.. an? . . . iguana. 5.x. .. ... $.33; .....=«..wflna.. in. $14. .a 05 . . 2.1.69 .15 . 3. .q .. . .. z n.) . .359. mm. . .. .u. . 5.5:. £6“: . . . . _ . 6w? ,. .. . . .. . karififii 5% . . _ _ L 6. S lllllflllfllflfllflllll.lllllllllfllllllll 1771 10 LIBRARY Michigan State University This is to certify that the dissertation entitled THE APPLICATION OF STATISTICAL METHODS TO SEED TESTING presented by Hongyu Liu has been accepted towards fulfillment of the requirements for Ph.D; degree in Crop and Soil Sciences 0?”.va Major prole$sor MS U is an Affirmative Action/Equal Opportunity Institution 0-12771 PLACE IN RETURN Box to remove this chedtout from your record. To AVOID FINES return on or before date due. MAY BE RECALLED with earlier due date if requested. DATE DUE DATE DUE DATE DUE mm is 4 33 JUN 1 9 2015 o 417 1 a use alumna-mu THE APPLICATION OF STATISTICAL METHODS TO SEED TESTING By HONGYU LIU A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Crop and Soil Sciences 1 999 ABSTRACT THE APPLICATION OF STATISTICAL METHODS TO SEED TESTING By HONGYU LIU In order to evaluate seed quality with accuracy and precision, it is very important that, first, a representative sample be drawn and, second, that appropriate test techniques be applied with adequate precision and repeatability. These studies were designed to measure variability in results of seed quality tests and performance of different probes in seed sampling under various conditions. Data were collected from conventional germination referee (CGR) tests and blind germination referee (BGR) tests on corn (Zea mays L.) and soybeans (Glycine max (L.) Merrill) conducted by laboratories of the Association of Official Seed Analysts (AOSA) and the Society of Commercial Seed Technologists (SCST) in the Midwest and Upper Great Lakes Region in 1994 to 1997. The results showed a positive inter-replicate bias in which a significant correlation existed among different replications within a laboratory in the CGR but not in the BGR tests. Tolerances were estimated and compared with those used by both the International Seed Testing Association (ISTA) and the AOSA. Data were collected from cold test referees on corn and soybean conducted by up to 51 AOSA and SCST laboratories in the Midwest and Upper Great Lakes Region in 1993 to 1995. Variation in corn cold tests was lower than that of soybean. Variation in SO-seed corn cold tests was equivalent to or less than that for IOO-seed warm germination test. Possibilities for standardization appear much better for corn than for soybean. Five soybean seed lots representing different seed sizes were counted with an electronic counter and/or manually in 11-16 AOSA/SCST laboratories in 1996-98. Both manual and electronic methods produced results suitable to meet the needs of the seed industry for supplying seed count information. Sample size was more important to test performance than number of replications. Adjustment of moisture content of the seed to a constant level increased test variation significantly. The 1.5% tolerance of the National Institute of Standards and Technology was not adequate to cover the variation in seed counting. Six seed lots representing various sampling conditions (various seed sizes, seed surface features, and mixture of different types of seed) were sampled with a total of 10 probes/triers plus hand grabbing. Performance of probes with different physical features varied among crops and sampling conditions. With certain exceptions, most probes provided representative samples from homogeneous seed lots. Seed lots containing blends of varieties or mixtures of contaminants with different seed sizes and flow characteristics produced different levels of accuracy with certain probes. Probes with smaller openings tended to provide samples that under-represented the longer, more chaffy seed types, while over-representing the shorter, more free-flowing components. The diameter of the opening is the most important feature of a probe that will enable it to provide a representative sample from such lots. To My Parents Whose unselfish and constant encouragement throughout my study in the United States has been an immeasurable value, this thesis is affectionately dedicated. IV ACKNOWLEDGEMENTS The completion of this thesis would not have been possible if not for the support, guidance, encouragement, patience and confidence shown me by my major professor, Dr. Lawrence Copeland. I could never have thought about my graduate study without what you have done for me. I would like to express my deepest appreciation to you for all you have provided to me for my personal, as well as professional development. I will forever consider myself the most fortunate of graduate students for all the wonderful opportunities you have provided. I am indebted to my committee members: Dr. Dennis Gilliland, Dr. Donald Penner and Dr. Oliver Schabenberger for your patience, mentoring, valuable guidance, advice and the continuous encouragement throughout my years of graduate study. Whenever I needed your help and went to you I was never disappointed. I only wish you could receive this special recognition for your contribution to my graduate study. I am also grateful to Dr. Dick Payne of National Seed Laboratory, Mr. Perry Bohn of Asgrow Seed Company, Mr. Ron Cook of Oregon State University, Mr. Jim Cramer of Society of Commercial Seed Technologist, Mrs. D. Jamieson of Illinois Seed Analysts Association, Mr. Steve McGuire of Michigan State Seed Laboratory, Mr. Joe Lamb of Great Lakes Hybrid Seed Company, Michigan Foundation Seed, and the staff of seed testing laboratories at Oregon State University and the Agriculture Departments of the states of Washington and Idaho who provided analyses for the seed probe study. I am also thankful to Mr. Marcelo Queijo and Mr. Marcos Morales in Dr. Copeland's project group for discussions, friendship, suggestions and encouragement during my stay here. I did not only enjoy the academic ideas but also shared diverse cultures, food and philosophy from you. Finally, I would like to thank my wife, Xiaoyu and my daughters, Xudan and Ellen for their consistently support and patience during my study. VI TABLE OF CONTENTS LIST OF TABLES LIST OF FIGURES CHAPTER ONE STATISTICAL BACKGROUND FOR SEED TESTING STATISTICAL DISTRIBUTIONS TYPE IAND TYPE II ERRORS VARIATION, TOLERANCE AND OUTLIERS SAMPLE SIZE AND NUMBER OF REPLICATIONS CORRELATION COEFFICIENT BETWEEN DIFFERENT READINGS WITHIN A LABORATORY REFERENCES CHAPTER TWO VARIABILITY OF GERMINATION TESTS OF CORN AND SOYBEANS (0030 ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS AND DISCUSSION SUMMARY AND CONCLUSIONS REFERENCES CHAPTER THREE VARIATION IN COLD TESTS OF SOYBEAN AND CORN SEED VIGOR ABSTRACT INTRODUCTION MATERIALS AND METHODS VII 13 14 15 20 25 28 29 29 3O 32 RESULTS AND DISCUSSION 35 SUMMARY 39 REFERENCES 41 CHAPTER FOUR VARIABILITY IN SEED COUNTS OF SOYBEANS DETERMINED BY MANUAL VS. ELECTRONIC METHODS 42 ABSTRACT 42 INTRODUCTION 43 MATERIALS AND METHODS 45 RESULTS AND DISCUSSION 50 CONCLUSIONS 58 REFERENCES 59 CHAPTER FIVE STUDY OF RELATIVE EFFICIENCY OF DIFFERENT PROBES FOR SEED SAMPLING 61 ABSTRACT 61 INTRODUCTION 62 MATERIALS AND METHODS 63 RESULTS AND DISCUSSION 69 CONCLUSIONS . 79 SUMMARY 81 REFERENCES 82 APPENDIX A FIGURES FOR GERMINATION, VIGOR AND SEED COUNT TESTS 84 APPENDIX B STATISTICAL ANALYSIS TABLES 97 APPENDIX C SAS CODE FOR MAJOR STATISTICAL PROCEDURES 112 VIII Table LIST OF TABLES Description of table Germination ranges of seed lots used in germination referee tests Correlation coefficient (p) among replications averaged across laboratories in germination tests Percentage of test cases that fall in certain range of ratio s/c (observed vs. expected standard deviation within a laboratory) in germination referee tests Relationship between standard deviation (germination %) and number of loo-seed replicates in corn BGR testing in 1997 Tolerance estimates for germination tests with 4 100-seed replicates at the 5% significant level one-sided test, compared with the ISTA and AOSA Rules Tolerance estimates for germination tests of 1 to 4 IOU-seed replicates at the 5% significant one-sided test Correlation coefficient (p) among replications averaged across laboratories in cold test results Percentage of data distribution of test results in cold referee and warm germination (WG) referee tests on corn and soybeans based on 4-replicate test Tolerances estimated for corn cold tests and their comparison with tolerances estimated from conventional germination referee tests and those in the Rules page 16 20 21 24 26 36 37 39 1O 11 12 13 14 15 16 17 18 19 20 Changes of test standard deviation after outliers were eliminated Standard deviations before and after outliers were eliminated with different sample sizes for electronic counts on soybean in 1997 Changes of the standard deviation among and within laboratories for seed counts when adjusting moisture content (MC) to a 10% level for all tests of soybean in 1996- 98. Estimation of seed count tolerances among laboratories and among replicates within a laboratory without adjusting moisture content of the seed Probes used for sampling probe study Performance of various probes and hand sampling on colored perennial ryegrass seed Relative efficiency (R.E.%) of probes for detecting colored seeds of perennial ryegrass Performance of probes sampling purity components of Ky bluegrass (K), P. ryegrass (R) and red fescue (F) mixture Relative efficiency (R.E.%) of probes for detecting colored seeds from the mixture lot Performance of probes for detecting colored seeds of Ky bluegrass (K), P. ryegrass (R) and red fescue (F) mixture Performance of various probes for detecting colored wheat seeds 51 52 53 64 69 7O 71 73 74 75 21 22 23 24 25 A-2 A-3 A-4 A-5 A-6 A-8 Relative efficiency (R.E.%) of probes for detecting colored wheat seeds Performance of various probes for detecting colored soybean seeds Relative efficiency (R.E.