 101 134 143 1.40 12 10 4 99 133 144 1.40 12 10 5 99 133 143 1.40 14 8 4 96 132 144 1.40 14 8 5 97 132 144 1.40 14 10 4 95 131 144 1.40 14 10 5 95 131 144 2.00 8 8 4 116 141 143 2.00 8 8 5 116 141 142 2.00 8 10 4 115 140 143 2.00 8 10 5 115 140 142 2.00 10 8 4 113 140 143 2.00 10 8 5 113 140 143 2.00 10 10 4 112 139 143 2.00 10 10 5 112 139 143 2.00 12 8 4 110 139 143 2.00 12 8 5 110 139 143 2.00 12 10 4 109 138 143 2.00 12 10 -5 109 138 143 2.00 14 8 4 107 137 144 2.00 14 8 5 107 137 143 2.00 14 10 4 106 136 144 2.00 14 10 5 106 136 143 A»: V4 .0. a—. 94 TABLE XXII - HIGH PROFIT POINT SOLUTIONS FOR FERTILIZER APPLICATIONS ON HONEYWOOD SILT LOAM, 1954 - LOCATION 2 - EQUATION 29. P P P P N P X y n p k Dollars/bu. - - - - Cents/1b. - - - - - - - lbs./acre - - - 1.00 8 8 4 64 97 143 1.00 8 8 5 63 96 141 1.00 8 10 4 6O 93 142 1.00 8 10 5 6O 92 140 1.00 10 8 4 56 94 142 1. 00 10 8 5 56 93 140 1.00 10 10 4 54 90 141 1.00 10 10 5 53 89 139 1.00 12 8 4 50 91 142 1.00 12 8 5 50 90 139 1.00 12 10 4 48 87 141 1.00 12 10 5 47 87 138 1.00 14 8 4 45 88 141 1.00 14 8 5 45 88 139 1.00 14 10 4 43 85 140 1.00 14 10 5 43 84 138 1.20 8 8 4 72 102 146 1.20 8 8 5 72 102 144 1.20 8 10 4 69 99 145 1.20 8 10 5 69 98 143 1. 20 10 8 4 65 99 145 1.20 10 8 5 64 99 143 1.20 10 10 4 62 96 144 1.20 10 10 5 62 95 142 1.20 12 8 4 58 97 145 1.20 12 8 5 58 96 143 1.20 12 10 4 56 93 144 1.20 12 10 5 56 93 142 1.20 14 8 4 53 94 144 1.20 14 8 5 53 94 142 1.20 14 10 4 51 91 143 1.20 14 10 5 51 91 141 1.40 8 8 4 79 106 148 1.40 8 8 5 79 106 146 1.40 8 10 4 76 104 147 1.40 8 10 5 76 103 146 1.40 10 8 4 72 104 147 1.40 10 8 5 72 104 146 1.40 10 10 4 70 101 147 1.40 10 10 5 69 100 145 > \S 95 TABLE XXII - continued 1.40 12 .8 4 66 101 147 1.40 12 8 5 65 101 145 1.40 12 10 4 63 98 146 1.40 12 10 5 63 98 144 1.40 14 8 4 6O 99 146 1.40 14 8 5 60 98 145 1.40 14 10 4 58 96 145 1.40 14 10 5 58 96 144 2.00 8 8 4 94 116 153 2.00 8 8 5 94 116 151 2.00 8 10 4 92 113 152 2.00 8 10 5 91 113 151 2.00 10 8 4 88 113 152 2.00 10 8 5 88 113 151 2.00 10 10 4 85 111 151 2.00 10 10 5 85 110 150 2.00 12 8 4 81 111 151 2.00 12 8 5 82 111 150 2.00 12 10 4 80 109 151 2.00 12 10 5 79 108 149 2.00 14 8 4 77 109 151 2.00 14 8 5 76 108 150 2.00 14 10 4 74 106 150 2.00 14 10 5 74 106 149 .96 TABLE XXIII - HIGH PROFIT POINT SOLUTIONS FOR FERTILIZER APPLICATIONS ON BRIGHTON FINE SANDY LOAM, 1954 - EQUATION 30. P P P P N P K y n p k Dollars/bu. - - - - Cents/1b. - - - - - - - 1bs./acre - - - 1.00 8 8 4 130 159 187 1.00 8 8 5 129 158 186 1.00 8 10 4 130 157 186 1.00 8 10 5 129 157 185 1.00 10 8 4 131 159 185 1.00 10 8 5 130 158 185 1.00 10 10 4 131 158 184 1.00 10 10 5 130 157 184 1.00 12 8 4 132 159 183 1.00 12 8 5 131 159 183 1.00 12 10 4 132 158 182 1.00 12 10 5 131 157 182 1.00 14 8 4 132 160 181 1.00 14 8 5 132 159 181 1.00 14 10 4 133 158 180 1.00 14 10 5 132 158 180 1.20 8 8 4 130 160 189 1.20 8 8 5 129 159 189 1.20 8 10 4 130 159 188 1.20 8 10 5 129 158 188 1.20 10 8 4 130 160 187 1.20 10 8 5 130 159 187 1.20 10 IO 4 131 159 187 1.20 10 10 5 130 158 186 1.20 12 8 4 131 160 186 1.20 12 8 5 130 160 186 1.20 12. 