JB 186 K5 «opy 2 STUDIES CONCERNING THE ELIMINATION OF EXPERIMENTAL ERROR IN COM- PARATIVE CROP TESTS By T. A. KlESSELBACH A THESIS PRESENTED TO THE FACULTY OF THE GRADUATE COLLEGE IN THE UNIVERSITY OF NEBRASKA IN PARTIAL FULFILLMENT OF REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF BOTANY LINCOLN, NEBRASKA December, 1917 Reprint from Nebraska Agricultural Experiment Station Research Bulletin No. 13 STUDIES CONCERNING THE ELIMINATION OF EXPERIMENTAL ERROR IN COM- PARATIVE CROP TESTS By T. A. Kiesselbach A THESIS PRESENTED TO THE FACULTY OF THE GRADUATE COLLEGE IN THE UNIVERSITY OF NEBRASKA IN PARTIAL FULFILLMENT OF REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF BOTANY LINCOLN, NEBRASKA December, 1917 Reprint from Nebraska Agricultural Experiment Station Research Bulletin No. 13 G^w £ AGRICULTURAL EXPERIMENT STATION OF NEBRASKA THE GOVERNING BOARD (the regents of the university) HONORABLE E. P. BROWN, President, Davey. HONORABLE J. E. MILLER, Vice President, Lincoln. HONORABLE FRANK L. HALLER, Omaha. HONORABLE VICTOR G. LYFORD, Falls City. HONORABLE PHILIP L. HALL, Lincoln. HONORABLE HARRY D. LANDIS, Seward. THE STATION OFFICERS *SAMUEL AVERY, Ph. D., LL. D., Chancellor, ex officio. W. G. HASTINGS, A. B., Acting Chancellor. E. A. BURNETT, D. Sc, Director. C. W. PUGSLEY, B. Sc, Director of Extension Service. J. S. DALES, M. Ph., Financial Secretary. C. A. LEWIS, B. Sc, Bulletin Editor. THE WORKING STAFF F. W. Upson, Ph. D., Agricultural Chemistry. *L. W. Chase, M. E., A. E., Agricultural Engineering. W. W. Burr, B. Sc, Agronomy. T. A. Kiesselbach, A. M., Agronomy. H. J. Gramlich, B. Sc, Animal Husbandry. J. H. Gain, M. D. C, Animal Pathology. J. H. Frandsen, M. S. A., Dairy Husbandry. Lawrence Bruner, B. Sc., Entomology. M. H. Swenk, A. M., Entomology. H. C. Filley, A. M., Farm Management. R. F. Howard, A. M., Horticulture. G. A. Loveland, A. M., Meteorology. E. Mead Wilcox, Ph. D., Plant Pathology and Physiology. F. E. Mussehl, B. Sc, Poultry. W. P. Snyder, M. S., Superintendent Experiment Substation, North Platte. James Cowan, M. E., Superintendent Experimental Substation. Valentine. James A. Holden, B. Sc, Superintendent Experimental Substation, Mitchell. tL. L. Zook, B. Sc, Agronomist, North Platte. *J. W. Calvin, B. Sc, Associate in Agricultural Chemistry. tG. K. K. Link, Ph. D., Associate in Plant Pathology and Physiology. Erwin Hopt, B. Sc, Assistant in Agronomy. W. B. Nevens, M. S., Assistant in Dairy Husbandry. R. R. Spafford, A. M., Assistant in Farm Management. *Granted leave of absence for military service. tDetailed from Office of Dry Land Agriculture, United States Depart- ment of Agriculture, Washington, D. C. tGranted leave of absence. tUG 2/. *mo CONTENTS Page Summary 5 Error due to competition between adjacent plats 14 Illustration of principle of competition between adjacent rows 14 Competition between adjacent rows of small grain 14 Row competition in rate-of-planting tests with wheat and oats 15 Relative stooling of two rates of planting when compared in alternating rows and alternating blocks 18 Row competition between varieties of wheat and oats 19 Evidence of plat competition in a wheat-breeding nursery 2 5 Competition between individual plants 2 7 Competition between corn test plats as a source of experi- mental error 2 9 Row competition in rate-of-planting tests with corn 31 Intra-hill and row competition in corn variety yield tests 33 Summary of plat competition studies 41 Variation of stand as a source of error in yield tests with corn 41 Relation of stand to yield in single-row test plats 4 3 Combination of rate planting with variety yield tests 45 Effect of removing suckers with different varieties 4 7 Reliability of estimating plat yields by means of fractional areas... 4 7 Experimental errors caused by soil variation 51 Use of check plats 5 3 Reduction of error by replication 61 Effect of size and shape of plat 64 Significance of the probable error 6 5 Probable error for 5 groups of four adjacent thirtieth-acre plats of Kherson oats 67 Probable error of 5 groups of four systematically distrib- uted thirtieth-acre plats of Kherson oats 72 Examples of limitation of the probable error 72 Effect of change in methods on agronomic equipment 7 4 Measuring improvement in yield thru breeding 7 5 Soil limitation as a source of error in pot experiments 78 Effect of the size of pot upon the growth of corn 80 Effect of planting at different rates upon the growth of corn in pots _ 8 5 Statement of methods in bulletins 8 9 Bibliography 91 The author wishes to take this opportunity to thank Professors R. J. Pool and W. W. Burr for the interest and advice they have given him in the preparation of this bulletin as a thesis for the degree of Doctor of Philosophy. SUMMARY 1. In determining the effect of competition between single-row test plats as a source of experimental error in crop yield tests, the relative yields of two crops planted in blocks containing several rows have been regarded as the true relative values for the crops tested. In ascertaining some of these true values, the outer rows of the plats have been discarded in order to eliminate almost entirely plat com- petition. Plats were sufficiently replicated to secure quite reliable relative yields for the conditions under which they were grown. In plat competition tests in 1913 with two rates of plant- ing Turkey Red wheat, the thin rate yielded 68 per cent as much as the thick rate when grown in single alternating rows, while in five-row blocks the thin rate yielded 90 per cent as much as the thick rate. Competition in rows with a thicker rate of planting caused the. thin rate to yield rela- tively 24.4 per cent too low. In a similar test in 1914 the thin rate yielded relatively 56.8 per cent too low. 2. In 1913, competition between alternating rows of two rates of planting with Kherson oats caused the thin rate to yield relatively 20 per cent too low. In 1914, similar single- row competition caused the thin rate to yield relatively 34.3 per cent too low. 3. In 1914, competition between alternating single-row plats of Turkey Red wheat sown at two rates reduced the relative number of stools per plant approximately 37 per cent for the thin rate. There was a similar reduction of 20 per cent for Kherson oats, due to plat competition. 4. The relative competitive effect of varieties varies in different years, due to difference in adaptation to the seasonal conditions. In 1913, competition with Turkey Red winter wheat in single rows caused Big Frame winter wheat to yield rela- tively 10.3 per cent too high. In similar competition in 1914 Big Frame yielded relatively 12.4 per cent too low. In 1913 there was practically no competitive effect be- tween alternating rows of Turkey Red and Nebraska No. 28 winter wheat varieties. This was due to abnormal climatic conditions. However, in 1914 under rather normal condi- tions competition between single-row plats caused the Ne- braska No. 28 to yield relatively 25.9 per cent too low. 6 Nebraska Agricultural Exp. Station, Research Bui. 13 5. In 1913 in alternating single-row test plats of Burt and Kherson oats, the Burt yielded relatively 16 per cent too high, while in 1914 the yield was relatively 37.6 per cent too high, due to plat competition. In 1913, competition with Kherson oats in alternating one- row plats caused Swedish Select oats to yield relatively 7 per cent too high, while in 1914 its yield was relatively 4.3 per cent too low. 6. When large and small seeds of wheat were planted in competition in the same row, the small seed, as a result of competition, yielded relatively 15 per cent too little grain, 20 per cent too little straw, and made 18 per cent too small total yield. Similar competition was found between varieties of wheat planted in the same row. 7. In a single-row test of 80 strains of Turkey Red wheat grown in the same order each of four years, there are evidences of plat competition between strains. As an aver- age for four years, the poorest strain, No. 75, grew between strains No. 74 and No. 76, ranking one and five. A special test of these three strains in 1915 and 1916 disclosed that strains No. 74 and No. 76 were favored 20 and 15 per cent respectively thru competition with a less vigorous strain. 8. In a rate-of-planting test with Nebraska White Prize corn, — in which two rates of planting, namely two and four plants per hill, were compared in alternating single row plats, — the thin rate yielded relatively 29.3 per cent too low in 1914 because of plat competition. In 1915 the thin rate yielded 9 per cent too low because of plat competition. In 1916 such competition caused the thin rate to yield relatively 16.1 per cent too low. 9. A large, medium, and small variety of corn were grown in plat competition studies during 1912 and 1914. These varieties were Hogue's Yellow Dent, University No. 3, and Pride of the North, respectively. In 1912, Pride of the North yielded 85 per cent as much as Hogue's Yellow Dent in alternating three-row plats, while it yielded 66 per cent as much in alternating single rows. When compared in the same hill by the intra-hill method, the Pride of the North yielded only 47 per cent as much as Hogue's Yellow Dent. Due to competition, the Pride of the North yielded relatively 44.7 per cent too low when compared in the same hill, and 22 per cent too low in alternating one-row plats. Experimental Error in Crop. Tests 7 10. In 1914, due to plat competition, Pride of the North corn yielded relatively 51 per cent too low when compared with Hogue's Yellow Dent in the same hill, while in alter- nating single-row plats it yielded relatively 28.3 per cent too low. In a comparison of University No. 3 with Hogue's Yellow Dent, the University No. 3 yielded relatively eight per cent too low in single-row plats, and within the hill it yielded relatively one per cent too high. The lack of competition within the hill in this case may have been due to there being only two plants of a rather similar type in a hill. When all three varieties were compared in the same hill, the relative yields for Hogue's Yellow Dent, University No. 3, and Pride of the North were respectively 100, 96, and 28, as compared with 100, 98, and 53 in the center row of three-row plats and 100, 98, and 38 in single rows. 11. In 1916, inbred Hogue's Yellow Dent corn which had been greatly reduced in vigor by five years of self-fertiliza- tion was compared with the more vigorous first generation hybrid of two such pure lines, in blocks, rows, and hills. Be- cause of competition with the larger plants in the same hill, the inbred corn yielded relatively 44 per cent too low, while in alternating single rows, it yielded relatively 16 per cent too low. 12. Studies with oats, wheat, and corn suggest that the yield of the border rows of narrow, adjacent test plats may be materially affected by plat competition. 13. \yiien surrounded by corn hills having a full stand of three plants, two-plant hills and three-plant hills respec- tively yielded 10.5 per cent and 35 per cent more than a one- plant hill in 1914. In a similar test in 1917, two-plant hills and three-plant hills respectively yielded 67 and 102 per cent more than a one-plant hill. 14. The average grain yield of a three-plant corn hill sur- rounded by a full normal stand of three plants per hill was 465.8 grams in 1914. This yield per hill was increased 2.7, 5.3, 13.1, and 43.1 per cent by the presence, respectively, of (1) one adjacent hill with two plants, (2) one adjacent hill with one plant, (3) one adjacent blank hill, and (4) two adjacent blank hills. In 1917 corresponding adjacent imper- fect hills increased the grain yield of three-plant hills, other- wise surrounded by a full stand, respectively 2, 9, 15, and 25 per cent. 8 Nebraska Agricultural Exp. Station, Research Bui. 13 15. Regarding three plants per hill as a perfect stand, the reduction in yield of corn was not proportional to a reduc- tion in stand. With single-row plats, stands averaging 92.8, 87.2, 82.7, 77.8, 73.1, 66.6, and 43.0 per cent yielded respec- tively 85.5, 88.1, 83.5, 82.2, 77.9, 74.8, and 56.7 bushels per acre. 16. Satisfactory yield correction for corn based upon per cent of stand cannot be made, because the effect upon yield depends upon the distribution of the missing plants and because the effect upon yield is not proportional to the per cent stand. Comparable yield tests of similar varieties or strains of corn may be secured by basing the yield upon a counted number of hills containing a uniform number of plants and surrounded by a full stand. 