%) of probes for detecting colored soybean seeds Performance of probes on soybean sampling with stove-piped colored seeds Performance of various probes and hand sampling on perennial ryegrass with red colored seed and stove—piped green seed Regression analysis for corn CGR tests Regression analysis for soybean CGR tests Regression analysis for corn BGR tests Regression analysis for soybean BGR tests Regression analysis for corn vigor tests with 50 seeds per replicate Regression analysis for corn vigor tests with 100 seeds per replicate Regression analysis for soybean vigor tests with 50 seeds per replicate Regression analysis for soybean vigor tests with 100 seeds per replicate XI 75 76 77 77 78 97 98 100 102 105 107 108 110 Figure A-2 A-4 LIST OF FIGURES Description of figure Construction of subsets of data with different number of replications Relationship between number of replicates and standard deviation for 50-seed cold tests on corn in 1993-95 [outliers (3.6% of the original data) were eliminated] Standard deviation for electronic counts as a function of sample sizes and number of replicates for seed lot 2 (5199 seeds/kg) of soybean tested in 1998 Probes tested in the study (Scale at 1:8) Inserted positions for shorter types (a) and longer types (b) of probes on a seed bag Relationship between number of replicates and standard deviation for 100-seed conventional germination referee (CGR) tests on corn in 1994-96 [outliers (7.8% of the original data) were eliminated] Relationship between number of replicates and standard deviation for 100-seed conventional germination referee (CGR) tests on soybean in 1994-96 [outliers (12.6% of the original data) were eliminated] Relationship between number of replicates and standard deviation for loo-seed blind germination referee (BGR) tests on corn in 1 997 Relationship between number of replicates and standard deviation for 100-seed blind germination referee (BGR) tests on soybean in 1997 XII Page 19 38 55 65 67 84 85 86 87 A-5 A-6 A-7 A-8 A-10 A-11 A-12 A-13 Relationship between number of replicates and standard deviation for 50-seed cold vigor tests on soybean in 1993-95 [outliers (35.6% of the original data) were eliminated] Relationship between number of replicates and standard deviation for 100-seed cold tests on corn in 1993-95 [outliers (23.8% of the original data) were eliminated] Relationship between number of replicates and standard deviation for 100-seed cold tests on soybean in 1993-95 [outliers (51.2% of the original data) were eliminated] Standard deviation for electronic counts as a function of sample sizes and number of replicates on soybean in 1995-96 Standard deviation for manual counts as a function of sample sizes and number of replicates for soybean tested in 1996-97 Standard deviation for electronic counts as a function of sample sizes and number of replicates for soybean tested in 1996-97 Standard deviation for electronic counts as a function of sample sizes and number of replicates for seed lot 1 (6240 seeds/kg) of soybean tested in 1998 Standard deviation for electronic counts as a function of sample sizes and number of replicates for seed lot 2 (5199 seeds/kg) of soybean tested in 1998 Standard deviation for electronic counts as a function of sample sizes and number of replicates for seed lot 3 (7610 seeds/kg) of soybean tested in 1998 XIII 88 89 90 91 92 93 94 95 CHAPTER ONE STATISTICAL BACKGROUND FOR SEED TESTING The foundations of science are mostly dependent on observation and description, both of which are important tools of statistics. Statistics was applied to seed testing as early as the 19th century (Rodewald, 1889). Leggatt (1942) indicated that seed analysis is essentially a statistical science, dealing as it does with quantitative data affected to a marked extent by a multiplicity of causes. STATISTICAL DISTRIBUTIONS Three types of statistical distributions are of principal concern to seed analysts and seed scientists, namely the Binomial, Poisson and Normal distributions. (1) Binomial distribution. The objective for a germination test is to know if a seed will germinate or not; for a purity test, whether a particle is a particular seed or not. In general, we consider an experiment or test as having n seeds or particles, each resulting in one of two outcomes, ‘success’ or ‘failure’, in our case for example ‘germinated’ or ‘non-genninated’, ‘seed interested’ or ‘not’. Let p = Pr (success occurs at any given test) and assume that p remains constant from test to test. Let the variable Y denote the total number of successes in n independent tests. Then Y is said to have a binomial distribution: Pr(Y=k)=[:]pk(l—p)“'k wherek=0,1,...,n. 1 The binomial distribution originated with Jacob Bernoulli in 1710 and Abraham DeMoivres in 1718 (Dodge, 1971 ). The mean, variance and standard deviation of Y are as follows: Themean =E(Y)=p=np The variance = E (Y-,u)2 = 02 = nPU‘P) The standard deviation = J02 = ‘lnp(l - p) For different sets of values of the parameters n and p, the shape of the binomial distribution varies. For p = 0.5, thejgraph of the binomial distribution is symmetric. That is, the probability of obtaining 0 success and n failures will be the same as the probability of obtaining n successes and 0 failure in n tests; the probability of obtaining 1 success and (n-1) failures will be the same as the probability of obtaining (n — 1) successes and 1 failure; and so forth. If p > 0.5, successes are more likely than failures, and the graph of the distribution is skewed to the left. If p < 0.5, the argument is reversed. An interesting characteristic of the graph of the binomial distribution for p close to 0.5 is the bell shape. It can be shown that when the number of tests n becomes larger and larger, the graph of the binomial distribution always becomes bell shaped. If p is very close to 0.5, this bell shape appearance is evident even when n is fairly small. When n 2 50 and hp 3 5, the binomial distribution can be approximated by the Poisson distribution. (2) Poisson distribution. Suppose the average number of noxious weed seeds in a seed lot is small, say 5 in one kilogram and there are 10,000 particles per kilogram. The rate for noxious weed seed is only 0.05%. The computation of the probability for such data in use of the binomial formula becomes laborious. Another distribution, namely the Poisson distribution can be applied to approximate the binomial distribution. In general, the Poisson distribution is approached when a population contains only a very small number of interested characteristics but a large sample has been examined. The distribution with probability function _ fly -y Pr(Y—k)=f(y)=V-e fory=0,l,2,... is called the Poisson distribution, named after Simeon Denis Poisson who introduced it in 1837 although DeMoivre may have discovered it almost a century earlier (Larsen and Marx, 1986). Instead of two parameters as in the binomial distribution, the shape of the distribution is dependent on only one, the mean u. As It increases, me probability shifts to the right and the distribution becomes more bell-shaped. When u is no more than 1, the distribution is extremely skewed to the right with almost all of the probability located at Pr(0) and Pr(1). One of the important characteristics of the Poisson distribution is that the mean ([1) equals to its variance. Therefore, the sample mean, 7 , provides an estimate of both u and of. (3) Normal distribution. As mentioned above, when the number of tests n becomes larger, the graph of the binomial distribution always becomes bell shaped. Then, another important distribution can be used to approximate the binomial distribution, that is, the normal distribution. When the number of tests is relatively large, calculating the binomial probability is very difficult and time consuming. Larsen and Marx indicated that "the limit proposed by Poisson was not the only, or even the first, approximation to the binomial. DeMoivre had already derived a quite different one, that is, normal distribution, in his 1718 tract, Doctrine of Chances. Like Poisson’s work, DeMoivre’s theorem did not Initially attract the attention it deserved; however, it did catch the eye of Laplace, though, who generalized it and published in 1812" (Larsen and Marx, 1986). The DeMoivre-Laplace theorem states: Let X be a binomial random variable defined on n independent trials each having success probability p. For any numbers c and d, X-n 1 (-x2)/2 - P c<fi2 Corn CGR test 94 204 33.8 48.5 15.7 1.0 1.0 95 205 38.0 42.9 17.6 1.5 0.0 96 157 47.8 37.6 11.5 3.2 0.0 Soybean CGR test 94 199 32.7 43.2 18.6 5.0 0.5 95 200 40.0 46.5 13.5 0.0 0.0 96 227 37.4 43.6 15.0 2.6 0.0 Corn BGR test 97 115 3.5 41.7 41.7 10.4 2.6 Soybean BGR test 97 125 0.0 46.4 35.2 15.2 3.2 21 within a laboratory was small for most of the tests and very small for one third to half of the tests. We called this phenomenon a positive inter-replication bias. The results from different replicates for the same lot within a laboratory were positively correlated. For BGR tests, the ratio $10 was symmetrically distributed around the expected value of 1. Among the 240 tests, 82.5% had ratios between 0.5 and 1.5. Only 1.7% of the 240 tests had ratios less than 0.5. It is necessary to keep in mind that heterogeneity of a seed lot would result in sky > 1. Thus, the positive inter-replicate bias did not occur with the BGR test by concealing the identity of the replicates. Sample Sizes Test variation decreased with the increase in sample sizes. Table 4 shows that standard deviation in germination percentage decreased as the number of 100-seed replicates increased from one to seven for corn BGR tests. However, the greatest drop in standard deviation among laboratories always occurred when number of replicates increased from 1 to 2. For example, for seed lot A in Table 4, the standard deviation decreased by 1.35 unit (or 39%) with an increase in the number of replicates from 1 to 2 while the additional decrease was only 0.31 unit (9%) for 3 replicates. Similar results were observed from all other tests in this study, suggesting that no more than two 100-seed replicates may be necessary for germination testing, depending on the accuracy desired (See Appendix A for the results from other seed lots). However, once the level of test variability is determined, the issue