10 4 131 159 185 1.20 12 10 5 131 159 185 1.20 14 8 4 132 160 185 1.20 14 8 5 131 160 184 1.20 14 10 4 132 159 184 1.20 14 10 5 131 159 183 1.40 8 8 4 129 160 190 1.40 8 8 5 129 160 190 1.40 8 10 4 130 159 190 1.40 8 10 5 129 159 189 1.40 10 8 4 130 160 189 1.40 10 8 5 129 160 189 1.40 10 10 4 130 160 188 1.40 10 10 5 130 159 188 97. TABLE XXIII - continued 1.40 12 8 4 131 161 188 1.40 12 8 5 130 160 188 1.40 12 10 4 131 160 187 1.40 12 10 5 130 159 186 1.40 14 8 4 131 161 187 1.40 14 8 5 131 161 186 1.40 14 10 4 132 160 186 1.40 14 10 5 131 160 186 2.00 8 8 4 129 162 193 2.00 8 8 5 129 161 193 2.00 8 10 4 129 161 193 2.00 8 10 5 129 161 192 2.00 10 8 4 130 162 192 2.00 10 8 5 129 161 192 2.00 10 10 4 130 161 192 2.00 10 10 5 129 161 192 2.00 12 8 4 130 162 191 2.00 12 8 5 130 -162 191 2.00 12 10 4 130 161 191 2.00 12 10 5 130 161 191 2.00 14 8 4 131 162 191 2.00 14 8 5 130 162 190 2.00 14 10 4 131 161 190 2.00 14 10 5 130 161 190 \ql' I. 98 TABLE XXIV - HIGH PROFIT POINT SOLUTIONS FOR FERTILIZER APPLICATIONS ON HONEYNOOD SILT LOAM, 1955 - EQUATION 32. P P P P N P K y n p k Dollars/bu. - - - - Cents/1b. - - - - - - - lbs./acre - - - 1.00 8 8 4 105 O 247 1.00 8 8 5 104 O 238 1.00 8 10 4 104 0 249 1.00 8 10 5 104 0 240 1.00 10 8 4 104 0 246 1.00 10 8 5 103 0 237 1.00 10 10 4 103 0 237 1.00 10 10 5 103 O 239 1.00 12 8 4 103 O 244 1.00 12 8 5 102 O 236 1.00 12 10 4 102 0 246 1.00 12 10 5 101 O 238 1.00 14 8 4 102 O 243 1.00 14 8 5 101 O 234 1.00 14 10 4 101 0 245 1.00 14 10 5 100 O 236 1.20 8 8 4 106 O 252 1.20 8 8 5 106 0 245 1.20 8 10 4 106 O 254 1.20 8 10 5 105 0 246 1.20 10 8 4 106 O 251 1.20 10 8 5 105 O 244 1.20 10 10 4 105 0 253 1.20 10 10 5 104 0 245 1.20 12 8 4 105 O 250 1.20 12 8 5 104 0 242 1.20 12 10 4 104 0 252 1.20 12 10 5 104 O 244 1.20 14 8 4 104 0 249 1.20 14 8 5 103 O 241 1.20 14 10 4 103 O 251 1.20 14 10 5 103 O 243 1.40 8 8 4 108 O 256 1.40 8 8 5 107 0 250 1.40 8 10 4 107 O 257 1.40 8 10 5 107 O 251 1.40 10 8 4 107 O 255 1.40 10 8 5 106 0 249 1.40 10 10 4 106 O 256 1.40 10 10 5 106 O 250 99 TABLE XXIV - continued 1.40 12 8 4 106 O 254 1.40 12 8 5 105 O 248 1.40 12 10 4 106 O 255 1.40 12 10 5 105 O 249 1.40 14 8 4 105 O 253 1.40 14 8 5 105 O 247 1.40 14 10 4 105 O 254 1.40 14 10 5 104 O 248 2.00 8 8 4 110 O 263 2.00 8 8 5 109 O 258 2.00 8 10 4 109 O 264 2.00 8 10 5 109 O 259 2.00 10 8 4 109 0 262 2.00 10 8 5 109 O 258 2.00 10 10 4 109 O 263 2.00 10 10 5 108 O 259 2.00 12 8 4 108 O 261 2.00 12 8 5 108 O 257 2.00 12 10 4 108 O 262 2.00 12 10 5 108 O 258 2.00 14 8 4 108 O 261 2.00 14 8 5 108 0 256 2. OO 14 10 4 108 O 262 2.00 14 10 5 107 0 257 100 ‘ TABLE xxv — HIGH PROFIT POINT SOLUTIONS FOR FERTILIZER APPLICATIONS ON GUELPH SANDY LOAM, 1955 - EQUATION 34. P P P P N P K y n p k Dollars/bu. — - - - Cents/1b. - - - - - - - lbs./acre - - - 1.00 8 8 4 91 313 104 1.00 8 8 5 90 307 107 1.00 8 10 4 90 312 92 1.00 8 10 5 89 306 95 1.00 10 8 4 90 311 102 1.00 10 8 5 89 305 105 1.00 10 10 4 89 311 91 1.00 10 10 5 88 305 93 1.00 12 8 4 88 310 100 1.00 12 8 5 88 304 103 1.00 12 10 4 88 310 89 1.00 12 10 5 87 304 92 1.00 14 8 4 87 309 99 1.00 14 8 5 87 303 102 1.00 14 10 4 86 309 88 1.00 14 10 5 86 303 90 1.20 8 8 4 93 318 111 1.20 8 8 5 93 312 113 1.20 8 10 4 92 317 101 1.20 8 10 5 92 312 104 1.20 10 8 4 92 317 109 1.20 10 8 5 92 311 112 1.20 10 10 4 91 316 100 1.20 10 10 5 91 311 103 1.20 12 8 4 91 316 108 1.20 12 8 5 91 310 111 1.20 12 10 4 90 315 99 1.20 12 10 5 90 310 101 1.20 14 8 4 90 315 107 1.20 14 8 5 89 309 109 1.20 14 10 4 89 314 97 1.20 