17. Corn varieties or types differing markedly in growth characteristics should be tested at several rates of planting, because the optimum rate for one is not necessarily that for another. Thus, as an average for two years, Pride of the North and Calico produced their maximum yield when grown at the rate of five plants per hill, while Mammonth White Pearl yielded best at the three-rate. In 1914, Pride of the North yielded most at the five-rate, University No. 3 did equally well at the two and three-rate, while Hogue's Yellow Dent produced best at the two-rate. 18. The removal of suckers affects the yield of varieties differently, and for this reason suckers should for no reason be removed in comparative variety tests. 19. In comparative yield tests where it is not conven- ient to harvest and thresh the entire plats, fairly reliable results may be obtained by harvesting and averaging a large number of systematically distributed small fractional areas or quadrates from each plat. The necessary number of quadrates to be representative will vary with the size of the plats. Twenty 32-inch quadrates harvested from thirtieth-acre wheat plats gave fairly reliable results. Less than 20 proved likely to be unrepresentative of the plats. Very satisfactory results were obtained by having 40 quadrates represent one- fifteenth acre of wheat. 20. Two hundred and seven thirtieth-acre plats were grown to a uniform crop of Kherson oats for the purpose of studying various phases of experimental error. Calcula- tions have been made from them to show: (1) The use and Experimental Error in Crop Tests 9 effectiveness of check plats for reducing test plats to com- parable yields; (2) the reduction of error by the replication of plats; (3) the relative reliability of plats of various sizes and shapes; and (4) the significance of the "probable error" as a measure of confidence which may be placed in mean results. When the odd and even numbered plats of these 207 are regarded as check plats and test plats respectively and the grain yield of each test plat is corrected by the mean of the two adjacent check plats, the coefficient of variability for the actual yields of these test plats is reduced from 7.85 per cent for the actual yields to 7.01 per cent for the corrected yields. Assuming every third plat to be a check, and correcting the intervening plats by the one adjacent check plat, the coef- ficient of variability was reduced from 7.79 per cent to 7.35 per cent. With every third plat regarded as a check plat, and the intervening plats corrected progressively by the two near- est checks, the coefficient of variability is reduced from 7.87 to 6.57 per cent. Thus it is seen that none of the three methods of check plat correction have been very effective. The yield of systematically distributed check plats can- not be regarded as a reliable measure for correcting and es- tablishing correct theoretical or normal yields for the inter- vening plats. 21. Systematic replication of plats is the most effective and satisfactory means for reducing error caused by soil or other environmental variations. When 200 thirtieth-acre plats were planted to a uniform crop of Kherson oats, the coefficients of variability for the grain yields of single plats and for the mean yields of two, four, and eight plats were 6.30, 4.59, 2.91, and 2.13 per cent respectively. The extreme variation between yields was also reduced from 20.7 bushels for single plats to 7.5 bushels for the means of eight plats. Reduction of error by averaging adjacent plats (which is equivalent to increasing the size of the plat) was far less effective than systematic replication. The coefficients of vari- ability for single plats and for the mean yields of two, four and eight adjacent plats were 6.30, 5.46, 5.28, and 4.78 per cent. Variation between long, narrow plats was less marked than for short, wide plats of the same area. The coefficient of variability for tenth-acre oats plats 48 rods by 5.50 feet was 10 Nebraska Agricultural Exp. Station, Research Bui. 13 3.84 per cent as compared with 5.18 per cent for plats 16 rods by 16.5 feet. 22. Two hundred uniformly planted thirtieth-acre Kher- son oats plats were arranged in 50 groups of four adjacent plats each, and also in 50 groups of four systematically dis- tributed plats. For both methods of grouping, the "prob- able error" has been calculated for the mean yield of each group of four plats. The results indicate that a small prob- able error cannot be regarded as sufficient reason for con- fidence in the reliability of data. Because of chance groupings of either large or small variations where relatively small numbers are used, a mean may be either more or less accurate than an application of the probable error would indicate. 23. In four comparative rate-planting yield tests with small grains in alternating single-row plats the probable error was less than 2 per cent in all cases, and yet there existed an average actual error of 34 per cent in relative yields due to plat competition. Similar results are indicated for variety tests with small grains. 24. An application of the probable error to tests made in 1916 concerning the relative water requirement for grain production of Hogue's Yellow Dent corn and Turkey Red winter wheat may result in greatly misplaced confidence. We may be confident from one test that Hogue's Yellow Dent corn uses considerably less water per pound of grain than does Turkey Red wheat, and from another test we may be equally confident that the corn uses more than twice as much water for grain production as does the wheat. The second comparative figures are unreliable because the soil was rela- tively overcropped by the corn. 25. Crop tests are subject to such a multitude of local environmental influences that errors in them cannot be regarded as occurring according to the formulas or rules of chance calculated mathematically from purely mechanical observations. The probable error may apply where only accidental variations occur but not where systematic varia- tions exist. Crop tests are subject to systematic variations. 26. In view of the precautions necessary to guard against the invalidating influences of various sources of experimental error, greater and better facilities should be provided experi- ment stations for the conduct of crop investigations. Experimental Error in Crop Tests 11 27. In crop breeding experiments improvement in yield over the original can only be measured accurately by grow- ing each year some of the original unselected seed for com- parison. The method of comparing the results of one period of years with those of another is unreliable. For example, Hogue's Yellow Dent corn which has undergone continuous ear-to-row breeding since 1902 yielded 39 per cent less during the seven-year period 1907-1913 than during the preceding seven years. However, a seven-year comparison with the orig- inal seed which has been grown as a check indicates that the inherent yielding power of the ear-to-row and the original corn are almost identical. 28. Soil limitation may be a serious source of error in pot experiments. The relative total moisture-free yields for individual corn plants grown in pots of six sizes in 1914 were, in order from the smallest to the largest, 100, 211, 324.1, 453.6, 643.8, and 747. The corresponding yields of ear corn were 100, 632.5, 1082.3, 2417, 2990, and 4046.7. A uniform application of 1.75 pound of sheep manure per plant (or per pot) increased the yields of total dry matter for the six sizes, in order from the smallest to the largest, 176.4, 95.3, 69.3, 26.1, 12.7, and 7.2 per cent. The corresponding increases in yield of ear corn caused by the manure were 722.5, 193.6, 149.2, 18.9, 14.1, and. 2.9 per cent. In 1915 the relative yields of total dry matter from the six sizes of pots, progressing from the smallest to the largest, were 100, 150, 229.6, 355.6, 586, and 578.7 per cent. The corresponding relative yields of ear corn were 100, 276.2, 819, 1647.5, 2771.3, and 2667. Applying manure in amounts proportional to the quan- tity of soil contained, in 1915 had far less striking effect upon the pot yields for the different sizes than when equal quantities were applied in 1914, regardless of the quantity of soil contained. 29. When two, four, or six corn plants were grown in pots of the proper size for growing one normal corn plant, the individual plant yields of total dry matter were respec- tively 50.8, 26.7, and 16.6 per cent as large as for the one-rate, while the corresponding yields of ear corn were respectively 3977, 15.9, and 2.8 per cent as large. 30. A review of several hundred experiment station bulletins dealing with variety, fertilizer, cultural, and pot 12 Nebraska Agricultural Exp. Station, Research Bui. 13 tests indicates that the statement of methods employed in securing experimental data is often inadequate to acquaint the reader with the manner in which the results were ob- tained. Such a statement is desirable in order that one may judge regarding the reliability of the results and the degree of confidence which the data merit. STUDIES CONCERNING THE ELIMINATION OF EXPERIMENTAL ERROR IN COMPARA- TIVE CROP TESTS By T. A. KlESSELBACH It is apparent that many sources of error have uncon- sciously entered into comparative crop yield tests. The very important matter of overcoming variation in soil conditions as a source of experimental error has been quite extensively studied and reported by various investigators during the past decade. The means suggested for reducing such error have been (1) repetition of plats and (2) correction of yields according to check plats planted to a uniform variety or treatment at stated intervals. Both methods have proved of value and a combination of both may often be used advan- tageously. Some danger always exists of error occurring in the check plats and that correcting according to them may introduce new errors in the yields of crops compared. The method should, for this reason, be used with caution. Studies in experimental error conducted at this Experi- ment Station prior to 1911 have been published by Prof. E. G. Montgomery, now of Cornell University, in Bulletin No. 269, of the Bureau of Plant Industry, U. S. Department of Agriculture, and in the Twenty-sixth Annual Report of the Nebraska Agricultural Experiment Station. These pub- lished results concern primarily the general problems of repe- tition and size of nursery small grain plats, and the use of check plats. The object of the following investigations was to secure further information regarding the elimination of error in comparative yield tests. Shortage of facilities for carrying on this character of work in addition to the regular crop investigations of the Experiment Station has in some cases necessitated intermittent experiments. The duration of some of the tests has for the same reason been shorter than would have been desired. Acknowledgment is gratefully made to Professor J. A. Ratcliff and Pro- fessor C. A. Helm for valuable assistance in field supervision and in keeping- records during - much of the time these experiments were in progress. Messrs. H. G. Gould, E. R. Bwing, R. E. Holland and H. B. Pier, have also rendered efficient assistance at various times. 