of sample size to use become somewhat arbitrary, depending on philosophical (e.g., seed law enforcement or 22 Table 4. Relationship between standard deviation (germination %) and number of 100-seed replicates in corn BGR testing in 1997. Number of Seed lot replications A(92%)‘ B(89%) C(86%) D(81%) E(70%) 1 3.46 4.07 5.25 5.85 6.03 2 2.11 3.17 4.00 4.35 4.72 3 1.80 2.92 3.56 4.18 4.00 4 1.73 2.84 3.48 4.21 4.06 5 1.75 2.88 3.40 4.13 4.09 6 1.64 2.89 3.43 4.00 4.03 7 1.64 2.83 3.37 3.95 3.90 8 1.64 2.83 3.37 3.95 3.90 ' Percentage in the parentheses was the average of germination test results for the seed lot. quality assurance) considerations. Some of the AOSA and ISTA gennlnation tolerances are based on a 5% significant level, implying a willingness to make a Type I error (is, rejecting a correctly labeled seed lot) 5% of the time. These tolerances are based on a given level of accuracy as reflected in the magnitude of tolerances required. For the most part, these tolerances are based on testing 400 seeds (four 100-seed replicates). Any decision to test fewer than 400 seeds should also recognize the necessity of using wider tolerance if the same level of accuracy is to be maintained. Suggested tolerance levels appear in the next section. Tolerance estimates For germination percentages between 50 and 99% for a four 100-seed replicate test, tolerances computed on the basis of variability from CGR and BGR are compared with these in the ISTA and AOSA Rules referees (Table 5). For 23 Table 5. Tolerance estimates for gennlnation tests with 4 100-seed replicates at the 5% significant one-sided test, compared with the ISTA and AOSA Rules. Germination Soybean Corn AOSA ISTA Level BGR test CGR test BGR test CGR test Rules Rules (kahunadoneé 99 l l 2 l 5 2 98 2 2 3 2 5 3 97 3 3 3 3 5 3 96 3 3 4 3 5 4 95 4 4 4 4 6 4 94 4 4 5 4 6 4 93 5 5 5 5 6 5 92 5 5 5 5 6 5 91 5 6 6 6 6 5 90 6 6 6 6 6 6 89 6 7 6 7 7 6 88 6 7 6 7 7 6 87 7 8 7 7 7 6 86 7 8 7 8 7 7 85 7 8 7 8 7 7 84 8 9 7 9 7 7 83 8 9 8 9 7 7 82 8 IO 8 10 7 7 81 9 10 8 10 7 8 80 9 10 8 ll 7 8 79 9 ll 8 ll 8 8 78 9 ll 8 12 8 8 77 10 12 8 12 8 8 76 10 12 9 l3 8 8 75 10 12 9 13 8 9 74 10 13 9 l4 8 9 73 ll 13 9 l4 8 9 72 ll 14 9 15 8 9 71 ll 14 9 15 8 9 70 ll 14 9 15 8 9 69 12 14 9 l6 9 10 68 12 15 9 16 9 10 67 12 15 10 17 9 10 66 12 16 10 17 9 10 65 l3 16 10 18 9 10 64 l3 16 10 18 9 10 63 13 16 10 18 9 10 62 l3 17 10 19 9 10 61 13 17 10 19 9 10 6O l4 17 10 20 9 10 59 l4 18 10 20 10 ll 58 l4 18 10 21 10 ll 57 l4 18 10 21 10 ll 56 14 18 10 21 10 ll 55 14 I9 10 22 10 ll 54 15 19 10 22 10 ll 53 15 19 10 22 10 11 52 15 20 10 23 10 ll 51 15 20 10 23 10 11 j!) 15 20 IO 23 10 ll 24’ germination of 90%, all estimates were identical to the AOSA and ISTA tolerances. The estimates from this study were closer to tolerances in the ISTA Rules than in the AOSA Rules for gennlnation above 93%. For germination below 85%, estimates from CGR tests on both crops and BGR tests on soybeans were generally higher than that under both Rules. Since more rigorous (smaller) tolerances work against the seller, tolerances for germination above 93% in the AOSA Rules are favorable to the seller while those for lower germination levels work against the seller. These results indicate that tolerances in both Rules can cover the variation for germination levels above 85% but not for lower germination levels. Tolerance estimates for different number of 100-seed replicates from this study are shown in Table 6 (see next page). SUMMARY AND CONCLUSIONS 1. Inter-replicate bias existed in routine CGR tests. The blind referee test method provided an effective approach to avoid inter-replicate bias that influence germination test results. Perhaps elements of the BGR concept could be incorporated into standard laboratory practice or other practices implemented to reduce the likelihood of inter—replicate bias. Two possibilities may be: (A) Conceal the identity of different replicates of the same lot. (B) Separate the replicates in time and/or space. 2. Variability in test results decreased with increase in the amount of seed used for the test, however, use of more than two 100-seed replicates did not reduce 25 Table 6. Tolerance estimates for germination tests of 1 to 4 100-seed replicates at the 5% significant one-sided test. Germination Soybean BGR Soybean CGR Corn BGR Corn CGR Icvel(%) 1 2 3 4 1 2 3 4 1 2 3 4 l 2 3 4 rep reps reps reps rep reps reps reps rep reps reps reps rep reps reps reps 99 3 2 2 l 4 3 2 2 4 3 2 2 3 2 2 1 98 5 3 3 2 5 4 3 3 6 4 3 3 4 3 3 2 97 6 4 4 3 6 5 4 3 7 5 4 4 6 4 3 3 96 7 5 4 4 8 5 4 4 8 6 5 4 7 5 4 3 95 8 6 5 4 9 6 5 4 9 6 5 4 8 5 4 4 94 9 6 5 4 10 7 6 5 10 7 6 5 9 6 5 4 93 10 7 6 5 10 7 6 5 ll 7 6 5 10 7 6 5 92 10 7 6 5 11 8 7 6 11 8 6 6 ll 8 6 5 91 11 8 6 5 l2 9 7 6 12 8 7 6 12 8 7 6 9O 12 8 7 6 l3 9 8 7 l2 9 7 6 13 9 7 6 89 13 9 7 6 14 10 8 7 13 9 7 6 14 10 8 7 88 13 9 8 6 15 11 9 7 13 9 8 7 14 10 8 7 87 14 10 8 7 16 11 9 8 14 10 8 7 15 ll 9 7 86 15 10 8 7 17 12 10 8 14 10 8 7 16 12 9 8 85 15 11 9 7 17 12 10 9 15 10 9 7 17 12 10 8 84 16 11 9 8 18 13 10 9 15 ll 9 8 18 13 11 9 83 16 12 9 8 l9 13 11 9 16 ll 9 8 l9 14 11 9 82 17 12 10 8 20 14 11 10 16 11 9 8 20 14 12 10 81 18 12 10 9 21 l4 12 10 16 11 9 8 21 15 12 10 80 18 13 10 9 21 15 12 ll 17 12 10 8 22 l6 13 ll 79 19 13 11 9 22 16 13 11 17 12 10 8 23 16 13 11 78 l9 14 11 9 23 l6 13 11 17 12 10 9 24 17 14 12 77 20 14 11 10 24 17 14 12 17 12 10 9 25 l8 14 12 76 20 14 12 10 24 17 14 12 18 12 10 9 26 18 15 13 75 21 15 12 10 25 18 14 13 18 13 10 9 27 19 15 13 74 21 15 12 10 26 18 15 13 18 13 10 9 28 20 16 14 73 22 15 13 11 27 19 15 13 18 13 11 9 29 20 17 14 72 22 16 13 ll 27 19 16 14 19 13 ll 9 30 21 17 15 71 23 16 13 11 28 20 16 14 19 13 11 9 30 22 18 15 70 23 l6 13 11 29 20 17 14 19 13 11 9 31 22 18 15 69 24 17 14 12 29 21 17 15 19 14 11 10 32 23 l9 16 68 24 17 14 12 30 21 17 15 19 14 ll 10 33 23 19 16 67 25 17 14 12 31 22 18 15 19 14 ll 10 34 24 20 17 66 25 18 15 12 31 22 18 16 20 14 11 10 35 25 20 17 65 26 18 15 13 32 23 18 16 20 14 11 10 36 25 21 18 64 26 18 15 13 33 23 19 16 20 14 ll 10 37 26 21 18 63 26 19 15 13 33 24 l9 17 20 14 12 10 37 27 22 18 62 27 19 16 13 34 24 20 17 20 14 12 10 38 27 22 19 61 27 19 16 13 35 24 20 17 20 14 12 10 39 28 23 19 60 28 20 16 14 35 25 20 18 20 14 12 10 40 28 23 20 59 28 20 16 14 36 25 21 18 20 14 12 10 41 29 24 20 58 28 20 16 14 36 26 21 18 20 14 12 10 42 29 24 21 57 29 20 17 14 37 26 21 18 20 I4 12 10 42 30 24 21 56 29 21 17 14 37 26 22 19 21 15 12 10 43 31 25 21 55 29 21 17 14 38 27 22 19 21 15 12 10 44 31 25 22 54 30 21 17 15 39 27 22 19 21 15 12 10 45 32 26 22 53 30 21 17 15 39 28 23 20 21 15 12 10 45 32 26 22 52 30 22 18 15 40 28 23 20 21 15 12 10 46 33 27 23 51 31 22 18 15 40 28 23 20 21 15 12 10 47 33 27 23 50 31 22 18 15 41 29 23 20 21 15 12 10 47 34 27 23 N O) test variability substantially. Although we did not test the significance of the increase in precision (decrease in variability) with decreased number of 100-seed replicates, we feel that the comparison in standard deviation values alone will be meaningful to seed analysts. In this context, a 200-seed test appears adequate for providing reliable germination results for corn and soybean. However, the use of a 200-seed test will necessitate the use of different tolerances. 3. Tolerance estimates for germination levels above 90% from both CGR and BGR test results were close to tolerances under ISTA Rules, but lower than those under the AOSA Rules. These studies indicate the need for further research to determine whether the AOSA germination tolerances should be reconsidered. 4. Tolerance estimates for lower germination levels from both CGR and BGR test results were generally higher than the present tolerances in both the ISTA and AOSA Rules. Our results indicate that consideration should be given to increasing the tolerances of both the AOSA and ISTA for germination below 85%. 5. When different sample size are tested, proper tolerances for that size should be applied. 27 REFERENCES . AOSA. 1917. Rules for Testing Seed. Proceeding of AOSA 1917: 15. . AOSA. 1998. Rules for Testing Seed. Journal of Seed Technology 19. . ISTA. 1963. lntemational Rules for Seed Testing. Proceeding Of ISTA 28(2). . Kenkel, J. L. 1989. Introductory Statistics for Management and Economics. 3"1 Edition. PWS-KENT Publishing Company, Boston: 88: 151. . Miles, R. S. 1961. Germination variation and tolerances. 51“ Annual Meeting, Proceeding of AOSA: 86-91. . Miles, R. S. 1963. The handbook of tolerances and of measures of precision for seed testing. Proceeding of ISTA Vol. 28, No.3. . Neter, J., W. Wasserman and M. H. Kutner. 1985. Applied linear statistical models. 2'“l Edition, Richard D. Irwin, Inc.: 6. . Rodewald, H. 1891. The theory of probability applied to seed testing (A translation of Landw. Versuchs-Stationen published in 1889). Agricultural Science 5(3): 74-105. . Tattersfield, J. G. 1979. Assessment of results of referee tests on gennlnation. Seed Science and Technology, 7: 247-257. 