14 10 5 89 309 100 1.40 8 8 4 95 321 116 1.40 8 8 5 94 317 118 1.40 8 10 4 94 321 108 1.40 8 10 5 93 316 110 1.40 10 8 4 94 320 115 1.40 10 8 5 93 316 117 1.40 10 10 4 93 320 107 1.40 10 10 5 93 316 109 101 TABLE XXV - continued 1.40 12 8 4 93 319 114 1.40 12 8 5 92 315 116 1.40 12 10 4 92 319 106 1.40 12 10 5 92 315 108 1.40 14 8 4 92 318 113 1.40 14 8 5 92 314 115 1.40 14 10 4 91 318 105 1.40 14 10 5 91 314 107 2.00 8 8 4 98 327 125 2.00 8 8 5 97 325 126 2.00 8 10 4 97 327 119 2.00 8 10 5 97 324 121 2.00 10 8 4 97 327 124 2.00 10 8 5 97 324 126 2.00 10 10 4 96 327 118 2.00 10 10 5 96 324 120 2.00 12 8 4 96 326 123 2.00 12 8 5 96 323 125 2.00 12 10 4 96 326 118 2.00 12 10 5 95 323 119 2.00 14 8 4 96 326 123 2. CO 14 8 5 95 323 124 2.00 14 10 4 95 326 117 2.00 14 10 5 95 323 118 102 TABLE XXVI - HIGH PROFIT POINT SOLUTIONS FOR FERTILIZER APPLICATIONS ON FOX LOAMY SAND, 1955 - EQUATION 36. P P P P N P K y n p k Dollars/bu. - - - - Cents/lb. - - - - - - - lbs./acre — - - 1.00 8 8 4 O 126 O 1.00 8 8 5 O 130' O 1.00 8 10 4 O 116 O 1.00 8 10 5 O 121 O 1.00 10 8 4 0 125 O 1.00 10 8 5 O 130 0 1.00 10 10 4 0 116 O 1.00 10 10 5 O 120 0 1.00 12 8 4 O 125 O 1.00 12 8 5 0 130 0 1.CO 12 10 4 O 115 0 1.00 12 10 5 0 120 0 1.00 14 8 4 0 125 0 1.00 14 8 5 0 129 O 1.00 14 10 4 0 115 O 1.00 14 10 5 0 120 0 1.20 8 8 4 0 129 0 1.20 8 8 5 O 133 0 1.20 8 10 4 0 121 O 1.20 8 10 5 0 125 O 1.20 10 8 4 O 129 O 1.20 10 8 5 O 133 O 1.20 10 10 4 O 121 O 1.20 10 10 5 O 125 O 1.20 12 8 4 0 128 O 1.20 12 8 5 O 133 O 1.20 12 10 4 O 121 O 1.20 12 10 5 O 125 O 1.20 14 8 4 O 129 O 1.20 14 8 5 O 132 O 1.20 14 10 4 O 120 0 1.20 14 10 5 O 125 O 1.40 8 8 4 O 132 0 1.40 8 8 5 O 135 O 1.40 8 10 4 O 125 O 1.40 8 10 5 O 129 O 1.40 10 8 4 0 132 O 1.40 10 8 5 O 135 O 1.40 10 10 4 O 125 O 1.40 10 10 5 O 128 O THESIS 103 TABLE XXVI - continued 1.40 12 8 4 0 132 O 1.40 12 8 5 O 135 O 1.40 12 10 4 0 125 O 1.40 12 10 5 O 128 O 1.40 14 8 4 0 131 O 1.40 14 8 5 O 135 0 1.40 14 10 4 0 124 0 1.40 14 10 5 0 128 0 2.00 8 8 4 O 3136 0 2.00 8 8 5 O 139 O 2.00 8 10 4 O 132 O 2.00 8 10 5 0 134 O 2.00 10 8 4 0 136 0 2.00 10 8 5 0 139 O 2.00 10 10 4 0 131 0 2.00 10 10 5 0 134 0 2.00 12 8 4 0 136 0 2.00 12 8 5 0 138 O 2.00 12 10 4 0 131 0 2.00 12 10 5 O 134 O 2.00 14 8 4 0 136 O 2. 00 14 8 5 0. 138 O 2.00 14 10 4 0 131 O 2.00 14 10 5 0 133 O THESIS 104 TABLE XXVII — HIGH PROFIT POINT SOLUTIONS FOR FERTILIZER APPLICATIONS ON FOX LOAMY SAND, 1955 - EQUATION 37. P P P P N P K y n p k Dollars/bu. - - - - Cents/lb. ~ - - - - - - lbs./acre - - - 1.00 8 8 4 10 55 3 l. 00 8 8 5 10 54 5 1.00 8 10 4 11 28 3 1.00 8 10 5 11 48 5 1.00 10 8 4 12 55 4 1.00 10 8 5 12 55 6 1.00 10 10 4 12 49 3 1.00 10 10 5 13 49 5 1.00 12 8 4 13 56 4 1.00 12 8 5 14 56 6 1.00 12 10 4 14 5O 4 1.00 12 10 5 15 5O 6 1.00 14 8 4 16 58 5 1.00 14 8 5 16 57 7 1.00 14 10 4 17 51 4 1.00 14 10 5 17 51 7 1.20 8 8 4 9 59 2 1.20 8 8 5 9 59 4 1.20 8 10 4 9 53 2 1.20 8 10 5 9 53 3 1.20 10 8 4 10 6O 3 1.20 10 8 5 10 59 4 1.20 10 10 4 10 53 2 1.20 10 10 5 11 54 3 1.20 12 8 4 11 6O 3 1.20 12 8 5 11 60 4 1.20 12 10 4 12 55 3 1.20 12 10 5 12 54 4 1.20 14 8 4 12 61 3 1.20 14 8 5 13 61 5 1.20 14 10 4 13 55 3 1.20 14 10 5 13 55 4 1. 