14 Nebraska Agricultural Exp. Station, Research Bui. 13 ERROR DUE TO COMPETITION BETWEEN ADJACENT PLATS It is a well known principle in ecology that a keen com- petition for soil moisture and nutrients may exist between plants which differ in growth habit, when grown in close proximity. Competition between adjacent rows of different varieties, selections, or rates of planting, had suggested itself as a possible source of error in crop tests. An inves- tigation was planned in 1912 to determine the relative merits of rows and blocks for making comparative yield tests in the small grain nursery and in corn experiments. The question was : Will two varieties give the same com- parative yields when planted in alternating rows as when planted in alternating blocks consisting of a number of rows? It was reasonable to assume that there would be less plat- competition between varieties planted in blocks than when planted in single rows. It has been a common practice in crop breeding experi- ments to compare the selected strains in adjacent one-row plats for a number of years. Many other comparative tests have also been made in single row plats. ILLISTKVTIOX OF PRINCIPLE OP COMPETITION BETWEEN ADJACENT ROWS On the right-hand side of Fig. 1 is shown a crop of Tur- key Red winter wheat planted in the fall of 1912. To the south of this was planted Scotch Fife spring wheat in the spring of 1913. The first row of spring wheat, spaced ten inches from the winter wheat, is seen to have grown only about four inches tall with no grain production. The sec- ond row of spring wheat made an almost normal growth, while the third row was entirely normal. The complete fail- ure of the first row of spring wheat may be accounted for by the shortage of both moisture and available plant food material, due to the more rapid and luxuriant growth of the adjacent winter wheat. While this is an extreme example of competition between adjacent rows, it illustrates a principle commonly applying in crop yield tests. COMPETITION BETWEEN ADJACENT HOWS OP SMALL GRAIN The plan of the experiment was to plant two crops under comparison in alternating one-row plats and alternating five- row plats. These were replicated 50 times each year in order Experimental Error in Crop Tests 15 Fig. 1 — Illustrating principle of competition between adjacent rows. Winter wheat on right; spring wheat on left. Due to competition with the winter wheat, the first row of spring wheat grew only- four inches tall wifh no grain production. The second row was nearly normal and the third row entirely normal. to eliminate the accidental mechanical and physical errors due to variation in soil, exposure, stand, etc. These nursery rows were spaced 10 inches apart. The relative yields in either the entire five-row block or the three inner rows, as indicated, were regarded as the correct relative yields for the season. A difference in the relative yields when tested in alternating rows, as compared with the relative yields in blocks, is chiefly due to, and measures, the competition be- tween the crops compared in rows. In part of the tests the blocks were harvested as individual rows, which permitted a study of the effect of plat competition upon the border rows of five-row plats. The straw yields as well as the grain yields were also secured in a portion of the tests. ROW COMPETITION IN RATE-OF-PLANTING TESTS WITH WHEAT AND OATS During the jrears 1913 and 1914, both oats and winter wheat were grown at two distinct rates of planting in both 16 Nebraska Agricultural Exp. Station, Research Bui. 13 alternating single-row plats and alternating five-row nur- sery plats, 16 feet in length. Wheat — Table 1 shows the results with the wheat rate- of-planting tests. When grown in single rows in 1913, the thin rate yielded 68 per cent as much as the thick rate, while in five-row blocks the thin rate yielded 90 per cent as much as the thick rate. Competition in rows with a thicker rate of planting caused the thin rate to yield relatively 24.4 per cent too low. (This percentage effect of competition is determined by dividing the difference between 68 per cent and 90 per cent, or 22, by 90.) In 1914 the thin rate in rows yielded 35 per cent as much as the thick rate, while in the center three rows of five-row plats it yielded 81 per cent as much as the thick rate. Due to competition, the thin rate yielded 56.8 per cent too low. If the two outside rows are averaged into the block yield, the Fig. 2 — Method of planting nursery small grain plats with a special nursery drill. 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  • > 01 M a 0) > < Ratio Kherson to Swedish Select w ■3 01 is w Kherson I o o t* 01 a a '3 M o "oi '£, 01 CD 01 > Ratio Kherson to Swedish Select +-> 01 01 OT ■3 01 % OT i e Kherson I o ca a 01 o M IS -C O NCO 1OC0 M -H o w M CO CC CD lO 00 lO CO -H -H -H -H CO __ * _;g £* H& c c 01 01 Experimental Error in Crop Tests 25 Table 7 summarizes the two years' data with Kherson and Swedish Select oats. In 1913 the Swedish Select yielded 18 per cent less than the Kherson when grown in alternating single-row plats, and 23 per cent less in alternating five-row plats. In alternating single rows the Swedish Select yielded relatively 7 per cent too high. In 1914 the Swedish Select yielded 89 per cent as much grain as Kherson in alternating single-row plats and 93 per cent as much in five-row plats. The Swedish Select straw yielded 13 per cent more in alternating rows and 17 per cent more in five-row plats. EVIDENCE OF PLAT COMPETITION IN A WHEAT-BREEDING NURSERY During the four years, 1910, 1911, 1912 and 1914, 80 strains of Turkey Red wheat were tested at the ordinary field rate of seeding in identically the same order each year, in single 16-foot rows ten inches apart. The entire series has been replicated ten times each year. It is probable that many of the yields have been subject to the effect of row com- petition. Table 8 contains a concrete example of competition be- tween strains in such a wheat-breeding nursery. In the four- year row test of 80 strains, strain No. 75 ranked 80, while strains No. 74 and No. 76 on either side ranked 1 and 5. Strain No. 75 is a slightly shorter and thinner stooling type. To determine whether the relative rankings of these strains might have been influenced by competition, they were com- pared in both rows and blocks for two years, 1915-1916. Table 8— Relative yields of three Turkey Red wheat strains when compared in five-row nursery plats and in single- rovj plats. Tivo-year average (1915-1916) Strain number Relative yields Blocks Rows GRAIN 74 75 76 106 100 108 126 100 123 STRAW 74 75 76 110 100 102 113 100 109 26 Nebraska Agricultural Exp. Station, Research Bid. 13 Strain No. 74 was favored 20 per cent and strain No. 76, 15 per cent in yield by being compared (with an adjacent less vigorous type) in rows rather than in blocks. Fig. 5 is a photograph of these strains. Strain No.: Ck. 74 Fig. 5 — Single-row nursery test plats of Turkey Red Winter wheat. Strain No. 75, in center, is seen to have a lower stooling capacity and is given and unfair test when growing between two high-stool- ing strains. The two adjacent strains in turn have an unfair advan- tage Experimental Error in Crop Tests 27 These 80 strains are now all being grown in five-row plats, replicated ten times, for the purpose of establishing the correct relative yields, free from competition as a source of experimental error. Single-row plats are now regarded as unreliable and misleading, because a strain is certain to be unduly favored when grown beside a strain lower in com- petitive qualities due to such factors as low stooling, slow growing, or partial winterkilling. It is important to have any crop being tested surrounded by a crop of its own kind. COMPETITION BETWEEN INDIVIDUAL PLANTS Altho the yields of small grain are never compared by planting alternating seeds of two varieties or two grades of seed in the same row, yet such a comparison may be of inter- est to throw further light upon the principle of competition. Table 9 — Relative yields, at the normal field rate of planting, of equal numbers of large and small wheat seeds when grown alone in blocks and, when grown in competition by alternation in the same row* Method of comparing large and small seeds Ratio of yield of small seeds to large seeds Grain Straw Total WINTER WHEAT, 1914 Grades alone in blocks I 90:100 I 94:100 Grades competing | 61:100 72:100 WINTER WHEAT, 1915 Grades alone in blocks I 99:100 I 98:100 Grades competing | 83:100 | 78:100 SPRING WHEAT, 1914 Grades alone in blocks I 88:100 I 93:100 Grades competing I 78:100 | 78:100 SPRING WHEAT, 1915 Grades alone in blocks I 80:100 I 93:100 Grades competing | 82:100 | 73:100 AVERAGE FOR WINTER AND SPRING WHEAT, 1914-1915 Grades alone in blocks ] 89:100 I 94:100 Grades competing | 76:100 \ 75:100 *Compiled from data in Nebraska Research Bulletin No. 11, 1917 94:100 71:100 98:100 79:100 92:100 78:100 90:100 75:100 93:100 76:100 28 Nebraska Agricultural Exp. Station, Research Bui. 13 During 1914 and 1915 large and small wheat seeds were planted alternatingly in the row at the normal field rate of planting. Two varieties were used and reciprocated so that the results in Table 9 represent the mean of two varieties for each grade. This reciprocation eliminates largely the varietal effects in the summary. It was necessary to use two distinct varieties (a bearded and a beardless) so that the plants from each grade might be separated at harvest. The same grades were also compared separately in nursery blocks to establish the relative yields when free from competition. As an average for two varieties each of winter and spring wheat for two years, the small seed in competition yielded relatively 15 per cent too little grain, 20 per cent too little straw, and made 18 per cent too small total yield. Table 10 — Relative yields at the normal field rate of planting, of two varieties when grown alone in blocks, and when grown in competition by alternation in the same row* Method of comparing varieties Relative yields Grain Straw Total Ratio Big Frame to Turkey Red \ Competition WINTER WHEAT, 1914 /Alone... 90:100 Ratio Scotch Fife to Marquis \ Competition 55:100 SPRING WHEAT, 1914 /Alone | 75:100 Ratio Big Frame / Alone to Turkey Red \ Competition 61:100 WINTER WHEAT, 1915 82:100 120:100 SPRING WHEAT, 1915 Ratio Scotch Fife / Alone to Marquis 1 Competition . 95:100 99:100 88:100 70:100 93-100 90:100 105:100 128:100 114:100 125:100 89:100 67:100 90:100 86:100 99:100 125:100 109:100 119:100 *Compiled from data in Nebraska Research Bulletin No. 11, 1917. The results for different years should not be averaged in this variety test, since varieties do not have the same relative competitive qualities in different years. We are interested here in what may happen any one year and not in an average of years. In similar manner, competition between two varieties planted within the same row was determined. Plants from each variety could be separated at harvest by the presence or absence of beards. The relative yields were also obtained in nursery blocks free from competition by harvesting the Experimental Error in Crop Tests 29 three inside rows of five-row blocks. The results in Table 10 indicate marked competition between varieties. Variety competition amounted to 61 per cent and 46 per cent for win- ter wheat yields in 1914 and 1915 respectively. For spring wheat this competition equaled 19 per cent and 4 per cent in 1914 and 1915 respectively. COMPETITION BETWEEN CORN TEST PLATS AS A SOURCE OP EXPERIMENTAL, ERROR In corn variety tests, corn breeding experiments, and various other corn yield tests the crops under comparison have customarily been planted in adjacent plats containing one, two, three, or four rows. The single-row plat is used almost universally in corn breeding experiments. In several instances where only three or four kinds of corn were to be compared, these have all been planted in the same hill, giving each kind of corn a definite position in the hill. This intra- hill method has been employed by Hartley, Brown, Kyle, and Zook (1912) and by Collins (1914).* Fig. (i — Planting experimental corn plats where accuracy is required. Hand planters are found tar superior to planting with a hoe. A stated number of kernels are placed in the planter for each drop *The year in parentheses following- an author's name in the text serves to associate the reference with a particular publication in the Bibliography (pp. 91-94), where the complete title is given. 