28 CHAPTER THREE VARIATION IN COLD TESTS OF SOYBEAN AND CORN SEED VIGOR ABSTRACT Seed vigor is widely recognized as an important attribute of seed quality. However, in practice, vigor test results are not labeled on containers of seed offered for sale. This is because the lack of standardized methods for vigor testing is thought to produce excessive variability among repeated test results, especially among tests performed in different laboratories. However, one vigor test, the cold test is routinely conducted on almost all corn and much of the soybean seed sold in the United States because it is known to be a valuable in-house method of assessing seed vigor where testing methods can be standardized. This study was designed to determine the extent of variation in cold test results conducted in routine tests among different laboratories throughout the Midwest corn and soybean area. Data were collected from cold referee tests on corn (Zea mays L.) and soybean (Glycine max (L.) Merrill) conducted by up to 51 member laboratories of Association of the Official Seed Analysts (AOSA) and Society of Commercial Seed Technologists (SCST) in the Midwest and Upper Great Lakes Region from 1993 to 1995. The results show that a significant positive correlation between replications within a laboratory existed in 100-seed tests but not in 50-seed tests for both crops. Variability in cold tests of com was much lower than that of soybean. Variation among results of four 50-seed corn cold tests was equivalent to 29 or less than that among results of warm gennlnation tests. Based on this study, four 50-seed replicates are suggested for corn cold tests. Tolerances for cold test levels of 90% or above were calculated. INTRODUCTION Germination tests are successful in predicting seed quality in at least two aspects. First, they have a high level of repeatability and second, they provide information about the potential germination of a seed lot under optimum conditions. The major problem with the gennlnation test is its inability to detect potential differences in performance among higher germinating seed lots (Hampton and TeKrony, 1995), especially under adverse conditions. Interest in vigor testing began when seed scientists realized that some aspects of seed quality could not be detected by the standard germination test (Byrum and Copeland, 1995). Therefore, various vigor tests are used to detect these quality differences. The cold test is the most widely used vigor test for corn, soybean and sorghum in North America and Europe (T eKrony, 1983; Ferguson, 1990; Hampton, 1992) and is widely accepted by the seed industry in many other parts of the world (Hampton and TeKrony, 1995). Today, the cold test is performed on almost all corn seed sold in the United States. It is also commonly used for soybean seed lots planted throughout the Midwest (Byrum and Copeland, 1995). However, the cold test method is still not a standardized test throughout the seed industry or from laboratory to laboratory. Thus, there are many reports of inconsistencies in test results among different laboratories conducted on the 30 same seed lot (Bradnock, 1975; Ader and Fuchs, 1978; Burris and Navratil, 1979; Fiala, 1987). Factors such as soil type, pH, substrate moisture content, crop rotation, substrate soil : sand ratio, temperature, oxygen supply in the substrate, seedborne diseases, fungicide seed treatment and duration of the cold period have been identified that may contribute to the reported variability in cold test results among different seed testing laboratories (Nijenstein, 1995). Because of the extent of variability that is thought to exist among cold test results, cold test levels are never labeled on seed offered for sale. For labeling purposes, a test method should be standardized and the variability in test results should be accounted for by tolerances. One of the few actual studies in which measurements were made of cold test variability by conducting a blind referee test on corn, showed that cold test variability did not vary substantially more than that for standard germination test results (Byrum and Copeland, 1995). Thus, it was concluded that cold test results might be covered by the same tolerances used for standard germination tests (warm germination test). Additional studies were suggested to further determine the variability in routine cold test results and to explore the possibility of establishing tolerances suitable for cold test results. The objectives of this study were to determine the extent of the variability among cold test results of corn and soybean seeds in routine tests to compare the variation in warm germination test results and to determine the potential factors that might contribute to test variation. 31 MATERIALS AND METHODS Data sources and vigor test methods Data on corn and soybean cold test results were collected from member laboratories of the Association of Official Seed Analysts (AOSA) and Society of Commercial Seed Technologists (SCST). These data were comprised of results from a cold test referee in which samples from the same seed lot were delivered to and tested by participating laboratories. From 1993 to 1995, 14 com and 13 soybean seed lots were tested in up to 27 laboratories for corn and 51 laboratories for soybeans throughout the Midwest and Upper Great Lakes region. Although officially standardized methods still do not exist in either AOSA or ISTA Rules, a handbook has been developed in which preliminary suggested cold test procedures are described (Hampton and TeKrony, 1995). The principle of the cold test is to expose seeds to cold temperatures (10°C, 7 days) in non-sterile field soil at approximately 60-70% of water-holding capacity followed by a 4-7 day grow-out period under ideal conditions (25°C). Two basic cold test methods are suggested: the rolled towel and the tray methods. For the rolled towel method, paper towels of the same weight and thickness as used for warm germination test are used. For the tray method, a 45 x 66 x 2.75 cm tray made of fibreglass, plastic or metal with sheets of creped cellulose paper is utilized. A minimum of four replicates of 50 seeds each for the rolled towel or four 100-seed replicates for the tray method are suggested in the handbook. The handbook also indicate that the soil component is a very important aspect of the test and the selection of proper soil source is critical to the reproducibility. It should be 32 from a field site that has supported some vegetation, preferably the crop to be tested. The data we collected showed that almost all (98% and 100% for soybean and corn, respectively) of the participating laboratories used either 50- seed or 100-seed tests. However, only about 75% of the laboratories applied 4- replication tests. The number of replications used by the laboratories varied from 1 to 16. Although different number of replicates and seeds per replicate were used by different laboratories, only those data from tests representing 4 replications of 50 or 100 seeds each were analyzed. Although some of the laboratories used sterile soil, we were unable to omit their data to have a minimum often laboratories in each test. Statistical analysis 1. Inter-replication correlation coefficient. Estimation of inter-replication correlation coefficient is a special case of the model 1.25b in "Applied Linear Statistical Models" by Neter et al. (1985). Let p be the vigor gennlnation rate for a population. For a vigor test of n replications of k seeds each, the correlation coefficient between replicates within a laboratory was estimated as: Correlation coefficient = p = 1 - —U— 202’ n n 2 .2 .2. (Xi ‘ Xj) 1=11=r+1 6+6) The hypothesis that no correlation existed (Ho: p=0), was tested as: where U: and Uzzkxpr-p). 33 2(a)?- rkn —1)2(n — 1) E-O ‘IVar(;3)/l z = where Var(/3) E and l is the number of laboratories in the test. If a significant correlation coefficient existed, results from different replications within individual laboratories were biased. A negative correlation implies a higher variation than random sampling error while a positive correlation may show biased readings within a laboratory. We call the latter a positive inter-replication bias. 2. Data distribution The expected random sampling standard deviation 0 = (pqln)”2, was computed for each sample using the mean of cold test results across laboratories for p and q = 1 - p. For each sample, the deviation, d, of each laboratory vigor test results from the all-laboratory mean was divided by c for that sample. Percentages of data distribution in terms of a were determined. 3. Variability and tolerance estimation To determine variability for estimating tolerances, outliers which are observations that are considered too far from the population mean to be useful in describing test variability were defined by the method described by Miles (1963). If a laboratory mean for a lot differed more than 4 standard deviations from the mean across laboratories, the data from that laboratory were considered as outliers and were omitted from the analyses. To study the impact of number of replicates on variation, data from the cold test results were generated as follows. One of the four 50- or 100-seed replicate test results within an individual laboratory was randomly selected to 34 construct a subset of data for a single 50- or 100-seed replicate for each seed lot. Likewise, for two 50- or 100-seed replicates, two of the four 50- or 100—seed replicate test results were randomly selected for the subset. Similar methods were used for other replicate sizes (Figure 1, page 19). A total of 30 subsets of data were obtained by repeating the procedure twenty-nine additional times for each replicate size for each seed lot. Standard deviation for each subset of data was obtained by the UNIVARIATE Procedure of SAS (SAS Institute, 1995). The mean standard deviation from thirty subsets of data for each replicate size was used to evaluate the relationship between number of replicates and variability. Tolerances were estimated with the method described by Miles (1963). The standard deviation, s, among laboratories was computed for each lot representing different levels of germination. The regression of the ratio, f(= sic), on germination percent (p) is calculated. Tolerance estimates are then calculated from the equation, T = f x <31 x to, where, to. = 1.65 (assuming a 5% significant one-sided test), 01 = {2 x [p x (100 - p)/n]}"2, and n = number of replicates. RESULTS AND DISCUSSION Inter-replication correlation coefficient Table 7 shows that a significant positive correlation existed in 100-seed vigor test results but not in 50-seed vigor test results for both crops. It may imply that personal bias more likely occurred when sample sizes were larger. 