4O 8 8 4 8 63 2 1.40 8 8 5 8 63 3 1.40 8 10 4 8 57 2 1.40 8 10 5 8 57 3 1.40 10 8 4 9 63 2 1.40 10 8 5 9 63 3 1.40 10 10 4 9 58 2 1.40 10 10 5 9 58 3 105 TABLE XXVII - continued 1.40 12 8 4 9 64 2 1.40 12 8 5 10 64 3 1.40 12 10 4 10 58 2 1.40 12 10 5 10 58 3 1.40 14 8 4 10 64 3 1.40 14 8 5 10 64 3 1.40 14 10 4 10 59 3 1.40 14 10 5 ll 59 3 2.00 8 8 4 6 7O 2 2.00 8 8 5 6 7O 2 2.00 8 10 4 7 65 2 2.00 8 10 5 7 65 2 2.00 10 8 4 7 7O 2 2.00 10 8 5 7 70 2 2.00 10 10 4 7 66 2 2.00 10 10 5 7 65 2 2.00 12 8 4 7 71 2 2.00 12 8 5 7 71 2 2.00 12 10 4 8 66 2 2.00 12 10 5 8 66 2 2.00 14 8 4 8 71 2 2.00 14 8 5 8 71 2 2.00 14 10 4 8 66 2 2.00 14 10 5 8 66 2 106 TABLE XXVIII - HIGH PROFIT POINT SOLUTIONS FOR FERTILIZER APPLICATIONS ON HONEYWOOD SILT LOAM, 1956 - EQUATION 38. P P P P N P K y n p k Dollars/bu. - - - - Cents/lb. - - - - - - - lbs./acre - - - 1.00 8 8 4 138 197 227 1.00 8 8 5 138 197 226 1.00 8 10 4 137 193 227 1.00 8 10 5 137 193 225 1.00 10 8 4 137 196 226 1.00 10 8 5 137 196 225 1.00 10 10 4 136 192 226 1.00 10 10 5 136 192 225 1.00 12 8 4 136 195 226 1.00 12 8 5 136 195 225 1.00 12 10 4 135 191 226 1.00 12 10 5 135 191 224 1. 00 14 8 4 13 5 194 225 1.00 14 8 5 135 194 224 1.00 14 10 4 134 190 225 1.00 14 10 5 134 190 224 1.20 8 8 4 140 200 228 1.20 8 8 5 139 200 227 1.20 8 10 4 139 197 228 1.20 8 10 5 139 197 227 1.20 10 8 4 139 199 228 1.20 10 8 5 139 199 227 1.20 10 10 4 138 196 228 1.20 10 10 5 138 196 226 1.20 12 8 4 138 199 227 1.20 12 8 5 138 198 226 1.20 12 10 4 137 195 227 1.20 12 10 5 137 195 226 1.20 14 8 4 136 198 227 1.20 14 8 5 137 198 226 1.20 14 10 4 136 195 227 1.20 14 10 5 136 195 226 1.40 8 8 4 141 202 229 1.40 8 8 5 141 202 229 1.40 8 10 4 140 202 228 1.40 8 10 5 140 200 228 1.40 10 8 4 140 202 229 1.40 10 8 5 140 202 228 1. 40 10 10 4 13 9 199 228 1.40 10 10 5 139 199 228 THESIS 107 TABLE XXVIII - continued 1.40 12 8 4 139 201 228 1.40 12 8 5 139 201 227 1.40 12 10 4 139 198 228 1.40 12 10 5 138 198 227 1.40 14 8 4 138 200 228 1.40 14 8 5 138 200 227 1.40 14 10 4 138 198 228 1.40 14 10 5 138 198 227 2. 00 8 8 4 143 206 231 2.00 8 8 5 143 206 230 2.00 8 10 4 142 204 230 2.00 8 10 5 142 204 230 2.00 10 8 4 142 206 230 2.00 10 8 5 142 206 230 2.00 10 10 4 142 204 230 2.00 10 10 5 142 204 230 2.00 12 8 4 141 ' 206 230 2.00 12 8 5 141 205 230 2.00 12 10 4 141 204 230 2.00 12 10 5 141 204 229 2.00 14 8 4 141 205 230 2.00 14 8 5 141 205 229 2.00 14 10 4 141 203 230 2.00 14 10 5 140 203 229 108 TABLE XXIX - HIGH PROFIT POINT SOLUTIONS FOR FERTILIZER APPLICATIONS ON FOX SANDY LOAM, 1956 - EQUATION 40. P P P P N P K y n p k Dollars/bu. - - - - Cents/1b. - - - - - - - 1bs./acre - - — 1.00 8 8 4 132 180 202 1.00 8 8 5 131 180 195 1.00 8 10 4 131 175 202 1.00 8 10 5 130 175 195 1.00 10 8 4 129 179 199 1.00 10 8 5 128 178 192 1.00 10 10 4 128 174 199 1.00 10 10 5 126 174 192 1.00 12 8 4 126 177 196 1.00 12 8 5 125 177 189 1.00 12 10 4 125 173 196 1.00 12 10 5 123 172 189 1.00 14 8 4 123 176 193 1.00 14 8 5 122 176 186 1.00 14 10 4 122 171 193 1.00 14 10 5 120 171 186 1.20 8 8 4 136 184 209 1.20 8 8 5 135 184 203 1.20 8 10 4 135 180 209 1.20 8 10 5 134 180 203 1.20 10 8 4 134 183 207 1.20 10 8 5 132 183 201 1.20 10 10 4 133 179 206 1.20 10 10 5 131 179 200 1.20 12 8 4 131 182 204 1.20 12 8 5 130 182 198 1.20 12 10 4 130 178 204 1.20 12 10 5 129 178 198 1.20 14 8 4 128 181 202 1.20 14 8 5 127 181 196 1.20 14 10 4 127 177 202 1.20 14 10 5 126 177 195 1.40 8 8 4 139 187 214 1.40 8 8 5 138 187 209' 1.40 8 10 4 138 184 213 1.40 8 10 5 137 184 209 1.40 10 8 4 137 186 212 1.40 10 8 5 136 186 207 1.40 10 10 4 136 183 211 1.40 10 10 5 145 217 211 S F. H T 109 .TABLE XXIX - continued 1.40 12 8 4 135 185 210 1.40 12 8 5 134 185 205 1.40 12 10 4 134 182 209 1.40 12 10 5 133 181 204 1.40 14 8 4 132 184 207 1.40 ' 14 8 5 131 184 203 1.40 14 10 4 131 181 207 1.40 14 10 5 130 181 202 2.00 8 8 4 144. 