30 Nebraska Agricultural Exp. Station, Research Bui. 13 Fig. 7 — A hill of checked corn with the three plants spaced in the hill in order that the plants may be readily counted without suckers being mistaken for separate plants In 1912 the Nebraska Experiment Station commenced a series of experiments to determine the reliability of the vari- ous kinds of corn test plats. The investigations were extended in 1913 but the corn was not harvested because of an almost total crop failure due to deficient rainfall. Good results were secured in 1914, 1915, and 1916. For planting, the land was marked off into hills three feet, eight inches apart and the corn planted at double the desired rate by means of hand planters. (Fig. 6.) When about four inches high the plants were thinned to the desired rate, thus producing an almost perfect stand. The plants were spaced within the hills so that the original plants could be easily distinguished from suckers. For the comparative yield tests, Experimental Error in Crop Tests 31 50 hills with the desired number of plants and surrounded by a normal stand were harvested from each row. This was accomplished by planting 72 hills in each row, which per- mitted the elimination of any hills having less than the full stand. Thus all yields were comparable so far as number of plants was concerned. The plats have been replicated eight or more times each year, as indicated in the tables, in order to eliminate soil variations. ROW COMPETITION IN RATB-OF-PLANTING TESTS WITH CORN Tables 11, 12, and 13 contain three years' results with planting Nebraska White Prize corn at the rate of two and four plants per hill in alternating single-row and three-row Fig. 3 — A hill of checked corn planted by the ordinary method without spacing the plants in the hill. It contains two plants, altho the number cannot be readily nor accurately determined as with the space-planted hill 32 Nebraska Agricultural Exp. Station, Research Bui. 13 Table 11 — Relative yields of two rates of planting with Ne- braska White Prize corn when compared in alternating one-row plats and in alternating three-row plats (191U) Yield per acre No. of rows in plat No. of plants per hill No. of replica- • tions No. of suckers per 100 plants No. of ears per 100 plants Average One-row plat or of two center row ' outside rows 1 1 4 2 15 15 7.4 26.6 67.0 93.0 Bushels 43.8 35.6 Per cent 100.0 82.0 Bushels 3 3 4 2 9 9 7.1 32.3 66.0 96.0 38.4 44.3 100.0 116.0 39.8 42.4 plats. The rows were harvested separately in the three-row plats. In 1914 the two-rate yielded 18 per cent less than the four-rate when compared in alternating single-row plats. In the center rows of alternating three-row plats, the two-rate yielded 16 per cent more than the four-rate. Due to compe- tition with a thicker stand, the two-rate yielded relatively 29.3 per cent too low in alternating single-row plats. In the two outer rows of the three-row plats, the ratio of the four- rate to the two-rate was 100:106.5 as compared with 100:116 for the center rows. Table 12 — Relative yields of two rates of planting with Ne- braska White Prize corn when compared in alternating one-row plats and alternating three-row plats (1915) Yield per acre No. of No. of No. of No. of No. of rows in plants replica- suckers ears Average plat per hill tions per 100 per 100 One-row plat or of two plants plants center row outside rows Bushels Per cent Bushels 1 4 8 8.5 95 101.7 100.0 1 2 8 21.8 110 64.2 63.1 3 4 8 11.9 93 90.0 100.0 91.2 3 2 8 29.7 112 62.0 70.0 63.0 Experimental Error in Crop Tests 33 In 1915 (Table 12), the two-rate yielded 36.9 per cent less than the four-rate when compared in alternating single-row plats. In the center rows of alternating three-row plats the two-rate yielded 30 per cent less than the four-rate. Due to competition, the two-rate yielded relatively 9.9 per cent too low in single-row plats. In the two outer rows the ratio of the four-rate to the two-rate was 100:69 as compared with 100 :70 for the center rows. Competition was far less marked in 1915 than in 1914 because of much more favorable moist- ure conditions. In 1916 (Table 13), the two-rate yielded 21.3 per cent less than the four-rate when compared in alternating single-row plats. In the center rows of alternating three-row plats the two-rate yielded 6.2 per cent less than the four-rate. As the result of competition, the two-rate yielded relatively 16.1 per cent too low in single row plats. In the two outer rows the ratio of the four-rate to the two-rate was 100:85.9 as com- pared with 100:93.8 for the center rows. Table 13 — Relative yields of two rates of planting with Ne- braska White Prize corn when compared in alternating one-row plats and alternating three-row plats (1916) No of No. of plants per hill No. of replica- tions No. of suckers per 100 plants No. of ears per 100 plants Yield per acre rows in plat One-row plat or center row Average of two outside rows 1 1 4 2 8 8 24.8 62.5 82 107.1 Bushels 52.7 41.5 Per cent 100 78.7 Bushels 3 3 4 2 8 8 23.0 60.0 79.9 115.6 51.8 48.6 100 93.8 53.4 45.9 INTRA-HILL AND ROW COMPETITION IN CORN VARIETY YIELD TESTS During the years 1912 and 1914, Pride of the North corn was compared with Hogue's Yellow Dent corn in (1) alter- nating single rows, (2) alternating three-row plats, and (3) in the same hill. A similar comparison was also made be- tween University No. 3 corn and Hogue's Yellow Dent in 1914. The relative yields of the above three varieties were also determined by planting all in the same hill. 34 Nebraska Agricultural Exp. Station, Research Bui. 13 The relative growth habits of these three varieties dur- ing 1914 is shown in Table 14. Hogue's Yellow Dent is a large variety of corn requiring the entire season to mature. Pride of the North is a small, early-maturing variety. Uni- versity No. 3 is normally somewhat earlier and smaller than Hogue's Yellow Dent. Table 14 — Relative growth characters of three corn varieties used in 191 U (Table 16) to determine the amount of error from variety competition when tested by the single-row and intra-hill methods (191 U) Variety Hogue's Yellow Dent University No. 3 Pride of the North . . Length of growing season Days 119 107 92 Height of stalk Inches 96 92 70 Leaf-area per plant Sq. In. 997 940 408 Fig. 9 — Alternating single-row plats of Hogue's Yellow Dent and Pride of the North corn, 1914. The row method of testing corn types which differ in growth habit is unreliable because of competition between the plats Experimental Error in Crop Tests 35 Fig. 10 — Alternating three-row plats of Hogue's Yellow Dent and Pride of the North corn, 1914. Pride of the North on the right. Compe- tition between test plats may be avoided and correct relative yields obtained by discarding the outside rows of three-row plats In 1912 Hogue's Yellow Dent and Pride of the North corn were grown in alternating single rows and in alternating three-row plats at the rate of three plants per hill in each case. These were also compared for yield by growing one plant of each variety in the same hill. For this reason the variety yields per acre in the hill method are on a different basis than in case of the rows and blocks, but nevertheless they are com- parable. The, three-row plat tests were replicated 10 times, the single row plats 20 times, and the hills 1,000 times. The results are contained in Table 15. In alternating three-row plats, Pride of the North yielded 85 per cent as much as Hogue's Yellow Dent, while in alter- nating single-row plats it yielded 66 per cent as much as the Hogue's Yellow Dent. Within the same hill, Pride of the North yielded 47 per cent as much as Hogue's Yellow Dent. Due to competition Pride of the North yielded relatively 44.7 per cent too low in the same hill, and 22.4 per cent too low in the alternating rows. 36 Nebraska Agricultural Exp. Station, Research Bui. 13 In 1914 Hogue's Yellow Dent corn was compared with University No. 3 corn in addition to a comparison with Pride of the North as made in 1912. All three varieties were also compared in the same hill. Plats were replicated the same as in 1912. The results are contained in Table 16. In the center row of alternating three-row plats, Pride of the North yielded 53 per cent as much as Hogue's Yellow Dent, while in alternating single row plats it yielded 38 per cent as much as Hogue's Yellow Dent. Within the same Fig. 11 — Relative growth of Hogue's Yellow Dent, University No. 3, and Pride of the North corn varieties when grown in the center row of three-row plats (1914) Experimental Error in -Crop Tests 37 hill, Pride of the North yielded 26 per cent as much as Hogue's Yellow Dent. Due to competition with Hogue's Yel- low Dent in the same hill, Pride of the North yielded rela- tively 51 per cent too low, while in alternating single-row plats it yielded relatively 28.3 per cent too low. Comparing the yields of Hogue's Yellow Dent and Uni- versity No. 3 in the center rows of alternating three-row plats we have a ratio of 100:98, while in alternating single- row plats this ratio was 100:90. In the same hill the ratio Fig. 12 — Relative growth of Hogue's Yellow Dent, University No. 3, and Pride of the North corn varieties when grown in the same hill (1.914) 38 Nebraska Agricultural Exp. Station, Research Bui. 13 J3 o ■£ S 3* U IC COC- t « Os g en « - w fe s Sooo h ^o oo O Oh a Tl ^_e ■ £ »h5 13^ S; os t> < 3- S w S> ■* 00O] »00O!0 fl*« Scomoj CQ °j§ o oo Oq.2 o 2; "■" v a CO COIN SI Pn m : : 03 . *| = t- u jg -C.S e«l bO C «.Sj) C bo m" 03 a a a ft 03 o3 T! O ess 0> a 03 13 "ft OS S -aj=j= ti ■" " T3 fczl 03 0> 0) o> J3.fi JS cd O Oo ft 0> OJ 01 B JTI'B a PhOhPh a c c -m 03 oj oj a a c > QQQ » & £ _o_o o 'HJ'o'aJ r w jm jn *o> "a> *o> 3 3 3 bo bo be o o o www CO s ■w* >> "tf 05 ^ *. cd W > S^ £ § o •fflfl c ■■■< cd O O , bflbfl S in m 11 to a) . cc ■-.-. 1-1 >o « . i d u rQtO p. 0) *htH ft -C -t- 1 CO W > o =»co"° C in,, ft ~ cd ^£aS ■c-9 ~* ■321 • fSE 53j-*o is S 53 §>^ 55 ft?! pq < ^ ^o cc o 0» OCD 00 ft* (M o OS oos IN „ (£' H rt 7-1 2 »OS CO Ti o OS t- t-; ai £ 03 m >H ^^ ~ c o t>cd t> CQco CO CO COIN a O , , to i2 o o o o o o O ft o3 a ~ o o o o oo o — dg.2.2 a:S c = s o o o a Z 1 *"^ HH ^ -5 O k k. s « «i s 5 > tt = eja >>£ --I ^H *-■ 03 o +3"^ ^" 03 a> PU oi — »j kl u o oc c c t-C co c o - % ftoj 2 « (S^ o _ IN Ml! HoSg ^^ CT CO fr- CO CQcr IN ee cc 0] 01 & "o cc c oc a o >-C ur c CT s o 2 o o> O CQcr K cc cc ki 0) CD O , | tfl eo :- A . O-03 a |e c o c 6 & % 2 r- H S^ 1- a-a 03 >. co CO co CO sa TJ 1 Fh 03 ft | 6 -i- +- +-> c c a 1 01 C i o c co 0) ^co -a •I c c c h o 03 "Sjg -^ ~z «5 > > 1 a . a! > T 'v "o> a c 01 *o» 9 01 bo.£ o 0) b — t. ."S C c a o c K £ w t— w p £ Experimental Error in Crop Tests 39 was 100:99. Due to competition, the University No. 3 yielded relatively 8.0 per cent too low, in single rows and within the same hill it yielded 1 per cent too high. The ap- parent lack of competition within the hill in this case may have been due to there being only two plants of rather similar type in a hill. When all three varieties were compared in the same hill the relative yields for the Hogue's Yellow Dent, University No. 3, and Pride of the North were respectively 100, 96, and 28, as compared with 100, 98, and 53 in the center rows of three-row plats, and 100, 90, and 38 in single-row plats. In the three-row plats (Table 16), the yields indicate that competition affects the outer rows to such an extent that they should be discarded in all yield tests of corns which dif- fer in growth habit. Single-row plats are unreliable for a comparative test of corn differing in growth habit or rate of planting. Two-row plats would probably be subject to one- half of the competition of single-row plats. In 1913 (Table 17), inbred and first generation hybrid Hogue's Yellow Dent corn were similarly compared in (1) alternating single rows, (2) alternating three-row plats, and (3) in the same hill. The inbred corn had been self-fertilized Table 17 — Relative yields of inbred Hogue's Yellow Dent corn and first generation hybrid seed of inbred strains when compared in three-row plats, single-row plats, and when planted in the sam,e hill (1916) Plants per hill No. of replica- tions Yield per acre Manner of planting Actual Relative Cross- bred 1 Inbred Crossbred and inbred strains of H. Y. D. corn alternat- ing in 3-row plats Crossbred and inbred strains of H. Y. D. corn alternat- ing in single rows Crossbred and inbred strains of H. Y. D. corn planted in the same hill* 4 4 4 9 6 300 Bus- hels 76.2 90.5 54.0 Bus- hels 28.1 28.0 11.2 Per cent 100 100 100 Per cent 36.9 31.1 20.7 *Where two plants each of two types were grown in the same hill, the actual yield for each type is given, based on the rate of two plants per hill. 40 Nebraska Agricultural Exp. Station, Research Bui. 13 Table 18 — Summary of relative grain yields when different rates of planting are tested in single-row plats and also in blocks containing several rows Crop tested at two rates of planting Turkey Red winter wheat. Turkey Red winter wheat . Kherson Oats Kherson Oats Nebraska White Prize corn Nebraska White Prize corn Nebraska White Prize corn Ratio thick to thin Year of test Alternat- Alternat- ing rows ing blocks 1913 100:68 100:90 1914 100:35 100:81 1913 100:64 100:80 1914 100:67 100-102 1914 100:82 100:116 1915 100:63 100:70 1916 100:78 100:93 Table 19 — Summa7*y of relative grain yields when different varieties are tested in single-row plats and also in blocks containing several rows Varieties compared in alternating rows and in alternating blocks Year of test Ratio of variety No. 1 to variety No. 2 in Alternat- ing rows Alternat- ing blocks Compet- ing in same hill (Corn) Turkey Red (1) and Big Frame (2) winter wheat 1913 1914 1913 1914 1913 1914 1913 1914 1912 1914 1914 1916 100:107 100:85 100:107 100:63 100:130 100:139 100:82 100:89 100:66 100:38 100:90 100:31 100:97 100:97 100:107 100:85 100:112 100:101 100:77 100:93 100:85 100:53 100:98 100:37 Turkey Red (1 ) and Big Frame (2) winter wheat Turkey Red (1) and Nebraska No. 28 (2) winter wheat. . . Turkey Red (1) and Nebraska No. 28 (2) winter wheat. . . . Kherson (1) and Burt (2) oats Kherson (1) and Burt (2) oats Kherson (1) and Swedish Se- lect (2) oats Kherson (1) and Swedish Se- lect (2) oats Hogue's (1) and Pride of the North (2) corn 100:47 Hogue's (1) and Pride of the North (2) corn 100:26 Hogue's (1) and University No. 3 (2) corn 100:99 Fi* Hogue's (1) and inbred Hogue's (2) corn . . . 