35 Table 7. Correlation coefficient (p) among replications averaged across laboratories In cold test results. Crop Sample size p P, (Ho: p=0) Corn 50 seeds -0.03932 0.6424 100 seeds 0.37819 0.0000 Soybean 50 seeds -0.05143 0.7658 100 seeds 0.35633 0.0000 Variability of the cold tests results Percentage of data distribution of cold test results in Table 8 shows that for soybean less than 50% of 100-seed test results and 65.4% of 50-seed test results were within four standard deviations. This compares with 87.4% of the warm germination test results that were within the same standard deviation range. However, for corn, 96.4% of the results of four 50-seed replicate cold tests were within four standard deviations. Compared to 92.2% in this range for warm germination results, the results of four 50-seed replicate cold test had less variability than that of four 100-seed replicate warm germination tests for corn. The variation in four 100-seed replicate tests was higher than that in warm germination tests. These results seem to indicate that the cold test may be able to perform as well or even better than standardized warm germination tests on corn if four 50-seed replicate tests are used. 36 Table 8. Percentage of data distribution of test results in cold referee and warm gennlnation (VVG) referee tests on corn and soybeans based on 4-replicate tests. Data range Corn Soybean Cold Test WG“ Cold Test WG 50-seed 100-seed 50-seed 100-seed 1: 1c" 49.1 20.8 35.4 15.7 9.0 30.5 :I: 20 76.4 45.4 61.1 29.9 25.3 56.8 1 30 87.3 60.8 82.4 48.8 34.3 75.7 :t 40 96.4 76.2 92.2 65.4 48.8 87.4 :t 50 98.2 84.6 95.8 74.8 60.2 94.8 1 60 98.2 90.0 97.8 84.3 70.5 96.3 :1: 70 98.2 93.8 98.5 90.6 79.5 97.4 :l: 100 100.0 96.9 100.0 100.0 90.4 100.0 "' WG = Warm germination referee test. ** o = standard deviation. Sample size Generally, test variation decreased with increase in number of replicates (Figure 2). The substantial decrease in test variation with an increase in number of replicates indicates the necessity of four replicates for 50-seed corn cold tests. Tolerance estimate Tolerances for four 50-seed replicate corn cold tests are given in Table 9. The Table shows that these calculated tolerances for corn cold tests are similar to tolerances estimated from warm germination test results and therefore, close to those in the ISTA Rules. Since only one seed lot tested had a vigor level below 90%, it may not be reasonable to estimate tolerances for vigor levels below 90% from these data. It also appears meaningless to estimate a tolerance table for soybean cold tests and for 100-seed corn cold tests from these data, since greater variability existed for those tests. 37 ..usmséa em; 58 .265 9: Lo 6.8 22.52 8&8? c_ 58 S was 28 38-8 .2 c2633 2357. new «23:52 Lo 6983: coming 25:26.3“ .N 939... § .26. .85. so. .88 cm: $me =me $va (0.04” . n . u. .. I...» 3.... . . x. r. n. .N. . ma . ., .. .. ”E... H...“ "mu” . ..n. , u. .. .4... .7... H . ., an”. .nh U. H. .u.” . ”a." H .. .33.. a. a“. . ..H... .. ... .. mm... a... "mm. m.» - . .U ....w m H n... .u , . . :me 1 T QDNCOIOV'CONx-O l I 32 So“. a F F mam. 62:... B NF mac. 9:. I 9. no. 25 I uorrernep preparers 38 Table 9. Tolerances estimated for corn cold tests and their comparison with tolerances estimated from conventional germination referee tests and those in the Rules. Germination Tolerance for or vigor level Corn cold test Warm germination test (four 100-seed (four 50-seed replicate test) from or in replicate test) (%) CGR" AOSA Rules ISTA Rules 99 1 1 5 2 98 2 2 5 3 97 2 3 5 3 96 3 3 5 4 95 4 4 6 4 94 4 4 6 4 93 5 5 6 5 92 6 5 6 5 91 6 6 6 5 90 7 6 6 6 * CGR = The conventional germination referee tests conducted in 1994-95 among AOSA/SCST member laboratories. See previous chapter for more details. SUMMARY A positive correlation among replications within individual laboratories existed in 100-seed vigor tests but not in 50-seed tests for both crops. It implies that a positive inter-replication bias more likely occur with larger sample sizes than with smaller sample sizes. Variation in cold test results was different for corn and soybean seed. The accuracy for corn was higher than that for soybean. Variation for 50-seed corn tests was equivalent to or less than that for the warm germination test. Based on this study, a four 50—seed replicate cold test is suggested for corn. Tolerances for vigor levels of 90% or above are suggested 39 in Table 9. Finally, the cold test for soybean appears far from being standardized on the basis of the variation in test results. However, possibilities for standardization appear much better for com. 40 10. 11. 12. REFERENCES Ader, F. and Fuchs, H. 1978. Einige Hinweise zur Bedeutung der Erde als Substrat fi'Jr die Kaltprr‘qung von Mais. Seed Science and Technology, 6, 877-893. Bradnock, W. T. 1975. Report of the vigor committee, 1971-1974. Seed Science and Technology, 3(1): 124-127. Burris, J. S. and Navratil, R. J. 1979. Relationship between laboratory cold-test methods and field emergence in maize inbreds. Agronomy Journal, 17: 985-988. Byrum, J. R. and L. O. Copeland. 1995. Variability in vigor testing of maize (Zea maize L.) seed. Seed Science and Technology, 23, 543-549. TeKrony, D. M. 1983. Seed vigor testing. Journal of Seed Technology, 8, 55-60. Ferguson, J. 1990. Report of seed vigor subcommittee. Journal of Seed Technology, 14, 182-184. F iala, F. 1987. Report of the vigor test committee 1983-1986. Seed Science and Technology, 15(2): 507-522. Hampton, J. G. 1992. VIQOI' testing within laboratories of the lntemational Seed Testing Association: a survey. Seed Science and Technology, 20, 1 99-203. Hampton, J. G. and D. M. TeKrony. 1995. Handbook of Vigor Test Methods. The lntemational Seed Testing Association, PO. Box 412, 8046 Zurich, Switzerland: 51 -65. Miles, R. S. 1963. The handbook of tolerances and of measures of precision for seed testing. Proceeding of ISTA Vol. 28, No.3. Nijenstein, J. H. 1995. Soil cold test - European perspective: Seed Vigor Testing Seminar (Edited by H. A. van de Venter). Copenhagen, Denmark, 7 June, 1995. International Seed Testing Association, Zurich, Switzerland. 34-52. SAS Institute. 1995. SAS Procedures Guide. Version 6, 3rd Edition. SAS Institute Inc., Cary, NC, USA: 617-634. 41 CHAPTER FOUR VARIABILITY IN SEED COUNTS OF SOYBEAN S AS DETERMINED BY MANUAL VS. ELECTRONIC METHODS ABSTRACT Soybean (Glycine max (L.) Merrill) seed counts are routinely conducted by seed suppliers throughout the seed industry for the purpose of providing their customers with information that can help them determine planting rates needed to achieve desired plant populations. These studies were conducted to determine the level of variability among both manual and electronic seed count methods for help in establishing meaningful tolerances that can be used for tnith-in-labeling purposes. Tests were also conducted to determine the best combination of sample and seed sizes needed for conducting the tests. The results showed that both manual and electronic methods can be used to meet the needs of the seed industry for supplying seed count information. Sample size was more important to test performance than number of replications. Adjusting moisture content of the seed to a constant level increased test variation significantly. The 1.5% tolerance of the National Institute of Standards and Technology was not adequate to cover the variation encountered in seed counting. No correlation between seed size and test variation was observed. 42 INTRODUCTION Seed count tests are offered by more and more seed laboratories for their clientele because of the interest in precision planting for a wide range of vegetable and agronomic crops. A survey of 34 laboratories by the joint Association of Official Seed Analysts (AOSA) Referee! Society of Commercial Seed Technologists (SCST) Research Committees (McGuire, personal communication) in the Midwest Region of the United State showed that only 7 did not offer seed count services. Many laboratories conduct hundreds and even thousands of seed counts, especially for corn and soybeans. Small grains were the third most frequent kind tested. Different methods are used to obtain seed counts for soybeans. About half of the laboratories use electronic counters. Less than half test moisture at the time of the count and report the result. Twenty-four of the 34 respondents clearly thought the AOSA should have official procedures or recommendations for seed count tests. Establishment of truth-in-labeling for seed count information requires the use of tolerances. It is well known that repeated tests on a seed sample for one or more quality factors do not necessarily give exactly the same results each time because of the variation which results from both random and non-random sources. However, it was not until 1929 that Statistical methods for handling such variability were first introduced into official seed testing rules (Collins, 1929), although the use of tolerances was suggested much earlier (Rodewald, 1891 ). Since that time, a body of literature has developed to help seed analysts 43 understand how seed testing results vary and to establish tolerances that are used to determine when differences are statistically significant, i.e., whether apparent differences represent a real difference between two values or can be explained by chance alone (Banyai et al., 1988; Dodge,1971; Leggatt, 1935; Miles, 1963). If a second test is outside of tolerance from the first (or labeled quality), a real difference is considered to exist between the two tests, while within tolerances, the variation most likely is due to chance alone. Tolerances for such factors as germination, purity, and noxious weed seed, have been established by either the lntemational Seed Testing Association (ISTA) or the AOSA, or both (ISTA, 1996; AOSA, 1998). Since no established AOSA/SCST tolerances are available for seed counts, the 1.5% tolerance of the National Institute of Standards and Technology (NIST) has been applied in some states. In 1994, Illinois (Lair, personal communication) reported 263 potential seed count violations with the use of the NIST tolerance. Another survey study (Payne, personal communication) showed that at least 10% and up to 36% seed count test results were out of the NIST tolerance during the period of 1994 to 1997. A survey from Asgrow Seed Company (Bohn, personal communication) showed that only 32% of the 256 seed lots tested had differences between labeled and tested seed counts within :1 %, 56% within 12%, 71% within 3% and 90% within i4%. Many questions have arisen about count methods and the tolerances applied. Many people in the seed industry believe that the NIST tolerances are too strict and not statistically valid for biological materials. Consequently, research was needed to answer such questions. The objectives of this study were to: (1) evaluate comparative results obtained by manual vs electronic methods, (2) determine proper sample size and number of replications which should be used for the test, and (3) provide information for the establishment of tolerances for seed counts. MATERIALS AND METHODS Samples from a soybean seed lot were counted by 11 AOSA/SCST laboratories in 1995-96 and samples from another soybean seed lot with larger seeds were counted by 15 laboratories in 1996-97. All of the laboratories involved offer routine seed count services. In 1998, 16 laboratories conducted an additional seed count referee test on soybeans. Each participating laboratory used the electronic counter that was used for its routine seed count services. 