193 223 2.00 8 8 5 143 192 219 2.00 8 10 4 143 192 219 2.00 8 10 5 143 190 219 2.00 10 8 4 143 192 221 2.00 10 8 5 142 192 218 2.00 10 10 4 142 190 221 2.00 10 10 5 141 189 218 2.00 12 8 4 141 191 220 2.00 12 8 5 140 191 217 2.00 12 10 4 140 189 220 2.00 12 10 5 140 189 216 2.00 14 8 4 139 191 219 2.00 14 8 5 139 191 215 2.00 14 10 4 139 188 218 2.00 14 10 5 138 188 215 THES‘S III III.) 110 TABLE XXX - HIGH PROFIT POINT SOLUTIONS FOR FERTILIZER APPLICATIONS ON FOX SANDY LOAM, 1956 - EQUATION 41. P P P P N P K y n p k Dollars/bu. - - - - Cents/1b. - - - - - - - lbs./acre - - ~ 1. 00 8 8 4 31 174 0 1. 00 8 8 5 19 198 O 1.00 8 10 4 30 156 O 1.00 8 10 5 17 178 O 1.00 10 8 4 29 173 0 1.00 10 8 5 17 197 0 1.00 10 10 4 28 154 0 1.00 10 10 5 16 176 0 1.00 12 8 4 27 171 0 1.00 12 8 5 16 196 0 1.00 12 10 4 26 153 0 1.00 12 10 5 15 175 0 1.00 14 8 4 25 170 0 1.00 14 8 5 16 194 0 1.00 14 10 4 24 152 0 1.00 14 10 5 14 174 0 1.20 8 8 4 37 183 O 1.20 8 8 5 32 192 0 1.20 8 10 4 36 166 0 1.20 8 10 5 31 175 0 1.20 10 8 4 35 181 0 1.20 10 8 5 30 191 0 1.20 10 10 4 34 165 0 1.20 10 10 5 29 173 0 1.20 12 8 4 33 180 O 1.20 12 8 5 28 189 0 1.20 12 10 4 32 164 0 1.20 12 10 5 27 172 0 1.20 14 8 4 31 179 0 1.20 14 8 5 . 27 188 0 1.20 14 10 4 30 163 0 1.20 14 10 5 26 171 0 1.40 8 8 4 41 193 0 1.40 8 8 5 38 197 0 1.40 8 10 4 40 177 0 1.40 8 10 5 37 181 0 1.40 10 8 4 39 191 0 1.40 10 8 5 36 196 0 1. 40 10 10 4 38 176 0 1.40 10 10 5 35 180 0 1.40 12 8 4 37 190 0 TH E515 111 TABLE XXX - continued 1.40 12 8 5 34 195 0 1.40 12 10 4 36 175 O 1.40 12 10 5 33 179 0 1.40 14 8 4 35 189 O 1.40 14 8 5 33 194 O 1.40 14 10 4 34 174 0 1.40 14 10 5 32 178 0 2.00 8 8 4 48 213 O 2.00 8 8 5 47 215 0 2.00 8 10 4 47 199 0 2.00 8 10 5 46 201 0 2.00 10 8 4 46 212 0 2.00 10 8 5 45 214 O 2.00 10 10 4 45 198 0 2.00 10 10 5 44 200 0 2.00 12 8 4 45 211 0 2.00 12 8 5 43 213 O 2.00 12 10 4 44 197 0 2.00 12 10 5 43 199 O 2.00 14 8 4 43 210 O 2.00 14 8 5 42 212 O 2.00 14 10 4 42 196 O 2.00 14 10 5 41 198 0 THESIS ‘112 TABLE XXXI - HIGH PROFIT POINT SOLUTIONS FOR FERTILIZER APPLICATIONS ON TIOGA LOAM, 1956 - EQUATION 44. P P P P N P K y n p k Dollars/bu. - - - - Cents/1b. - - - - - - - 1bs./acre - - - 1.00 8 8 4 157 224 227 1.00 8 8 5 156 224 226 1.00 8 10 4 156 221 227 1.00 8 10 5 156 221 226 1. 00 10 8 4 156 223 227 1.00 10 8 5 156 223 226 1.00 10 10 4 155 220 226 1.00 10 10 5 155 220 225 1.00 12 8 4 155 223 226 1.00 12 8 5 155 222 225 1.00 12 10 4 154 220 226 1.00 12 10 5 154 220 225 1.00 14 8 4 154 222 226 1.00 14 8 5 154 222 225 1.00 14 10 4 154 219 225 1.00 14 10 5 153 219 224 1.20 8 8 4 158 226 228 1.20 8 8 5 158 226 228 1.20 8 10 4 157 224 228 1.20 8 10 5 157 224 228 1.20 10 8 4 157 226 228 1.20 10 8 5 157 225 227 1.20 10 10 4 157 224 228 1.20 10 10 5 156 223 227 1.20 12 8 4 156 225 228 1.20 12 8 5 156 225 227 1.20 12 10 4 156 223 227 1.20 12 10 5 156 223 226 1.20 14 8 4 156 224 227 1.20 