100:21 'First generation hybrid of inbred strains. Experimental Error in Crop Tests 41 for five years and was greatly reduced in size and vigor. The results indicate the error which might be expected if two inbred parents were to be compared with their hybrid and the original check seed. In alternating three-row plats, the inbred corn yielded 38.9 per cent as much as the hybrid seed, while in the alternating single-row plats it yielded 31.1 per cent as much. When compared in the same hill, the inbred seed yielded 20.7 psr cent as much as the hybrid seed. Because of competition with the larger plants in the same hill, the inbred corn yielded relatively 44 per cent too low. while in alternating single rows, it yielded relatively 16 per cent too low. SUMMARY OF PLAT COMPETITION STUDIES The effects of single row plat competition upon compara- tive grain yields, are summarized for wheat, oats, and corn, in Tables 18 and 19. These data are taken from Tables 1 to 7 and 11 to 17. The ratios given for the comparative yields in blocks are for the middle row or middle three rows of either three-row plats or five-row plats, except in 1913, when the block-rows were not harvested separately. VARIATION OF STAND AS A SOURCE OF ERROR IN YIELD TESTS WITH CORN In order to secure information regarding the effect of variation in stand upon the accuracy of comparative corn tests, 2,000 hills of corn were planted in 1914 and 8,500 hills in 1917, in which were methodically distributed two, one and no-plant hills among hills with a full stand of three plants. Each hill was harvested separately. The results are contained in Tables 20 and 21. In 1914 (Table 20), when surrounded by hills having a full stand of three plants, the respective relative grain yields of three-plant, two-plant and one-plant hills were 100, 82, and 74. In 1917 the corresponding relative yields were 100, 83, and 50. In 1914 (Table 21), when three-plant corn hills, other- wise surrounded by a full stand of three plants per hill, were adjacent to (1) one hill with two plants, (2) one hill with one plant, (3) one blank hill, (4) two blank hills, the respec- tive grain yields per hill were 3 per cent, 5 per cent, 13 per cent and 43 per cent greater than when surrounded entirely by three-plant hills. 42 Nebraska Agricultural Exp. Station, Research Bui. 13 In 1917 corresponding hills with missing plants increased the grain yields of three-plant hills respectively 2 per cent, 9 per cent, 15 per cent and 25 per cent over the yield of three-plant hills entirely surrounded by three-plant hills. The data indicate that irregularity of stand in corn yield tests may cause inaccurate yields and should be avoided. Error due to variation in stand of corn may be largely overcome by planting the corn thick and thinning to a uni- form stand soon after coming up. If grown in hills, the seed may be space-planted in the hill so that the actual number of plants may be readily counted at harvest with- out suckers being mistaken for separate plants. It is desir- able, just before husking, to count out a given number of hills having a full stand and surrounded by a normal stand, upon which to base the yield per acre. This may be facili- tated by planting an additional number of hills to permit dis- carding. Space-planting in the hill for experimental yield tests may be accomplished by first marking off the field cross- wise with a sled marker and then making three separate spaced plantings in each intersection by means of a hand corn planter adapted for the purpose. Where three plants are grown per hill, the marker runners should be double so that all three plantings may be made in a runner mark, thus insuring uniform planting conditions for all three plants. There are exceptional kinds of corn experiments in which planting thick and thinning to insure a perfect stand would conflict with the object of the investigation. Table 20 — Relative yields of one, two, and three-plant corn hills when surrounded, uniformly by three-plant hills (1914 and 1917) Number of plants in hills surrounded by uniform three-plant hills Number of hills • averaged Number of tillers per 100 plants Number of ears per 100 plants Average grain yield per hill Actual Relative Hills with three plants?.. Hills with two plants . . . Hills with one plant. . . . Hills with three plants. YI 310 70 16 YE 288 ]AR 1914 8 38 112 ]AR 1917 83 96 168 95 102 114 Grams 466 380 344 509 422 252 Per cent 100 82 74 100 Hills with two plants. . . 50 64 83 Hills with one plant. . . . 50 Experimental Error in Crop Tests 43 Table 21 — Relative yields of three-plant corn hills adjacent to hills with missing plants (1911+ and 1917) Three-plant hills sur- rounded by three- plant hills except as indicated below Number of hills averaged Surrounded by hills with three plants Adjacent to one hill with two plants Adjacent to one hill with one plant Adjacent to one blank hill Adjacent to two blank hills Surrounded by hills with three plants Adjacent to one hill with two plants Adjacent to one hill with one plant Adjacent to one blank hill Adjacent to two blank hills Number of plants per hill Number of ears per 100 plants YEAR 1914 YEAR 1917 Average grain yield of three-plant hills Actual Grams Relative 310 3 83.6 465.8 149 3 87.0 478.2 44 3 86.3 490.3 132 3 88.0 526.6 57 3 91.0 666.5 288 3 95 509 211 3 96 519 258 3 102 555 234 3 99 585 198 3 101 631 Per cent 100 103 105 113 143 100 102 109 115 125 RELATION OF STAND TO YIELD IN SINGLE-ROW TEST PLATS The data in Table 22 were compiled from records of exten- sive ear-to-row tests of Hogue's Yellow Dent corn made by Lyon and Montgomery at the Nebraska Station during the four years 1904-1907. Rows 72 hills in length had been planted by hand at the rate of three kernels per hill, 3 feet 8 inches apart. The entire plats were harvested regardless of the actual stand secured, altho a record was taken of the per cent stand. In Table 22 the plat yields have been assembled into groups for each year according to the per cent stand. Since a rather large number of plats are averaged in each group, this may overcome in large measure any inherent difference in yield- ing power of the individual ears tested, and the differ- 44 Nebraska Agricultural Exp. Station, Research Bui. 13 Table 22 — Relation of per cent germination in the field to yield of single-rotv test plats of Rogue's Yellow Dent corn (1904-1907) Year Number of plats averaged Kernels planted p?r hill Average field germi- nation Per cent GERMINATION 00-05 PER CENT ■00 PER CENT S5 PER CENT GERMINATION 75-80 PER CENT GERMINATION 70-75 PER CENT -70 PER CENT GERMINATION BELOW 60 PER CENT Yield per acre Bushels 1904 10 3 92.1 76.8 1905 9 3 92.3 94.6 1906 2 3 93.0 84.8 1907 22 3 94.0 85.9 Average 43 3 92.8 85.5 1904 12 3 87.6 81.3 1905 25 3 88.1 95.2 1906 10 3 87.0 92.4 1907 16 3 86.0 83.7 Average 63. 3 87.2 88.1 1904 27 3 83.1 75.4 1905 40 3 83.2 88.4 1906 32 3 82.6 85.4 1907 18 3 82.0 85.0 Average 117 3 82.7 83.5 1904 12 14 18 16 3 3 3 3 78.0 78.4 78.0 77.0 76.2 1905 85.5 1906 83.3 1907 83.9 Average 60. 3 77.8 82.2 1904 11 6 19 10 3 3 3 3 74.0 73.2 73.4 72.0 68 1 1905 79 9 1906 82 9 1907 80 6 Average 46. 3 73.1 77.9 1904 13 3 10 10 3 3 3 3 66.2 67.3 68.1 65.0 67 3 1905 77 3 1906 80 1 1907 74.7 Average 36. 3 66.6 74.8 1904 21 6 11 7 3 3 3 3 35.6 51.5 42.1 43.0 42 6 1905 70 7 1906 56.9 56.8 1907 Average 45 3 43.0 56.7 Experimental Error in Crop Tests 45 ence in yield for the groups may be assigned primarily to the difference in stand. During the four years, consid- ering three plants per hill a 100 per cent stand, stands aver- aging 92.8, 87.2, 82.7, 77.8, 73.1, 66.6, and 43.0 per cent yielded respectively 85.5, 88.1, 83.5, 82.2, 77.9, 74.8, and 56.7 bushels per acre. It appears from these results that what was regarded a perfect stand, namely three plants per hill, was too thick for a maximum yield with this variety, since an 87.2 per cent stand outyielded a 92.8 per cent stand. The yield by no means decreased in proportion to the stand. An average stand of 43 per cent yielded 66.3 per cent as much as a 92.8 per cent stand. It would appear unreliable to correct yields upon a basis of stand. The yield of an individual row plat planted at a given rate will vary greatly according to the stand in adjacent rows. For this reason the data in Table 22 must not be regarded as necessarily indicating the true relative yields, during the years tested, for the different stands as would be obtained in a proper rate-of-planting test. Because of the chance variations in stand of single-row plats, no reliable formulas can be established for the correc- tion of yields according to the per cent stand. For example, very different results may be expected from a row with 75 per cent stand, according to whether it falls between rows having a 50 per cent or a 100 per cent stand. This is borne out by the rate-of-planting tests in rows and blocks during the three years 1914-1916 (Tables 11, 12, and 13). COMBINATION OF RATE-PLANTING AND VARIETY YIELD TESTS It has been a rather common practice in variety yield tests to plant all varieties at one arbitrary "standard" rate, regardless of their growth habits. During 1907 and 1908, three varieties were tested at five different rates of planting. The Pride of the North and Calico, which are respectively small and medium-sized vari- eties, increased regularly in yield with the rate of planting, and produced their maximum at the rate of five plants per hill. On the other hand, Mammoth White Pearl, which is _a large late corn, yielded its maximum at the three-rate and then fell off sharply. 46 Nebraska Agricultural Exp. Station, Research Bui. 13 In 1914, three varieties, differing distinctly in size and length of growing season, were planted at five different rates. Pride of the North produced its maximum yield at the rate of five plants per hill. University No. 3 produced identical and maximum yields at both the two and the three-rate and then fell off sharply. Hogue's Yellow Dent produced its max- imum yield at the two-rate and then fell off sharply. The data in both Tables 23 and Table 24 indicate that the relative yielding power of varieties differing in growth habit can only be determined by planting at several rates. Different varieties have a different optimum rate of planting. Table 23 — Relation of rate of planting to yield of corn varie- ties differing in growth habit grown in two-row plats* (1907-1908) Plants per hill Length growing period Yield per acre 1907 1908 Average Days Bushels Bushels Bushels PRIDE OF THE NORTH MAMMOTH WHITE PEARL 135 135 134 133 133 45.6 59.1 70.7 52.0 61.1 43.8 65.6 71.9 59.4 56.2 1 127 33.7 25.0 29.3 2 126 48.2 37.5 42.8 3 126 55.3 45.5 50.0 4 125 63.8 51.6 57.7 5 125 CALICX 69.4 ) 48.4 58.9 1 127 43.1 28.1 35.6 2 123 53.4 40.6 47.0 3 126 71.0 53.1 62.0 4 125 74.8 56.2 65.5 5 124 78.7 64.1 71.4 44.7 62.3 71.3 55.7 58.6 "Plats not duplicated. Experimental Error in Crop Tests 47 EFFECT OF REMOVING SUCKERS WITH DIFFERENT VARIETIES Occasionally an investigator has removed the suckers from his corn varieties or selections in order to avoid annoyance by them. The data in Table 25 indicate that the removal of suckers may affect different varieties differently, and that a new error in testing may be introduced thereby. Table 24 — Relation of rate of planting to yield of corn varie- ties differing in growth habit grown in three-row plats (191 V Plants per hill No. of replica- tions 1 3 2 3 3 3 4 3 5 3 1 3 2 3 3 3 4 3 5 3 Length growing Period Barren stalks Two- eared stalks Days Per cent Per cent PRIDE OF THE NORTH No. of ear bearing suckers per 100 plants Yield per acre (center row) Bushels 92 92 92 92 92 107 107 107 107 107 UNIVERSITY NO. 3 8 7 17.4 1 2 28.2 35.5 39.8 44.4 1 6 8 15 14 3 1 20 2 40.2 59.6 59.5 52.7 47.3 HOGUE'S YELLOW DENT 1 3 119 10 19 44.4 2 3 119 1 1 2 63.9 3 3 119 2 59.0 4 3 119 7 59.8 5 3 119 13 53.7 RELIABILITY OF ESTIMATING PLAT YIELDS BY MEANS OF FRACTIONAL AREAS In conducting field experiments in cooperation with farmers, experiment stations frequently encounter difficulty in having test plats properly harvested and threshed. In some states the yields of such plats are estimated by harvesting a number of very small apparently representative areas from each of the plats to be compared. The small