1. 1995-96 tests A randomly selected 500-9 sample from one soybean lot, with a seed size of approximately 7500 seeds/kg (3400 seeds/lb) was mailed in a sealed polyethylene bag to each laboratory from the referee coordinator. A purity test according to the AOSA Rules on the entire 500-g sample was performed, then each of the subsequent tests was conducted on the pure seed portion. A moisture test was made at the time of each count. For the manual count, eight 45 100-seed replicates were randomly counted out without replacement by hand from the 500-g sample as prescribed in the ISTA Rules (ISTA, 1996). The weight of each sample was recorded to three decimal places in grams. This was repeated five additional times to obtain a total of six replicate tests. For the tests with electronic counters, counts were made on six randomly selected successive samples with replacement on sample sizes of 375, 250 and 125 g with the electronic counter. Results for six replicates of tests for each sample size were recorded. 2. 1996-97 tests Based on the preliminary results from the previous year, a 1000-g random sample of a soybean seed lot with a larger seed size of approximately 5700 seeds/kg (2600 seeds/lb) was mailed in a sealed polyethylene bag to each participating laboratory from the referee coordinator. Fifteen AOSA/SCST laboratories completed the referee. While most of the procedures used were the same as those in 1995—96, modifications included: ( 1) for the manual count, the number of replicates was decreased from eight to four and four different sample sizes were used instead of one in previous year in order to evaluate impact of the sample size on the results. Therefore, four random samples for each sample size of 100, 200, 300 and 400 seeds were counted by hand and weighed; (2) for electronic counts, a sample size of 500 g was added, while the number of replicates for each sample size was maintained the same. 46 3. 1998 tests Three different soybean seed lots representing seed sizes of 5199, 6240, and 7610 seeds/kg (2360, 2830 and 3450 seeds/lb, respectively) were counted. Three 1000-9 samples, one for each size, were provided to each participating laboratory. The samples remained in their polyethylene bags until tested. Purity and moisture content were determined before the following procedures were conducted on the pure seed portion. A. Counts on four replications of 500-9 each. The 1000-g sample was divided though a Boemer (or Garnet) divider into two 500-g samples. Each sample was counted separately. Then, the two samples were recombined and the process repeated three additional times to obtain four replications. B. Counts on four 375-g samples. The 1000-g sample was divided though the divider twice, achieving four 250-g samples; then, one of the 250-9 samples was divided one additional time, giving two 125-g samples. One of the 125-g samples was combined with one of the three 250-9 samples obtained previously, giving a sample of 375 9. Any deviation from 375-g was corrected manually. After performing a seed count on this 375-g sample, all of samples were recombined, mixed well, and the process repeated three additional times to give a total of four counts on samples of 375 g each. C. Counts on four 250-g samples. The 1000-g sample was divided twice into four 250-g samples. Exactly 250 g were achieved by manually moving seed to or from the container. After performing a seed count on this sample, the entire 47 sample was recombined, mixed, and the process repeated three additional times to give four replications. D. Finally, the process was repeated as described above to obtain a 125-g sample and seed counts performed before recombining with the entire sample and repeating the process three additional times to give counts on four 125-g samples. Seed count for each sample was calculated as: 1000 x number of seed counted in the sample Seed count (seeds/k8) = sample weight (g) x (pure seed %) Both seed control officials and seed company representatives have expressed concern about the effect that variation in seed moisture content could have on the accuracy of seed counts. It was thought that changes in the percent moisture of a sample due to environmental conditions, would cause corresponding increases or decreases in the number of seeds per unit. In order to evaluate the impact of moisture content of the seed, the following formula was used to convert the data into a comparative seed count on the basis of 10 % moisture content: 1000x(1-0. l)xnumber of seed counted in the sample Seed count (seeds/kg) = sample weight (g) x (l-mc% tested/100) x (pure seed %) Observations that were disproportionately small or large were defined as outliers. Many approaches can be used to detect outliers (Miles, 1963; Tattersfield, 1979 and Kenkel, 1989). For this study the box plot method is 48 applied (Kenkel, 1989; SAS, 1990). The bottom and top edges of the box are located at the sample 25‘" and 75‘" percentiles with the sample media as the center of the box. The distance between the 25‘" and the 75‘" percentiles is called an interquartile range. Any data that are more than 2 interquartiles away from the media will be defined as outliers. Such outliers were excluded when calculating test results to avoid their influence on population means. In order to detect the impact of outliers in this study, both data with or without outliers were analyzed separately. The ANOVA model II y, = u, + e, for j"‘ reading of the i‘" laboratory and c’. = c2 . + 02.. was applied (Neter et al., 1996). 62. was the total variance, c2 . and oz w were the variance among and within laboratories, respectively. Suggested tolerances (two-sided test at the 5% significant level) for comparison of results obtained by different laboratories were calculated with the formula: Tolerance (%) = (1 .96x 2 x 092 )/(seeds/kg.) Suggested tolerances among replications within a laboratory (two-sided test at the 5% significant level) were calculated with the formula: Tolerance (%) = 100 x [1.96 x J number of replicates x azw/n] / (seeds/kg) where n is the number of readings (replications in each laboratory). 49 RESULTS AND DISCUSSION Impact of the outliers on seed count results As defined above, outliers are the observations that are considered too far from the population mean to be useful in describing test variability. Thus, they are extreme numbers, either much higher or much lower than the population mean. The standard deviation among and within laboratories decreased an average of 35.2% and 12.1%, respectively, after outliers were eliminated (Table 10, next page). In some cases, the reduction in standard deviation was as high as 99.2% (variation within a laboratory from 500-g electronic counts in 1997) after outliers were eliminated. The existence of outliers might also diminish the efficiency of increasing sample size or number of replications. Table 11 shows that if outliers were included, the standard deviation among and within laboratories for the sample sizes of 500 g was 1.60 and 2.31, respectively, which was much higher than that for smaller sample sizes in the same test. However, after outliers were eliminated, the standard deviation decreased with the increase in sample size. If all outliers were used, the resulting tolerances would have been as high as 14 to 15% (data not shown). Thus, we believe that variation from outliers should not be considered for establishing tolerances; instead, the test technique of laboratories producing outliers should be improved with the aid of a regular program for calibrating electronic seed counters, along with routine participation 50 Table 10. Changes of test standard deviation after outliers were eliminated. Seed lot Sample size Standard deviation chapges (1%) Amonglaboratories Within a laboratory 1998 [Electronic] 1 125 g/tcst -53.9 -9.5 250 g/test -24.9 -1 1.5 375 g/test 0.0 0.0 500 g/test 0.0 0.0 2 125 g/test -89.1 -56.4 250 g/tcst -l4.6 -33.6 375 g/test 0.0 0.0 500 g/test 0.0 0.0 3 125 g/test -93.2 7.8 250 g/test -43.3 5.6 375 g/tcst -49.4 2.7 500 g/test -79.2 12.5 1997 (electronic) 4 125 g/test 0.0 0.0 250 g/test -0.4 -0.2 375 g/test -4.9 -0.5 500 g/test -83.3 -99.2 1997 manual 4 100 seeds/test -63.9 -60.9 200 seeds/test -83.0 -42.8 300 seeds/test -75.l -O.7 400 seeds/test -42.3 8.2 1996 electronic 5 125 g/test 0.0 0.0 250 g/test 0.0 0.0 375 g/test -8.2 0.1 1996 m nual 5 100 seeds/test 0.0 0.0 Average -35.2 -12.1 51 Table l 1. Standard deviations before and after outliers were eliminated with different sample sizes for electronic counts on soybean in 1997. Standard deviation (%) Sample size Before outliers eliminated After outliers eliminated (g/test) Among,r Within'r Among Within 125 0.70 0.77 0.70 0.77 250 0.75 0.40 0.75 0.40 375 0.78 0.24 0.76 0.24 500 1.60 2.31 0.65 0.21 I Among = among laboratories; Within = within a laboratory in referee and seed count educational programs. A wide range of electronic counters is used throughout the industry that collectively, along with improper seed counting techniques (including improper calibration of equipment), may contribute to the magnitude of variability observed in this study. Although laboratories were asked to calibrate their electronic counters, inconsistencies in doing so may have also contributed