14 8 5 155 224 226 1.20 14 10 4 155 222 227 1.20 14 10 5 155 222 226 1.40 8 8 4 159 228 229 1.40 8 8 5 158 228 229 1.40 8 10 4 158 226 229 1.40 8 10 5 158 226 228 1.40 10 8 4 158 227 229 1.40 10 8 5 158 227 228 1.40 10 10 4 158 225 229 1.40 10 10 5 157 225 228 THESIS TABQ XXX; - continued 1.40 12 8 4 157 227 229 1.40 12 8 5 157 227 230 1.40 12 10 4 157 225 228 1.40 12 10 5 157 225 228 1.40 14 8 4 157 226 228 1.10 14 8 5 157 _226 228 1.40 14 10 4 156 225 228 1.40 14 10 5 156 224 227 2.00 8 8 4 160 231 231 2.00 8 8 5 160 231 230 2.00 8 10 4 160 229 231 2.00 8 10 5 160 229 230 2.00 10 8 4 160 230 231 2.00 10 8 5 160 230 230 2.00 10 10 4 160 229 231 2.00 10 10 5 159 .-229 230 2.00 12 8 4 160 230 230 2.00 12 8 5 159 230 230 2.00 12 10 4 159 229 230 2.00 12 10 5 159 229 230 2.00 14 8 4 159 230 230 2.00 14 8 5 159 230 230 2.00 14 10 4 159 228 230 2.00 14 10 5 158 228 230 THESIS .Lvhu. 114 A P P E N D I X D Analysis of Variance of Data for 1955 and 1956 THESIS 115 TABLE XXXII - SUMMARY OF ANALYSIS OF VARIANCEI- GUELPH SANDY LOAM, 1955. Source of Variation D.F. S. of S. Variance "f" necessary "f" 5% 1% Replications 2 281.15 140.57 0.13 3.17 5.01 Blocks within Reps 6 33006.80 5501.13 5.13 ** 2.27 3.15 Nitrogen 2 13295.78 6647.89 6.19 ** 3.17 5.01 Phosphorus 2 20941.23 10470.61 9.75 ** " " Potassium 2 36345.85 18172.92 16.94 ** " " Nitrogen x Phosphorus 4 3923.30 980.82 0.91 2.54 3.68 " x Potassium 4 1125.62 281.40 0.26 " " Phosphorus x Potassium 4 2179.83 544.96 0.51 " " Nitrogen linear 1 12598.05 12598.05 11.74 ** 4.02 7.12 “ quadratic 1 697.72 697.72 0.65 " " Phosphorus linear 1 20862.41 20862.41 19.44 ** " " " quadratic 1 78.82 78.82 0.07 " " Potassium linear 1 35635.62 35635.62 33.21 **' " " a quadratic 1 710.23 710.23 0.66 " " Error 54 57944.77 1073-05 Total 80 169044.23 30v = ‘v1073:§5 x 100 = 14.3 228.8 THESIS 116 TABLE XXXIII - SUMMARY OF ANALYSIS OF VARIANCE - HONEYNOOD SILT LOAN, 1955. Source of Variation D.F. S. of S. Variance "f" necessary “f" A 5% 1% Replications 2 2072.21 1036.10 11.52 3.17 5.01 Blocks within Reps 6 654.13 109.02 1.21 2.27 3.15 Nitrogen 2 5047.13 2523.56 28.08 ** 3.17 5.01 Phosphorus 2 756.84 478.42 5.32 ** " " Potassium. 2 352.29 176.14 1.96 " " Nitrogen x Phosphorus 4 269.18 67.29 0.74 2.54 3.68 " .x Potassium 4 983.94 245.98 2.74 * " " Phosphorus 4 390.78 97.69 1.09 " " Nitrogen linear 1 49764.90 49764.90 55.37 ** 4.02 7.12 " quadratic 1 706.50 706.50 0.78 “ “ Phosphorus linear 1 6960.90 6960.90 7.75 ** " " " quadratic 1 607.40 607.40 0.67 " " Potassium.linear 1 - “ quadratic l — Error 54 4853.16 898.7, Total 80 15380.11 %cv V??? x 100 = 8.2% “7“:- THESIS 117 TABLE XXXIV - SUMMARY OF ANALYSIS OF VARIANCE - FOX LOAMY SAND, 1955. Source of Variation D.F. S. of S. Variance "f" necessary "f" 5% 1% Replications 2 37523.27 1876.63 67.86 ** 3.17 5.01 Blocks Within Reps 6 5512.05 918.67 3.32 ** 2.27 3.15 Nitrogen 2 3771.28 1885.64 6.82 ** 3.17 5.01 Phosphorus 2 14279.83 7139.91 25.82 ** " “ Potassium 2 2529. 17 1264. 58 4. 