quantity 48 Nebraska Agricultural Ex%>. Station, Research Bui. 13 Table 25 — Effect of removing tillers from corn varieties dif- fering in growth habits (1912 and 1911+) Pride of the North. . . University No. 3 Hogue's Yellow Dent . Pride of the North . . . University No. 3 Hogue's Yellow Dent. Plants per hill No. of Yield per acre* Variety replica- tions Tillers on Tillers removed Differ- ence Bushels Bushels Bushels YEAR 1912 2 10 38.6 30.9 2 10 47.7 42.9 2 10 53.7 43.5 3 10 40.9 38.2 3 10 56.9 54.2 3 10 43.6 38.8 Pride of the North University No. 3 Hogue's Yellow Dent Pride of the North University No. 3 Hogue's Yellow Dent. . . . * Yield per acre based on center row of three- single-row plats in 1 it 1:2. YEAR 1914 2 3 35.3 32.5 2 3 49.2 50.5 2 3 52.3 55.0 3 3 38.8 33.6 3 3 45.8 46.6 3 3 54.4 54.3 7.7 48 10 2 2.7 2.7 4.8 2.8 + 1.3 +2.7 5.2 +0.8 0.1 row plats in 1914 and on of grain harvested in this manner can readily be shipped to the central station for threshing and estimation of yield. In order to secure information relative to the reliability of such a method the following test was made in 1917 : Duplicate thirtieth-acre field plats of each of seven differ- ent varieties or selections of winter wheat were chosen from among a large number of plats for this study. These plats measured 16 rods by 66 inches and contained eight rows. Twenty systematically distributed fractional areas or quadrates were harvested from each plat. These were 32 inches square, contained four rows of wheat, and were .0001632 acre in area. Quadrates were located 10 feet from each end and at intervals of 14 feet on alternate sides of the plat, as indicated in the following diagram. m s [u &r~ " — H — R — Diagram showing distribution of 2 quadrates in thirtieth-acre plats (Table 26) Experimental Error in Crop Tests 49 The quadrates were accurately laid out by means of an iron frame, as shown in the following figure. A rectangular frame is more reliable than a round one where the grain is planted in rows. Frame used for laying off quadrates (Table 26) Because of severe and variable winterkilling the 14 plats differed markedly in the percentage of plants surviving, and in yield. There was also much greater variation between the quadrates within a single plat than would normally be expected. Opportunity was provided to compare the mean results of 5, 10, and 20 systematically distributed quadrates with the entire plat from which they were harvested. In making four groups of five quadrates each, group (a) contained quad- rates Nos. 1, 6, 9, 14, and 17; group (b) contained Nos. 3, 8, 11, 16, and 19; group (c) contained Nos. 2, 5, 10, 13, and 18; and group (d) Nos. 4, 7, 12, 15, and 20. For two groups of 10 quadrates each, group (a) contained Nos. 1, 4, 5, 8, 9, 12, 13, 16, 17, and 20, and group (b) contained Nos. 2, 3, 6, 7, 10, 11, 14, 15, 18, and 19. The results of these various groupings are shown in Table 26 in comparison with the yields of the entire respective plats. The average yield determined from 20 quadrates deviated 1,4 bushels from the average plat yield. For individual plats the 20-quadrate yield estimation varied from 0.2 to 3.2 bushels per acre. Smce each kind of wheat was grown in duplicate plats the mean of 40 quadrates can be compared with the mean of two field plats. In this comparison the average of these 50 Nebraska Agricultural Exp. 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When the quadrates from each plat were grouped into sets of five and ten each, there was considerable variation in yield between the separate groups, which suggests that not less than 20 quadrates should be harvested from compara- tive plats of this character. It appears that the results from 20 systematically dis- tributed quadrates may be fairly safely substituted for the yield of the entire plat from which they are taken. EXPERIMENTAL ERRORS CAUSED BY SOIL VARIATION The lack of uniformly productive land for comparative crop tests has given rise to a number of methods frequently used for ascertaining and overcoming the resultant experi- mental error. Chief among these methods are : ( 1 ) The use of frequent, systematically distributed check plats planted to a uniform crop for the purpose of (a) indicating the degree Fig. 13 — A relatively uniform field containing 2 07 thirtieth-acre plats sown for a method study to a uniform crop of Kherson oats (1916) 52 Nebraska Agricultural Exp. Station, Research Bui. 13 of variation due to the soil or (b) correcting the results from the intervening - test plats. (2) Replication of plats and bas- ing the conclusions upon the mean yield. (3) Use of long, narrow rather than short, wide plats. (4) Calculating the probable error for the mean results of replicated plats, to indicate the degree of confidence which may be placed in the results. The results from 207 thirtieth-acre Kherson oats plats, grown in 1916, illustrate each of the four practices mentioned above. These plats were planted to a uniform crop upon a seemingly uniform field for the purpose of studying varia- tion in plat yields as a source of experimental error. The Fig. 14 — Two hundred and seven thirtieth-acre Kherson oats plats planted to a uniform crop for studying experimental error in 1916 entire field had been cropped uniformly to silage corn for a period of eight years. It had been plowed each year and was also plowed in preparation for the oats in 1916. The oats were drilled during two successive days in plats 16 rods by 66 inches, which equaled one drill width. The plats were separated by a space of 16 inches between outside drill rows. A wide discard border of oats was grown around the outer edge of the field, so that all plats should have a similar expo- sure. General views of this field are shown in Figures 13 and 14. Experimental Error in Crop Tests 53 USE OF CHECK PLATS During the past 15 years it has become the general prac- tice in crop investigations to plant check plats at regular stated intervals. These plats are planted to a uniform crop and should yield alike except for various environmental sources of experimental error. The use of check plats may be twofold: (1) To indicate the error caused by variation in normal plat yields. The variation in the check plats is regarded as indicative of the error in the test plats. (2) Check plats are more commonly used to calculate the normal or theoretical yield of all plats in the field. All crops or treatments are then compared directly with each other by their increased or decreased yield above or below the calculated normal yield for the plats upon which they grew. This difference is best expressed in percentage of the normal plat yield. Comparative yields per acre may then be calculated for each crop, variety, or treatment by adding (or subtracting) the difference between it and the normal yield for the plat to (or from) the mean yield for all check plats in the field. This recalculation of yields is usually spoken of as correction according to check plats. The check plats may be variously distributed in the field according to the manner in which the corrections are to be made. Three methods of correction are in common use: (1) The normal or theoretical yield of the test plat is determined by, and is equivalent to, the average of two adjacent check plats. (Alternating plats are check plats.) (2) The normal or theoretical yield of the test plat is determined by, and is equivalent to, the yield of a single adjacent check plat. (Two test plats are planted between checks.) (3) The soil between two or more check plats is regarded as varying gradually from one check plat to the other and a progressive correction is used to establish the normal or theoretical yields of the intervening test plats. Thus, if two test plats lie between checks which yield 51 and 60 bushels respectively, the nor- mal yields assigned to the two test plats by this progressive method would be 54 and 57 bushels. Progressing from the lower to the higher yielding check the normal yield of the first test plat is greater than the poorer check by one-third of the difference, while the normal yield of the second test plat is greater than the poorer check by two-thirds of the difference. The proportion of the difference added to each successive test plat will depend upon the number of plats be- tween checks. 54 Nebraska Agricultural Exp. 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Station, Research Bui. 13 1 s? s « ft I ^ HO 18 o ^ *3 "*o ° l> 09 a SO to r^O CO ft 03 &» to . se a> £ Qo 0; a <^;D©osiocoosos©©ww^rot>ooost^^©ooost^osas:DGOoswcocN]t^c>ico QQX0000tr-t>t>[^Q0t>t^t^t>^t>l>-C>t^t>l>t-t>L^t>t^G0t>t^t^t^t^-t>t-t- sz " cdldu3CCldaicOT]<^o6cdcCcdldoja6cDrHcdcdo^CCcdcOCOTfCDCO©CMCOkn t-t-t- t-t-r-t-t-t-C-COCOC-COOOt-COCOe-C-t-C-COCOt-t-C-t-t-t-t-t- 35 Ss a; £ Q p co cd ^£ ££ Q o ? 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HH lO^f CJH h c- 00 t> t- t-to c-c- t-t- C-C- C-C- ooo H tO oo CO lO ON oo 10 c-c- C-C- c-cs c-c- (MCO 00 00 00 00 otoiooimtooo50Tjt>uorHco^ocacoMtOrHtoocoojHCOoacoiOHcooo NHailOrHCOCOo6c0^tOC>5Ht>OOt^C0^03U5COoiHN cooococ-c-c-cotoc-ooc-ooc-c-c-c-c-tDcoc-c-c-ooc-c-c-c-ooo5C-oococoooc- 10'«MNHOffl00t-t0li:'*C0INHOai00l-tDl0"*MC]HOOJ00t-IDlO^ l WNHO 00000005050505050505050505COOOCOOOOOOOOOOOOOCOC-C-C-C-C-C-C-C-C-C- coiNcoHiNco^NOOHiNHasiNH^iNtooiiNiN^c^H^cooj^iNcvicoo^ou^N oco^to^oo^oo^iNoooico^H'cocoo^oooiio^tooooo^o&oi^odTiIcooo' c- c- c- c- c- c- c- c- c-oo c- t-to C- CO C-C- 00 C- C-C- C-C- 0000 c- ooo c— t— t— c— t— t— t— 05 C0O5 HCO W U3 c-oo (NtO 005 -*o (NtO tDH H(M t-lO COH 005 H 00 C-05 Tj<05 o NN OC- H»C i— 1 1-< COH CO HC0 OIM 05"3 H Hio 1 1 1 + 1 1 + + 1 + 1 + + + 1 + + 1 + + + 1 1 oca H0J «5H 05H O lO in co OOO O5C0 C0^00t>^0000t>r^00OI>^C00^^C0OO^C0^^C0C0t>C0C^ iHoioo^iHcooococ^wooo^aicowaic^^coco^^^ oooooot^oooot-oooooot^t-cot-ooi>oooooooooot>t>oooot>coooi>t-oot>t-t>ooi> CJOUVOOCJWUOOCJ T?lCCDl>00C7aOHC>]C0^^C0t>000^Oi-lCC)00^Oi~C00^ COCOCOCOCOCO^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^ 59 60 Nebraska Agricultural Exp. Station, Research Bui. 13 The three foregoing tables (27-29) show the exact ar- rangement in which the 207 Kherson oats plats were grown in the field. Certain plats have been designated as check plats according to each of the above three methods, and the intervening plats have been treated as test plats. The test plats have been corrected in yield according to the check plats. If such correction had been effective, the coefficient of variability for the corrected yields would have been ma- terially reduced below the coefficient of variability for the actual yields. On the contrary, however, the coefficients of variability were reduced less than 1 per cent, being 7.8 per cent for the actual yields and 7.0 per cent for the corrected yields, as an average for the three methods of correction. Table 30 gives the coefficients of variability for the actual and corrected vields of the test plats indicated in Tables 27, 28, and 29. Table 30 — Effect upon yield from correcting thirtieth-acre Kherson oats field plats according to various accepted means of check plat correction* (1916) Arrangement of check plats used for correction Fre- quency Intervening plat yields Standard devia- tion from mean for Coefficient of variability for Actual yields Cor- rected yields Actual yields Cor- rected yields Actual yields Cor- rected yields Alternate check plats. Correc- tion based upon average of two adjacent checks Checks every third plat. Correc- tion based upon one adjacent check plat . ... Checks every third plat. Correc- tion by progres- s i v e method based upon two nearest checks . . 102 138 132 Bushels 78.2 78.0 78.0 Bushels 78.1 77.7 77.7 Bushels 6.14 6.08 6.13 Bushels 5.47 5.71 5.10 Per cent 7.85 7.79 7.87 Per cent 7.01 7.35 6.57 ♦Calculated from data in Tables 27, 28, and 29. Experimental Error in Crop Tests 61 REDUCTION OF ERROR BY REPLICATION The actual yields from the first 200 of these similarly treated plats of Kherson oats, described on pages 52 to 60, have been compiled to show the extreme variations, average and standard deviations from the mean, and the coefficients of variability for single plats and for the mean yields of two, four, and eight plats averaged together. These groupings have been arranged for both adjacent and systematically dis- tributed plats. The results are given in Table 31. It is clearly shown that replication greatly reduces the extreme variation and coefficient of variability in the yield of field plats. A given number of replications are also much more effective when systematically distributed than when adjacent plats are averaged. Fig. 15 — Harvesting thirtieth-acre plats of Kherson oats. The binder has a gasoline engine attached which cuts and binds the grain. This facilitates cleaning out the binder quickly at the end of each plat. Note the narrow bare spaces between plats. If the plats are tangled by lodging, they are separated by hand before being cut. This shape of plat is very convenient, since it is one drill in width and may be harvested by one swath of the binder 62 Nebraska Agricultural Exp. Station, Research Bui. 13 -to ^ SO C3 -+o <=> £ .» <° O £ SO "Oa <» S £^ *» CY) W -+3 ? 