to the number of outliers found in this study. The impact of seed moisture content on seed count variability The adjustment of the seed moisture content increased the standard deviation in test results among laboratories by an average of 41.6% (Table 12). The results of moisture content among different laboratories for individual seed lots varied from 7% to over 10%, a wider range than expected, since samples were kept in sealed bags that were not opened until when they were tested. This wide range could be due to different types of moisture meters used by the 52 Table 12. Changes of the standard deviation among and within laboratories for seed counts when adjusting moisture content (MC) to a level of 10% for all tests of soybean in 1996-98. Seed size Sample No MC adjusted MC adjusted Change (:l:% ) if MC (seeds/kg) size adjusted Among Within Among Within Among Within 1995-96 1 r nic 7560 125g 1.04 0.80 1.60 0.81 53.4 1.0 250g 0.62 0.67 1.40 0.68 125.3 1.3 375g 0.80 0.37 1.37 0.37 71.3 1.3 1995-96 manual 7606 100 seeds 0.94 0.95 0.96 0.95 2.7 1.0 1996-97 (electronic) 5764 125g 0.70 0.77 1.24 0.77 78.5 -0.2 250g 0.75 0.40 1.11 0.40 48.7 0.1 375g 0.76 0.24 0.92 0.24 20.9 -0.1 500g 0.65 0.21 0.90 0.21 39.4 0.0 1996-97 menu I 5747 100 seeds 0.95 1.16 1.29 1.20 35.8 3.9 200 seeds 0.50 0.64 0.83 0.69 67.4 7.8 300 seeds 0.47 0.74 0.57 0.69 20.8 -6.8 400 seeds 0.70 0.67 0.76 0.64 8.7 -3.9 1998(electronic] 6240 125g 1.12 0.55 1.43 0.54 26.7 -0.3 250g 0.84 0.50 1.16 0.50 37.3 0.3 375g 0.83 0.30 1.16 0.29 39.3 -0.2 500g 0.70 0.30 1.06 0.30 50.4 0.2 5199 125g 1.85 0.72 2.07 0.72 11.5 0.0 250g 1.38 0.62 1.41 0.62 2.1 0.2 375g 1.07 0.63 1.07 0.63 -0.4 0.1 500g 1.02 0.52 0.94 0.52 -8.2 0.0 7610 125g 1.41 0.69 1.70 0.69 21.1 -0.1 250g 1.05 0.46 1.68 0.47 59.2 0.1 375g 0.88 0.42 1.55 0.41 76.1 -0.1 500g 0.75 0.49 1.58 0.49 110.8 -0.3 Avergge 41.6 0.2 53 laboratories and the lack of a standardized procedure for conducting moisture tests. Comparison of manual vs. electronic counts The manual and electronic methods in this study were comparable in test performance although electronic counts may be more cost effective (e.g., time, labor) than manual counts. Both manual and electronic counts provided reliable results if sample size was adequate (Table 12). In most cases, test variation within a laboratory was higher for manual counts than for electronic counts while variation among laboratories was smaller for manual counts than for electronic counts. This shows that improvement in manual counting should focus on the test method itself, while improvements in electronic counts should focus more on attempts to attain consistency among laboratories. The use of standardized equipment and routine equipment calibration should be an effective approach in reducing test variability among laboratories. Sample size vs. number of replicates In general, increase in sample size and number of replicates decreased test variation. However, the results of this 3-year study for both manual and electronic counts showed that increase in sample size was more important than number of replicates. For example, when the number of replicates for electronic counts (Figure 3, see appendix A for figures of other seed lots tested) increased Standard deviation (%) 2.5 a One rep I Two reps ElThree reps _ Four reps 2.0 - 1.5 - 1.0 - 0.5 7 0.0 ~ 1259 2509 3759 5009 SamMesRe Figure 3. Standard deviation for electronic counts as a function of sample sizes and number of replicates for seed lot 2 (5199 seeds/k9) of soybean tested in 1998. 55 from 1 to 4, the decrease in standard deviation was 0.1 (from 5 to 8.7%) for all four sample sizes tested in 1998. However, the standard deviation decreased 0.47 (24.5%) with increase in sample size from 125 to 250 gltest, 0.29 (19.8%) from 250 to 375 gltest and 0.08 (6.7%) from 375 to 500 gltest. The same trend was observed for results from all other seed counts in this study. Based on limited data for manual counts, a sample size of at least 200 seeds and two replicates should be tested. For electronic counts, a sample size of 500 gltest resulted in a smallest standard deviation in all tests (the 500-9 sample was not included in the 1995-96 test). Increase in number of replicates beyond one 500- 9 test did not reduce standard variation substantially. Tolerances A. W Results of this study clearly demonstrated that the 1.5% tolerances of the National Institute of Standard and Technology (NIST) are too small to cover seed count variation for both electronic and manual methods. Projected tolerances at the 95% level of certainty based on the variability found in this study appear in Table 13. None of the projected tolerances are equal to or less than 1.5%. Perhaps this explains why 10% to 36% of test results of seed counts in the 1994-97 survey were in violation to the NIST tolerance and may also explain results of the 1998 Asgrow survey. It is important to note that this study Table 13. Estimation of seed count tolerances among laboratories and among replicates within a laboratory without adjusting moisture content of the seed. Seed Sample size Tolerance (%) lot (per test) Among replicates Among laboratories within a laboratory l-rep 2-rep 3-rep 4-rep 2-rcp 34g) 4-rep 1998 I r ni 1 125-g 1.5 1.9 2.1 3.5 3.3 3.2 3.2 250-g 1.4 1.7 2.0 2.7 2.5 2.5 2.4 375-g 0.8 1.0 1.2 2.4 2.4 2.4 2.3 500-g 0.8 1.0 1.2 2.1 2.0 2.0 2.0 2 125-g 2.0 2.4 2.8 5.4 5.3 5.2 5.2 250-g 1.7 2.1 2.4 4.2 4.0 3.9 3.9 375-g 1.7 2.1 2.5 3.4 3.2 3.1 3.1 500-g 1.4 1.8 2.0 3.1 3.0 2.9 2.9 3 125-g 1.9 2.3 2.7 4.3 4.1 4.0 4.0 250-g 1.3 1.6 1.8 3.1 3.0 3.0 2.9 375-g 1.2 1.4 1.6 2.7 2.5 2.5 2.5 500-g 1.4 1.7 1.9 2.4 2.3 2.2 2.1 1996-97 le roni 4 125-g 2.1 2.6 3.0 2.9 2.5 2.3 2.2 250-g 1.1 1.3 1.6 2.4 2.2 2.2 2.2 375-g 0.7 0.8 0.9 2.2 2.2 2.2 2.2 500-g 0.6 0.7 0.8 1.9 1.9 1.8 1.8 1996-97 m n I 4 100 seeds 3.2 3.9 4.5 4.2 3.5 3.2 3.1 200 seeds 1.8 2.2 2.5 2.3 1.9 1.7 1.7 300 seeds 2.1 2.5 2.9 2.5 2.0 1.8 1.7 400 seeds 1.9 2.3 2.6 2.7 2.4 2.2 2.2 1995-96 [elegtronic] 5 125-g 2.2 2.7 3.1 4.8 4.3 4.1 4.1 250-g 1.9 2.3 2.6 3.3 2.8 2.7 2.6 375-g 1.0 1.3 1.4 3.2 3.1 3.0 3.0 1995-96 In nual 5 100 seeds 2.6 3.2 3.7 4.9 4.2 4.0 3.8 only measured the variability in seed counts from samples from a single bag. This assumes acceptable uniformity (homogeneity) within the seed lot from bag 57 to bag. It must be recognized that count variability will be larger if heterogeneity exists among bags in the lot. However, it should be noted that although a larger tolerance will give more certainty of avoiding the rejection of a correct label (statistically a Type I error), it will also increase the likelihood of accepting an incorrect label (Type II error). Thus, further study is needed to focus on the heterogeneity among bags within commercial seed lots. B. Tolerances for Lesults from different replicates within a laboratogy. Projected tolerances between replicates within a laboratory are given in columns 3-5 of Table 12 for the 95% level of certainty. The maximum differences allowed between any two replicates for the 250-g sample size for electronic counts varied from 1.1 to 1.9% and, for a sample size of 200 seeds/test for manual counts, was 1.8%. Thus, projected tolerances for inter- replicate variability are smaller than those for inter-laboratory test results because of the smaller levels of variability involved. Seed size and test variation No correlation between seed size and test variation was observed from this study. CONCLUSIONS 1. Routine seed count referee tests should be maintained to continuously monitor and improve test performances of laboratories because some laboratories are more likely to give outliers than others. Tolerances 58 should not be expected to cover the variation from outliers. Moisture content of the seed should not be adjusted to a certain level since more variability could result from the moisture test itself. Such adjustments greatly increased test variation in this study. Both manual and electronic counts can provide reliable results, provided the sample size is adequate. However, increase in sample size is more important than the number of replicates for both methods. The 1.5% tolerance of the National Institute of Standard and Technology (NIST) is too restrictive to cover seed count variation for both electronic and manual methods. Tolerances for different sample sizes and methods based on individual tests were estimated and listed on Table 13. For example, projected tolerances for a one-replicate test of 500 g ranged from 1.9% to 3.1%. Thus, the widest tolerance, 3.1% is suggested for a full coverage of test variation. No correlation between seed size and test variation was observed. REFERENCES AOSA. (1998). Rules for Testing Seeds. Journal of Seed Technology: 19. Banyai, J., J. Fischer and 23. Lang. (1988). Tolerances based on Poisson Distribution. Seed Science and Technology 16:321-329. Collins, G. N. (1929). The application of statistical methods to seed testing. USDA Circulars 2921-17. Dodge, Y. (1971). Statistical analysis for tolerances of noxious weed seeds. 59 10. 11. 12. 13. Master thesis, Utah State University. ISTA (1996). lntemational Rules for Seed Testing. Seed science and technology. Vol. 24, Supplement, Rules. Kenkel, J. L. (1989). Introductory statistics for management and economics. PWS-KENT 3"I Edition: 131-133. Leggatt, C. W. (1935). Contributions to the study of statistics of seed testing. Proceeding of ISTA. 1935:38-48. Miles, R. S. (1963). The handbook of tolerances and of measures precision for seed testing. Proceeding of ISTA. Vol. 28, No. 3. Neter, J., M. H. Kutner, C. J. Nachtsheim and W. Wasserman. (1996). Applied linear statistical models. 4'” Edition, IRWIN, 958-976 Rodewald. (1891). The theory of probability applied to seed testing (a translation of Landw. Versuchs-Stationen published in 1889). Agricultural Science 3(5): 74- 105. SAS. 1990. SAS Procedures Guide. Version 6, Third Edition. SAS Institute Inc., Cary, NC. Tattersfield, J. G. 1979. Assessment of results of referee tests on gennlnation. Seed Science and Technology, 7: 247-257. 