57 " " Nitrogen x PhoSphorus 4 2896.49 724.12 2.62 * 2.54 3.68 " x Potassium 4 854.62 213.65 0.77 " " Phosphorus x Potassium 4 934.40 233.50 0.84 " " Nitrogen linear 1 2706.54 2706.54 9.79 ** 4.02 7.12 " quadratic 1 1064.65 1064.65 3.85 " " Phosphorus linear 1 13667.64 13667.64 49.44 ** " “ " quadratic 1 611.33 611.33 2.21 " " Potassium linear 1 2475.25 2475.25 8.95 **' " " " quadratic 1‘ 53.85 53.85 .19 " " Error 54 14928.59 276.45 Total 80 83229.70 %cv = %x100 = 11.8% I 9;. TH E818 118 TABLE XXXV - SUMMARY OF ANALYSIS OF VARIANCE - HONEYWCOD SILT LOAN, 1956. Source of Variation D.F. S. of S. Variance "f" necessary "f" 5% 1% Replications 2 12723.95 6361.98 2.47 3.17 5.01 Blocks within Reps 6 42890.61 7148.44 2.77 * 2.27 3.15 Nitrogen 2 56758.39 28379.20 11.00“ 3.17 5.01 Phosphorus 2 37021.44 18510.72 7.18 ** ' " Potassium_ 2 189857.06 94928.53 36.81 ** ' " Nitrogen x PhoSphorus 4 14257.96 3564.49 1.38 2.54 3.68 Nitrogen x Potassium 4 10502.99 2625.75 1.02 " " PhOSphorus x Potassium 4 9651.28 2412.82 0.94 " " Nitrogen linear 1 53304.65 53304.65 20.67 ** 4.02 7.12 " Quadratic 1 3453.73 3453.73 1.34 " " PhoSphorus linear 1 36795.78 .36795J78 14.27 ** " " " quadratic 1 225.66 225.66 0.87 " “ Potassium linear 1 184088.49 184088.49 71.37 ** " u ” quadratic 1 5768.57 5768.57 2.24 " " Error 54 139270.12 2579.08 Total 80 512933.80 zcv = 5%):100 - 16.7% TH ES‘IS 119 TABLE XXXVI - SUMMARY OF ANALYSIS OF VARIANCE - FOX SANDY LOAM, 1956. Source of Variation D.F. S. of S. Variance "f" necessary "f" 5% 1% Replications 2 9813.13 4906.57 6.07 ** 3.17 5.01 Blocks within Reps 6 20698.00 3449.67 4.27 ** 2.27 3.15 Nitrogen 2 10671.74 5335.87 6.60 ** 3.17 5.01 Phospjorus 2 40679.02 20339.51 25.17 ** " “ Potassium 2 6782.29 3391.15 4.19 * " " Nitrogen x Phosphorus 4 2340.23 585.06 0.73 2.54 3.68 " x Potassium 4 6743.52 1685.88 2.09 " " Phosphorus x.Potassium 4 5248.74 1312.19 1.62 " " Nitrogen linear 1 7608.91 7608.91 9.42 ** 4.02 7.12 " quadratic 1 3062.84 3062.84 3.79 " " PhOSphorus linear 1 34767.56 34767.56 4.30 * " " " quadratic 1 5911.47 5911.47 7.32 ** “ " Potassium linear 1 5102.22 5102.22 6.32 * " " “1 quadratic 1 1680.07 1680.07 2.08 “ " Error 54 43623.79 807.85 Total 80 146600.46 %c = W x 100 = 11.6% V 245.1 THESIS 120 TABLE XXXVII - SUMMARY OF ANALYSIS OF VARIANCE - BOOKTON LOAN, 1956. Source of Variation D.F. S. of S. Variance "f" necessary "f" 5% 1% Replications 2 1931.20 965.60 1.26 3.17 5.01 Blocks within Reps 6 3743.72 623.95 0.82 2.27 3.15 Nitrogen 2 3405.05 1702.53 2.23 3.17 5.01 Phosphorus 2 120803.28 60401.64 79.00 ** " " Potassium 2 10410.67 5205.33 6.81 ** " " Nitrogen x Phosphorus 4 7088.80 1772.20 2.32 2.54 3.68 " x.Potassium 4 1321.73 330.43 0.43 " " Phosphorus x Potassium 4 3602.49 900.62 1.18 " " Nitrogen linear 1 3404.99 3404.99 4.45 * 4.02 7.12 " quadratic 1 0.099 0.099 " " Phosphorus linear 1 106488.96 106488.96 139.27 ** " " " quadratic 1 14314.32 14314.32 18.72 ** " " Potassium linear 1 9610.67 9610.97 12.57 ** " " “ quadratic 1 800.00 800.00 1.05 " " Error 54 41286.53 764.57 Total 80 193593.47 %C - 'NIEEEEI x 100 = 17.1% V - 1620 O TH 5'95 I . o . I V - '~ o c n o v 0 ' O O o n ' O Q I . » v 0 i ' G O O O 0 r u I ‘ TABLE XXXVIII — 121 SUMNARY OF ANALYSIS OF VARIANCE - TIOGA LOAN, 1956. Source of Variation D.F. S. of 5., Variance "f" necessary "f" 5% 1% Replications 2 17382.06 8691.03 2.42 3.17 5.01 Blocks within Reps 6 46131.41 7688.57 2.14 2. 