5 s i.£> §g .S"« ■g.5 1| so § SO <^° © so • I; Coefficient of varia- bility ft* a > WT3 "3 CO s 0) g be 2 oj.S > > CO 3 oq a> fl £.2 «- as "5 to Mean yield per acre CO Is 5 be a V S 'w ■ ■^^oiot~5£>coai J -. On E3 rH M CO t- lO N Tf rH E -1 MHrHOOlOHCOlO GO ^j ccooooNOiaoM >T OOOOOOOiOOOOOOOO -* t- ■* O M t- OO t> tX>«D«Jt-cX)CDiO o I — I DO Xfl En o Q o Oh o o PL, l W lO lO lO lO lO lO I -t-T "a ^3 > > Experimental Error in Crop Tests 63 O i 2.5 s, § %$ CD ^ o fl"H 73 s I* *•! 03 > +j CD GGT3 0) S c3 +i > > S.2 H S.2 * O a. cq m — < Ph Cq U < 1-3 Q i*t-Nt- ooohco Q OOt-OOt- GO O ' Ph Oh P o - Ph O Ph > 03 > ■r-j < t? O r^ £ bfl H w m Q ooco t— y^ OJ OS OS co 3 co co' oj SO H Nt-O r-j HH lO H K5 CO m NNN GO P — o I— I co Ph co co -h< co 5^ io^*c oo oo oo co g «om^ 00 t-H i-H 01 CD (/J t- t- t- Eh -• o Ph o m Eh * bfl 03 S-c O) > s « O °3 go. Si's. Mo3 c8 j§ CD +S CD ^ 03 ^5 03 ft a a a go go 64 Nebraska Agricultural Exp. Station, Research Bui. 13 The yield of the 200 individual plats varied from 56.7 to 92.8 bushels per acre. The mean for eight groups of 25 single plats each gives an extreme difference between single plats of 20.7 bushels per acre. When two, four, and eight systematically distributed plats are averaged, the extreme differences in yield are respectively 14.9, 8.9, and 7.8 bushels. When two, four, and eight adjacent plats are averaged, these extreme differences are 19, 16.7, and 15 bushels. For sys- tematically distributed plats the coefficients of variability for one, two, four, and eight plats in a group are 6.30, 4.5D, 2.91, and 2.18 per cent. For adjacent plats the coefficients of variabilitv for one, two, four, and eight plats in a group are 6.30, 5.46, 5.28, and 4.78 per cent. Systematic distribution of replicated plats is seen to be very effective in reducing experimental error due to environ- mental variations. EFFECT OF SHAPE AND SIZE OF l'1-AT The 207 thirtieth-acre Kherson oats plats described in the preceding discussion were grouped to enable a compari- Various ways of combining plats to make plats of different sizes and shapes (Table 31) Experimental Error in Crop Tests 65 son of long narrow plats with short wide plats. The group- ings illustrated in the following diagrams were compared. (In the 1x9 grouping, three groups were necessarily irregu- lar in shape since 9 is not a multiple of 69.) The results are included in Table 31. Long, narrow plats are indicated to be more reliable than short wide plats of the same area. Increasing the size of the plat is less effec- tive in overcoming experimental error than the systematic distribution of plats equal in combined area. SIGNIFICANCE OF THE "PROBABLE ERROR" The "probable error" calculation is being used somewhat by field crop experimenters. Its use is rather inviting since a small "probable error" is customarily regarded as indicat- ing accuracy in the results. Davenport's interpretation is generally accepted, namely: "It (the probable error) indi- cates the degree of confidence which we should place in results obtained by statistical methods." Where plats are replicated two or more times, the prob- able error of the mean, is based upon the standard deviation, and is determined by the following formula : standard deviation - Probable error of mean = ± 0.6745 — === ===== . , l number of vanates a which is also stated E: m — ± 0.6745 — t= 1 n The probable error is regarded as an upper and lower limit of divergence for which the chance is even that the true mean does not lie outside of these limits. Commenting upon the likelihood of the true mean lying outside of the limits set by the probable error, Davenport (1907) states: "Of course the error in a determination has also an even chance of lying outside the limits set by the probable error (E) , but the following table will show that it is very unlikely that the error is many times as great as E. Thus the chances that the true value lies within the range set by ± E, ± 2E, etc., are as follows : 66 Nebraska Agricultural Exp. Station, Research Bui. 13 ± E the chances are even ±2 E the chances are 4.5 to 1 ±3 E the chances are 21 to 1 ±4 E the chances are 142 to 1 ±5 E the chances are 1310 to 1 ±6 E the chances are 19,200 to 1 ±7 E the chances are 420,000 to 1 ±8 E the chances are 17,000,000 to 1 ±9 E the chances are about 1,000,000,000 to 1 "It is extremely improbable, therefore, that an error will be many times as large as the probable error. For instance, it is practically certain that the error is not as large as 9 E, since the table shows that the chances are about a billion to one in favor of its being smaller than 9 E. "Thus by giving, along with any result, the calculated probable error, the reader may know what degree of con- fidence is to be placed in the results." In common usage, it is stated that the actual difference in the yield of two plats must be three times the probable error before the difference in yield is significant. It should be agreed at the outset that the probable error of a mean yield has significance only when the variations entering into the mean are purely accidental rather than sys- tematic. This distinction is understood by biometricians who universally attach importance to the probable error cal- culation when used in a legitimate manner. There appear to be strong possibilities of misusing the probable error and overestimating its value in agronomic studies. This need not be regarded as any defect in the probable error formula, but rather as a misapplication thereof to experimental results possessing either visible or invisible systematic errors. Field crop investigators consider it good technique to repli- cate test plats. It has been proposed that, in such tests, small probable errors for the mean yields of the various varieties or treatments would indicate reliability and justify con- fidence in the comparative yields. For the purpose of studying the significance of the prob- able error in field crop tests, the first 200 consecutive thir- tieth-acre Kherson oats plats described on pp. 52 to 64 have been grouped in 50 sets of four adjacent plats and also 50 sets of four systematically distributed plats, and the prob- able error calculated for the mean yield of each group of four plats. Experimental Error in Crop Tests 67 PROBABLE ERROR FOR FIFT\' GROUPS OF FOUR ADJACENT THIRTIETH-ACRE PLATS OF KHERSON OATS That the probable error cannot apply to the mean yields of adjacent duplicate plats in a variety test is brought out by the following data : In Table 32 are given the mean yields for 50 groups of four adjacent plats, together with the average deviation, standard deviation, and probable error for each group. The average deviation of each group from the mean yield for the entire 200 plats is also indicated and in the last column of the table is given the ratio of this deviation to the probable error. If it is permissible to assume that one group of four dupli- cate plats is comparable with another group of four plats in the same field, then it would also seem permissible to assume that in the present instances, the mean yield for the entire 200 similarly treated oats plats should represent the correct yield or true value of any or all of the individual groups within the field. If this assumption be made with the adja- cent duplicate plats (Table 32), the actual error of these group means exceeded their probable error approximately 0, 1, 2, 3, 4, 5, 6, 7, 8, 10, 11, and 15 times respectively in 9, 5, 7, 7, 8, 4, 4, 1, 2, 1, 1, and 1 groups. (See Col. 11, Table 32). This is very inconsistent with the table of probabilities quoted from Davenport on page 66, and shows that a uniform ap- pearing field may be so heterogeneous in soil conditions that its mean yield cannot be regarded as correctly representing the true value of its various parts. Since all the plats were treated and planted alike any dif- ference in the yields of the groups represents experimental error, either in mechanical operations or in soil variation. Among the 50 groups of adjacent plats, one group yielded 14.2 bushels less and another group 7.3 bushels more per acre than the 200-plat mean. These extremes represent an experi- mental error of 21.5 bushels since both should have yielded alike if the method of comparison were reliable. Should we presume that groups No. 30 and No. 50 (Table 32) are distinct varieties in a comparative variety test, we would have a difference in yield of 21.5 bushels per acre. After multiplying the probable error of each mean by three, there remains a net difference of 11.63 bushels between the probable error ranges. Placing confidence in the probable error calculation, we would believe that there is a difference 68 Nebraska Agricultural Exp. Station, Research Bui. 13 -^ -to O <+~, Co © g £g t: g 41 1 £ pq < HoiotoN!Ooii)0[-o!Ot-o>«u:oot-m ,2 cU c °££ X: O 0> c £ £ OTT3 v ~ retoooit-Nroi- co^ , ooO"i>cO'-".oin'Otr^ 'I+ + + + CM ■sf ■* OIM Hftont- w t- »o o o? I I l + l : n o n m t- co oo oo -h o io o o oo n -h ■* h ro c io n » io w ;^iomoiocoo^>n^oi>c-N'H^oooi^c-ooooo(X3t- ;NfliOHe^HBNI>HOq«lNN*BOMrtTjH00H f^^i-ieCTiiin'nc>ic<5io»H'«jiotr-avocKO' 3 00 LO -5)1 r+ co oc :CJtO«ir!™05C-O»t-N0!)XOfflH^i00»HN»'* !M0O0OWt-0Ol-«0O0COOC-O0;t-t-0Ot-O0COt-t-t-C-t-t- !^00000OT«tOO"OConOt-'*!D it^cot-ooocc-ooooomninaocoooNiot-NN^O! ;«cccMi-ioooo[-»m'^ooooTOO'^'t-c»c>;esiooioou50»o "* WtC^HairtOOCC-D'OCMCOlOOOlOlOtOOKDloaiOOCOt-TfUJCO ^-"Sooooc-oot-t-toooooooccc-oot-c^c-c-ooc-c-e-toc^t-oo ;cccot^co-i-cooorf-'Ccio^j'iocDcoeocnoooocN-HcM--ioai «TflO01(0MU3lOC0HHN0)N'-iiO00O00 1 ^ *•. i- CO ■+o © •§ CO so -to o i so O S5, CM CO W pq < aJ [-. oj a o e OlOlOHQOHHNmCOOrH^lOCOHt-COOCOtMWCOWlO +++ j(N "iHiH 't-HOJ * "i-Hi-H ' ' " rn t-h N iH r-3 C3 ■H-H-H-H-H-H-H-H-U-H-H-H-H-H-H-H-H-H-H-H-H-H-H-H-H iCOHOOOOOt-OOO^NW^OHN^CD^tOaiiOOtOOOl .^01C0^W^I>(>a^C0C0C<]WC^C ajioioooooiooowoomiooowioicioiooooo ^t-^OlOiOOtM^CIMlOiOlMt^OO^t-^INfMiOOOiO i^O0COOOCO00tr-0OO000t-t>t-t>t>t~-t-t-I>t>t~-t-t>t>'X) ;0"X>^o^c^c^cocoooiu^t>-rHtr-oo(Ncc^coc>t>c^^t soooooooooot>ooocoooct>t-t>t-t-t-ot-xcr-t-coc-oom ^wt-coocnoowo^tDcoocot-oicococooocoioMO^ot ^ ^t-OOOOt-OOOCDt^-OOOOt^OOt-t-t-t-tr-t-t-t-t^^OCDtr-C w =Str-CX>t>000OOG^-t-00O000t-I>t-t-t>I>t-t>t>000OI>XiC> 70 Nebraska Agricultural Exp. Station, Research Bui. 13 HO S- co 5?> © ?S5 <» e go I CO CO S> < _ ° 5-cO !? o a S t- a> i- - £ . ■m a; G0T3 '"> t-NOrt(fl05MO!t- ^ ~ O -tfCO^*CCCO(M00CO^00C0CO^ ■^ooo^o^«3'*o>ira-!i;cj-HcoiNOOooi>0'Hoqcoc- ; too-H . «CJ H rHrt -H rHlH ' ' C>j >-H 1-4 1-5 rH ' ' H CO oj i-5 r4 H " rH T"5 tS-H-H-H-H-H-H-H-H-H-H-H-H-H-H-H-H-H-H-H-H-H-H-H-H-M JiOWOiOWCiOWiOlOOOOOOOOOiOiOOOiOlOO ;lNC-iCt>^Ot-I>(M(NOOlCiOiOO>OO^NOO(Nt>'0 ° «inoirrdo6acHNo6^o'6Ndt^o6t>«3o6oJwHa!6td w St>t>GO00t>t>000Ot>t-0000OC00t-t>t^I>t>tr-0000t>O0I> ■t-t>t-t-C-t-QOt-C-t-t-C-t>C-t>t'-C-t-t~ n^ WO>W«SO^^COWHCO^HOjoqWrjO(»NOO -+ 1 «HiOOiiHNHWOO)00«DTj ^-a» ^ooco^cocc^oqwt>C^owco^ooic^oqcD^cooowoo . «iOTfXT- r L'r--i'oa5aicootOHt»iooooooNioooooo sq t- 0000 00 00 0C 00 00 0OC-C- 00 0000 00 t-C- CD r-oc 00 00 t>oot> t-cCOOCT>Oi-ltNtWi" Experimental Error in Crop Tests 71 SO • •^> >-H ^3 Oi 5^ HO O g S3} ?* 5S co -^ §> ©> co <» ^ S £5} -to 55 ^ g o © 5s ^ CO. (Ji Ho 55 co I co '-£ ?> PS ° co. |s fa < ^ o '43 . "o O P3 0&OU •5 60 « 0)i S ' CST) fill etc ,0 0) r I' a, oj '|+ I + : I +++++ I I I I I + I I II + I I I I ^0)tO^)OWlOlOOff)E>' J'W^a)t>rl-H iH tH CSl l>j CO rH 1-1 .H ih oj iH ^H (N i-H CO CO l-H-H-H-H-H-H-H-H-H-H-H-H-H-H-H-H-H-H-H-H-H-H-H-H-H :cdt>id>-Hcoco^t ( ^t , )Oioc-coo2io)cmco«rco-*'0t-lOWMt-iOC-lOC-OOt^t'Nt-Nic^co^^^'tdt>cRicu;idco>dcM' , *idcCOOOt-OC'-it>OCcOlO'— t- i-H to l> C-; l> © a H^OX000)C000)0)t>t0in^'OOt>tDf-iO0)^ , ^m(N SoOC-OOt>t>t>COt>t>t>t>t>t>OI>OOC-C-t-C-t-t>t>C-C- J«5COt-COCOOT-'lO[-O l 'X)COC-CO-!t , a5(M-*'-<0)OCOCOC-t> > »OON00t-w^iONNl0rifO«liO0)0!C0t-NHH(0l> ' S00t-e-r-t-00t-t-t-00tOt>tDt-tOt-C-tOt>tT)00t-t-*O)O Jt-NWOocoomocj^oOHNtfiqaincoqqqqioqH >^5q©e»t>eNioNt-^^oit>i^eoeo>dc-'orau5jc-er .SoOHNOoo(DHqmMNqqraHqh;i>cm^;qqcq '300tCtOt-[-C-t-C-00t-00O©00t- NScot>rtai^tot>T!