27 3.15 Nitrogen 2 139228.76 69614.38 19.35 ** 3.17 5.01 Phosphorus 2 90677.14 45338.57 12.60 ** " " Potassium 2 197637.75 98818.87 27.47 ** n n Nitrogen x Phosphorus 4 26085.06 6271.26 1.74 2.54 3.68 " x Potassium 4 30183.50 7545.87 2.10 " " Phosphorus x Potassium 4 46103.06 11525.75 3.20 * “ " Nitrogen linear l 136987.26 136987.26 38.08 ** 4.02 7.12 “ quadratic 1 2241.52 2241.52 0.62 " " Phosphorus linear 1 75114.74 75114.74 20.88 ** “ " " quadratic 1 15562.40 15562.40 4.33 * " " Potassium linear 1 184403.91 184403.91 51.27 ** " “ " quadratic 1 13233.84 13233.84 3.68 " " Error 54 194217.41 3596.62 Total 80 787646.15 9:10V = ‘Q-gz—EE—g—Z-xwo = 22.6% 114E515 122 -A P P E N D I X E -Revised Design for Fertilizer Response Experiments THE‘E‘S .l‘ ii.li 1! F A...- 123 Revised Design for Fertilizer Response Experiments - 1962. Oats: Two trials, each of 140 plots - 1 on clay loam or clay, 1 on sandy loam or loam. Trials to be located on fields of low soil test and not after legumes. Eggigg - 53 factorial in one complete block with a central compo- site rotatable design (Cochrane and Cox, p. 347) set within the main experiment. Four extra check plots will also be included. The compo- site plots will be placed adjacent to each other but the position of this group within the main block will be randomly selected. All other plots will be located at random. Rates - lbs./acre -2 -1.682 -1 0 1 1.682 2 N O 6.36 20 4O 60 73.64 80 P205 0 9.54 30 60 90 110.46 120 K20 0 9.54 30 6O 90 110.46 120 All fertilizer up to and including 20 lbs. N, 30 lbs. P205, 30 lbs. K20 to be drilled with the seed. Additional fertilizer above these rates to be drilled before seeding with the drill set as deep as possible. Corn: Two trials of the same design as oats. Rates - lbs.[acre -2 -1.682 -1 0 1 1.682 2 O 19.08 60 120 180 220.92 240 P205 0 19.08 60 120 180 220.92 240 K20 O 19.08 60 120 180 220.92 240 THESES 124 All fertilizer up to and including 60 lbs. N, 60 lbs. P205, 60 Additional fertilizer above lbs. K20 to be banded close to the seed. these rates to be applied after planting in bands 6-9" to the side of the seed. Treatment Levels of 53 Factorial Design No. No. N No. -2 -l —2 ~2 -2 -2 0 0 51 52 53 54 -2 -1 -2 -2 —2 -2 -2 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 26 27 28 29 30 -2 -1 -2 -2 -2 -2 -2 -l -1 -l -1 -l -2 —2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 1 2 -2 —1 -1 -1 -1 -1 0 O 56 57 58 59 -2 -1 31 -2 -1 32 7 33 34 35 -1 -l -1 -2 10 11 12 36 63 64 65 13 —2 -2 -2 -2 —2 -2 -2 15 41 -2 l6 l7 18 19 20 21 22 23 68 69 -1 7O 45 -2 -2 -2 -l 71 —2 -1 -1 46 72 73 74 75 -2 ~2 -2 25 THES‘S No. N p K 76 1 -2 -2 77 1 -2 -l 78 1 -2 o 79 1 -2 1 80 1 -2 2 81 1 -1 -2 82 1 -1 -1 83 1 -1 84 _1 -1 1 85 1 -1 2 86 1 o -2 87 1 o -1 88 1 o o 89 1 o 1 9o 1 o 2 91 1 1 -2 92 1 1 -1 93 1 l 91 1 1 1 95 l 1 2 96 1 2 -2 97 1 2 -1 98 1 2 o 99 1 2 1 100 1 2 2 125 No. N P K 101 2 -2 -2 102 2 '-2 -l 103 2 -2 0 104 2 -2 l 105 2 -2 2 106 2 -1 «2 107 2 -1 -l 108 2 -l 0 109 2 ~1 110 2 -1 2 111 2 O -2 112 2 0 -1 113 2 0 114 2 0 1 115 2 0 2 116 2 l -2 117 2 l -1 118 2 l 119 2 l 1 120 2 1 2 121 2 2 -2 122 2 2 -1 123 2 2 124 2 2 1 125 2 2 2 Treatments with are 2K points (+ one centre point) of rotatable design. In addition to complete the rotatable design No. 126 127 128 129 130 0 131 -1.682 0 132 0 -l.682 0 133 0 O -l.682 134 0 0 1.682 135 0 1.682 0 136 1.682 0 0 0000 OOOOO’U OOOOOON plus 4 extra check plots. NOTE: 126-130 5 centre points 131-136 6 star points. THESIS "I11111111111141