^j;oq©t>ic '^id^cotdcodc^co^ddcHT^cooo^wwcocncjoococnN cq tot-oomOT-NTO^iotot-oociOrtNK^ioBt-cooq W.nt Per cent Per cent Per cent 12x12 36 169.5 99.1 103.1 112.7 12x24 83 103.5 106.2 114.9 104.1 16x24 161 88.4 110.1 107.7 101.8 16x36 253 561 117.3 118.8 125.7 108.0 104.7 103.7 97.4 24x36 96.6 30x36 920 118.2 109 6 106.6 96.6 l);iia calculated from Table 41. Experimental Error in Crop Tests 85 EFFECT OF PLANTING AT DIFFERENT RATES UPON THE GROWTH OF CORN IN POTS In 1915, corn was planted at four different rates, namely one, two, four, and six plants in pots 16 by 36 inches in size and containing 253 pounds of soil. The results are contained in Tables 44, 45, and 46. Without manure (Table 45) the individual plants in the six, four and two-rate yielded respec- Table 44 — Summary of data showing the effect of different rates of planting upon growth of corn in pots. Hogue's Yellow Dent corn (1915) Total Rates of planting per pot Moisture-free contents No. pots averaged Dry matter* leaf- area per Height of stalk Soil Manure Ear Total plant f Pounds Pounds Grams Grams Sq. in. Inches 1 253 4 232 476 1334 123 1 253 1.55 8 262 539 1457 115 2 253 4 92 242 1210 120 2 253 1.55 4 118 279 1153 112 4 253 4 37 127 895 106 4 253 1.55 4 37 151 990 105 6 253 4 6.5 79.0 714 90 6 253 1.55 4 ' 16.7 101.9 861 93 *Where more than one plant was grown in a pot, the average yield per plant is given. tThe leaf-area is not very significant inasmuch as the lower leaves died prematurely according - to the rate of planting — due to malnutrition. Table 45 — Summary of data shoiving the effect of different rates of planting upon growth of corn in pots. The results at different rates of planting without manure are here expressed in per cent of the results from one plant per pot. Hogue's Yellow Dent corn (1915)* Rate of planting Wt. of soil (moisture -free) No. of pots averaged Dsy matter per plant Total leaf-area per plant Height of stalk per pot Ear Total 1 2 4 6 Pounds 253 253 253 253 4 4 4 4 Per cent 100 39.7 15.9 2.8 Per cent 100 50.8 26.7 16.6 Per cent 100 90.7 67.1 53.5 Per cent 100 97.5 86.2 73.2 ;: Data calculated from Table 44. 86 Nebraska Agricultural Exp. Station, Research Bui. 13 Fig. 18 — Normal plants of Hogue's Yellow Dent corn, grown one plant per pot, 1915 Experimental Error in Crop Tests 87 Fig. 19 — Plants in the foreground grown six, four and two plants per pot 88 Nebraska Agricultural Exp. Station, Research Bui. 13 1 3 8 Fig. 2 0- Crop harvested from four pots planted at each of the follow- ing rates per pot. Left to right, 1 and 2, one plant per pot; 3 and 4, two plants per pot; 5 and 6, four plants per pot; 7 and 8, six plants per pot. Odd numbers without manure, even numbers with manure. (Table 44.) 1914 Experimental Error in Crop Tests 89 tively 16.6, 26.7, and 50.8 per cent as much total dry matter as the one-rate, and their yield of ear corn was respectively 2.8, 15.9, and 39.7 per cent as much per plant. An application of 1.55 pounds of manure per pot (Table 46) increased the yields of total dry matter for the one, two, four and six-rates respectively 13.2, 15.3, 18.9, and 29.0 per cent. The yields of ear corn were 112.9, 128.3, 100.0, and 257.0 per cent as large with manure as without manure in the one, two, four, and six-rates respectively. Table 46 — Summary of data showing the effect of different rates of planting upon groivth of corn in pots. The results at the different rates of planting with manure are here expressed in per cent of the results without manure. Hogue's Yellow Dent corn (1915)* Rate of planting per pot Wt. m< free co Soil )isture- ntents Manure No. of pots averaged Dry n per i Ear natter )lant Total Total leaf- area per plant Height of stalk 1 2 4 6 Pounds 253 253 253 253 Pounds 1.55 1.55 1.55 1.55 8 4 4 4 Per cent 112.9 128.3 100.0 257.0 Per cent 113.2 115.3 118.9 129.0 Per cent 109.2 95.3 110.6 120.6 Per cent 93.5 93.3 99.1 103.3 :; Data calculated from Table 44. STATEMENT OF METHODS IN BULLETINS A knowledge of the methods employed in crop testing is vital for intelligently evaluating the published results. With- out a statement of methods, the reader is obliged to assume that reliable methods were employed. Such an assumption is not warranted, since many methods used are known to be faulty. Not only the experiment station worker but the farmer as well should be given an opportunity to know in detail how the tests, were made. Increased experimentation by farmers has led many of them to be interested in methods. The following brief summary table indicates the extent to which experiment station bulletins dealing with crop tests and published in the United States during the years 1900- 1914 report details as to methods. A mere statement of re- sults is incomplete and does not carry conviction. 90 Nebraska Agricultural Exp. Station, Research Bui. 13 Table 47 — Extent to which experiment station bulletins report the methods of investigation Method details Years' duration of tests Size of plats Shape of plats Number of duplicates averaged Distribution of duplicates Use of check plats Number of check plats Distribution of check plats .... Uniformity of conditions Size of pots Capacity of pots Maturity of crop in pots Per cent bulletins* reporting method details for Variety tests Per cent 71 29 23 13 5 3 41 Fertilizer tests Per cent 25 21 3 3 11 14 5 21 Cultural tests Pot tests Per cent Per cent 55 25 10 20 20 5 40 55 45 45 *The total number of bulletins reviewed were: variety tests, 253; fer- tilizer tests, 146; cultural tests, 52; pot tests, 20. Experimental Error in Crop Tests 91 BIBLIOGRAPHY ALWOOD, W. B., and PRICE, R. H. 1890. Suggestions Regarding Size of Plats. (Virginia Agricul- tural Experiment Station, Bui. No. 6, pp. 2 0.) BARBER, C. W. 1914. Note on the Accuracy of Bushel Weight Determinations. (Maine Agricultural Experiment Station, Bui. 226, pp. 69-75.) 1914. Note on the Influence of Shape and Size of Plats in Tests of Varieties of Grain. (Maine Agricultural Experiment Sta- tion, Bui. 226, pp. 76-84.) 1914. Note on the Influence of Shape and Size of Plots in Tests of Varieties of Grain. (Maine Agricultural Experiment Sta- tion, Bui. 226, pp. 76-84.) BULL, C. P. 1909. The Row Method and the Centgener Method of Breeding Wheat, Oats and Barley. (Jour, of the American Society of Agronomy, Vol. I, pp. 9 5-98.) BRIGGS, L. J., and SHANTZ, H. L. 1913a. The Water Requirement of Plants. I. Investigations in the Great Plains in 1910 and 1911. (U. S. Department of Agriculture, Bureau of Plant Industry, Bui. 284, 49 pp.) 1913b. The Water Requirement of Plants. II. A Review of the Literature. (U. S. Department of Agriculture, Bureau of Plant Industry, Bui. 2 85, 9 6 pp.) CARLETON, M. A. 1909. Limitations in Field Experiments. (Proc. Soc. Prom. Agr. Science, Vol. 30, pp. 55-61.) COFFEY, G. N. 1913. The Purpose and Interpretation of Field Experiments. (Jour, of the American Society of Agronomy, Vol. 5, pp. 222- 230.) COLLINS, G. N. 1914. A More Accurate Method of Comparing First Generation Maize Hybrids with Their Parents. (U. S. Department of Agriculture, Jour. Agricultural Research 3, No. I, pp. 85-91.) 92 Nebraska Agricultural Exp. Station, Research Bui. 13 CORY, v. L. 19 08. The Use of Row Plantings to Check Field Plats. (Jour, of the American Society of Agronomy, Vol. I, pp. 6 8-70.) DAVENPORT, E. 1907. Principles of Breeding. (Boston, pp. 721.) DAVENPORT, E., and FRAZIER, W. J. 18 9 6. Experiments with Wheat, 18 8 8-18 9 5. (Illinois Agricul- tural Experiment Station, Bui. 41, pp. 153-155.) FARRELL, F. D. 1913. Interpreting the Variation of Plat Yields. (U. S. Depart- ment of Agriculture, Bureau of Plant Industry, Circ. 109, pp. 27-32.) HARTLEY, C. P., BROWN, ERNEST B., KYLE, C. H., and ZOOK, L. L. 1912. Crossbreeding Corn. (Bureau of Plant Industry, Bui. 218, 66 pp.) HILGARD, E. W. 1901. Soil Tests and Variety Tests. (Proceedings of the Society for the Promotion of Agricultural Science, 19 01, pp. 8 9-94.) JARDINE, W. M. 1908. Methods of Studying the Relative Yielding Power of Ker- nels of Different Sizes. (Jour, of the American Society of Agronomy, Vol. I, pp. 104-108.) KIESSELBACH, T. A. 1916. Transpiration as a Factor in Crop Production. (Nebraska Agricultural Experiment Station, Research Bui. 6, pp. 214.) LEHN, D. 1913. New Works on Methods for Variety Testing. ( Bl. Zucker- riibenbau, 20, No. 3, pp. 33-39; 4, pp. 52-55.) LOVE, H. H. Methods of Determining Weight per Bushel. (Jour, of the American Society of Agronomy, Vol. 7, No. 3, pp. 121-12 8.) LYON, T. LYTTLETON. 1910. A Test of Planting Plats with the Same Ears of Corn to Secure Greater Uniformity in Yield. (Jour, of the American Society of Agronomy, Vol. II, pp. 3 5-3 7.) 1910. A Comparison of the Error in Yields of Wheat from Plats and from Single Rows in Multiple Series. (Jour, of the American Society of Agronomy, Vol. II, pp. 38-39.) Experimental Error in Crop Tests 93 1911. Some Experiments to Estimate Errors in Field Plat Tests. (Jour, of the American Society of Agronomy, Vol. Ill, pp. 89-116.) MERCER, W. B., and HALL, O. D. 1911. Experimental Error of Field Trials. (Jour, of Agricul- tural Science, No. 4, pp. 107-132.) MONTGOMERY, E. G. 1910. Methods for Testing the Seed Value of Light and Heavy Kernels in Cereals. (Jour, of the American Society of Agronomy, Vol. II, pp. 59-70.) 1911. Variation in Yield and Methods of Arranging Plats to Secure Comparative Results. (Nebraska Agricultural Experi- ment Station, 25th Annual Report, pp. 164-180.) 1913. Experiments in Wheat Breeding. (U. S. Department of Agriculture, Bureau of Plant Industry, Bui. 2 69, pp. 60.) MORGAN, J. OSCAR. 19 08. Some Experiments to Determine the Uniformity of Certain Plats for Field Tests. (Jour, of the American Society of Agronomy, Vol. I, pp. 5 8-67.) PEARL, R., and MINER, J. R. 1914. A Table for Estimating the Probable Significance of Statis- tical Constants. (Maine Agricultural Experiment Station, Bui. 226, pp. 85-88.) PIPER, C. V., and STEVENSON, W. H. 1910. Standardization of Field Experimental Methods in Agron- omy. (Jour, of the American Society of Agronomy, Vol. II, pp. 70-76.) PRICHARD, F. J. 1916. The Use of Checks and Repeated Plantings in Varietal Tests. (Jour, of the American Society of Agronomy, Vol. 8, pp. 65-81.) SALMON, CECIL. 1913. A Practical Method of Reducing Experimental Error in Varietal Tests. (Jour, of the American Society of Agronomy, Vol. V, pp. 182-184.) 1914. Check Plats — A Source of Error in Varietal Tests. (Jour, of the American Society of Agronomy. Vol. 6, pp. 128-131.) SCHNEIDEWIND, W. 1914. Experiments with Different Sized Plats. (Mitt. Deut. Landw. Gesell, 29, No. 21, pp. 298-300.) 94 Nebraska Agricultural Exp. Station, Research Bui. 13 SCHOLZ, H. 1910. Methods of Conducting Variety Tests. (Fiihling's Landw. Ztg. 59, No. 22, pp. 776-785; and No. 23, pp. 807-830.) SPRAGG, FRANK A. 1910. Methods of Keeping Crop Records at Michigan Experiment Station. (Jour, of the American Society of Agronomy, Vol. II, pp. 43-55.) SMITH, LOUIS H. 1909. Plot Arrangement for Variety Experiments with Corn. (Jour, of the American Society of Agronomy, Vol. I, pp. 84-89.) STOCKBERGER, W. W. 1916. Relative Precision of Formulae for Calculating Normal Plot Yields. (Journal of the American Society of Agro- nomy, Vol. 8, pp. 167-175.) SURFACE, F. M., and PEARL R. 1916. A Method for Correcting for Soil Heterogeneity in Variety Tests. (U. S. Department of Agriculture, Jour, of Agr. Research, Vol. 5, No. 22, pp. 1039-1049.) TAYLOR, F. W. 19 08. The Size of Experiment Plots for Field Crops. (Jour, of the American Society of Agronomy, Vol. I, pp. 56-58.) THORNE, CHAS. E. 19 08. The Interpretation of Field Experiments. (Jour, of the American Society of Agronomy, Vol. I, pp. 45-55.) 1909. Essentials of Successful Field Experimentation. (Ohio Agricultural Experiment Station, Circular 9 6, pp. 38.) VINALL, H. N., and ROLAND, McKEE. 1916. Moisture Content and Shrinkage of Forage and the Rela- tion of These Factors to the Accuracy of Experimental Data. (U. S. Department of Agriculture, Bui. 3 53.) VON RUMKER, LEIDNER, K. R., and ALEXANDROWITSCH, J. 1914. The Application of a New Method for Testing Cereal Varieties and Selections. (Ztschr. Pflanzenzucht, 2, No. 2, pp. 189-232.) WHEELER, H. J. 1908. Some Desirable Precautions in Plat Experimentation Work. (Jour, of the American Society of Agronomy, Vol. I, pp. 39-44.) Experimental Error in Crop Tests 95 WOOD, T. B., and STRATTON, F. J. M. 1910. Interpretation of Experimental Results. (Jour, of Agri- cultural Science, 3, 417-440.) WIANCKO, A. T. 1914. Use and Management of Check Plats in Soil Fertility In- vestigations. (Jour, of the American Society of Agronomy, Vol. 6, pp. 122-124.) f t-26-*18 — 4M] 000 934 594 2 #