60 CHAPTER FIVE STUDY OF RELATIVE EFFICIENCY OF DIFFERENT PROBES FOR SEED SAMPLING ABSTRACT This study was designed to compare the relative effectiveness of different seed sarnpling probes/triers in common use among seed control officials and the seed industry. A secondary objective was to identify the most effective sampling instruments for representative kinds of seed to help establish criteria for evaluating sampling instruments for different sampling conditions. Six seed lots representing different sampling conditions (various seed size, seed surface features, and mixture of different types of seed) were sampled with a total of 10 probes/triers plus hand grabbing. Results showed that performance of probes with different physical features varied among crops and sampling situations. With certain exceptions, most probes provided representative seed samples from homogeneous seed lots when properly used. However, representative samples are unlikely to be obtained by any probe from heterogeneous seed containers. Furthermore, seed lots containing blends of varieties or mixtures of contaminants with different seed size and flow characteristics, can not be sampled accurately with certain probes. Probes with smaller openings tended to provide samples that under-represented the longer, more chaffy seed types, while over- representing the shorter, more free-flowing components. We believe that the diameter of the opening is the most important feature of a probe that will enable it to provide a representative sample from such lots. Finally, all probes should be long enough to reach across the entire width or length of the container. 61 INTRODUCTION The first requirement in generating any seed test is to carefully obtain a representative sample. No matter how accurately a seed analysis is made, it can only show the quality of the sample that is submitted for analysis (ISTA, 1938). Hence, it is of fundamental importance that the sample properly represents the quality of the seed lot from which it is drawn. While the correct result would be obtained by analyzing the entire lot, practicality dictates that a small sample be drawn in such a way that truly represents the quality of the entire lot. A survey of 34 states by the American Association of Seed Control Officials (AASCO) (Nees, 1990) showed that a wide range in equipment is used for sampling seeds of various crop types existed even among seed control officials. An even wider range of sampling instruments is used for quality control in the seed industry. These include a variety of probes and triers, ranging from small 15.2-cm probes to double-sleeve triers up to 122 cm in length, depending on the type of seed and container. Several studies have been conducted on sampling methods. In the 1930’s, M.T. Munn observed the movement of seeds in bags when sampled with various instruments and found that the most practical and satisfactory type of probe or trier for closed bags was the German type (Munn, 1935). Later, a type of probe called the "sticker" was designed to obtain more representative samples (Leggatt, 1938). Debney (1960) introduced a dynamic sampling technique which was shown to be more accurate than any other device for 62 sampling from bags at that time. Although a simple sampling trial carried out at Dublin illustrated that the triers could produce biased samples even from homogeneous lots (Mullin, 1965), a study in Australia showed that certain triers did not differ significantly with regard to different seed components (Bean, 1970). At almost the same time Grisez and Hardin (1972) found that different sampling accuracy existed among sampling tools and methods. This research was conducted to compare the relative effectiveness of various seed sampling probes/triers in common use among seed control officials and the seed industry and to identify the most effective sampling instruments for different kinds of seed to help establish criteria for evaluating sampling instruments for different sampling conditions. MATERIALS AND METHODS 1. Probes: Ten probes were tested for their effectiveness and precision in sampling from different kinds of seeds. These are illustrated in Figure 4, and their characteristics are described in Table 14. 2. Seed lot preparation: (A). Ryegrass: One thousand eight hundred and fourteen kilograms of perennial ryegrass seed were thoroughly mixed with 22.7 kg of stained (red) perennial ryegrass by a commercially accepted blending facility. Then, the seed was bagged into eighty 22.7-kg bags. (B). A second ryegrass seed lot weighing 1,792 kilograms was thoroughly mixed with 22.7 kg of stained (red) perennial ryegrass by a commercially accepted 63 blending facility. Then, the seed was bagged into eighty 22.7-kg bags. As the bags were being filled, a 227-g sample of stained (green) ryegrass seed was placed in the center core of each with a "stove-piping" method using a small steel cylinder 61 cm long and 2 cm in diameter. Table 14. Probes used for sampling probe study. Probe No. Length Diameter OpeninL (mm) (mm) Number Length (mm) Vlfidth (mm) 1 1017 21 6 65 12 2 813 15 3 220 12 3 461 13 1 48 12 4 203 15 1 84 7-1 1 5 305 23 1 1 12 7-21 6 750 12 9 44 6 7 483 12 5 44 6 8 458 12.7 1 50 12.5 9 966 12.7 1 788 12.5 10 864 23 2 330 21 Note: See Figure 4 (page 65) for more details. (B) Mixture: One thousand eight hundred fourteen kilograms of perennial ryegrass, red fescue, and Kentucky bluegrass seed (1:1 :1) were thoroughly mixed with 7.71 kg each of stained (red) perennial ryegrass, red fescue, and bluegrass seeds (1 :1 :1) by a commercially accepted blending method. Then the seed was bagged into eighty 22.7-kg bags. (C) Wheat: One thousand eight hundred and fourteen kilograms of wheat were thoroughly mixed with 22.7 kg of stained (red) wheat by a commercially accepted blending methods. Then the seed was bagged into eighty 22.7-kg bags. . .3 1:34 fiwfie‘Sé-m ;. 12%» ‘ "."5‘35 '4“: ' ~. e \ 6326a ”833%???” " Figure 4. Probes tested in the study (Scale as 1:8). 65 (D) Soybeans: One thousand eight hundred and fourteen kilograms of soybean seed were thoroughly mixed with 22.7 kg of stained (green) soybeans by a commercially acceptable blending method. Then the seed was bagged into eighty 22.7-kg bags for sampling. (E) A second lot of soybean seed of equal size was prepared. This was bagged into eighty 22.7-kg bags around a core of 626 grams green stained soybean seed which was "stove-piped" into a cylindrical core (a 5.1 cm x 58.4 cm pipe) from bottom to top of the center of each bag. 1. Sampling and analysis: (A)An equal-sized sample was drawn from 13 randomly selected bags from each 80-bag lot as prescribed in the Association of Official Seed Analysts (AOSA) Rules with each of the probes immediately after bagging. These were combined and mixed thoroughly, then subdivided into a proper-sized working sample as specified by the AOSA Rules. (B) The process above was repeated three additional times to obtain a total of four independent replications from different positions within the bag. For shorter probes, samples of the four replicates were drawn from two positions along the side of the bag at equal distances from each respective corner while for others, the sample was taken diagonally through the bag from each of the four corners (Figure 5). r—N ==.'> <==I r=:::> <== g4 (8) Probe numbers: (b) Probe numbers: 3,4,5,7and8 1,2,6,9and10 Figure 5. Inserted positions for shorter types (a) and longer types (b) of probes on a seed bag. (C)A hand sample was taken by the "grab" method before the bag was sealed by randomly choosing another set of 13 bags and grasping a handful of seed from the bag for seed lots A (perennial ryegrass), B (perennial ryegrass, stove- piped) and C (mixture of Kentucky bluegrass, perennial ryegrass and red fescue). (D) From the sampling procedures above we obtained 204 samples which were further divided into smaller working samples for the following analysis: 0 Thirty-two 50-9 samples of the Lot A (perennial ryegrass) analyzed for the number of red colored ryegrass contaminants. o Thirty-two 50-g samples of the Lot B (perennial ryegrass, stove-piped) analyzed for the number of both red and green colored ryegrass contaminants. 0 Two sets of samples from seed lot C (mixture of Kentucky bluegrass, perennial ryegrass and red fescue): A) thirty-six 30-g samples analyzed for the number of the red colored seeds of each species; and B) thirty-six 39 samples analyzed for the percent composition of each of the three components. 67 o Twenty-eight 500-g samples of wheat from seed lot D analyzed for the number of red colored wheat caryopses. o Forty 500-g samples of soybean from seed lots E and F analyzed for the number of green colored soybeans. (E) Samples from seed lot A were analyzed at the Washington State Department of Agriculture Seed Laboratory, samples from seed lot B were analyzed at the Idaho State Department of Agriculture Seed Laboratory. Samples from seed lot C were analyzed by the Oregon State University Seed Laboratory and the remainder were analyzed in the Seed Research Laboratory at Michigan State University. 2. Statistical Analysis: The number of colored seed found was compared with the expected number for each sample from each lot. The average difference between the number of colored seed found and expected was squared to obtain a common comparable index of accuracy. The variance was calculated from the average of the four replicates as an index of precision. The overall performance of the different sampling probes and hand grab method was evaluated by combining the mean square error (MSE) of accuracy and precision together and the ratios of the MSEs of two probes were compared as a measure of their relative efficiency (RE), i.e., RE (%) = MSEJMSE,, where i, j = probe numbers or hand sampling, and i ¢ j. Finally, the Chi-square test was used to evaluate the agreement between test results and expected values. 68 RESULTS AND DISCUSSION Perennial ryegrass contaminated with red-colored ryegrass In general, all probes except prdbe number 2 provided samples in which the incidence of red-colored seeds was over-represented (Table 15). Probe number 2 was the most efficient, 38% more efficient than probe number 6, the second ranked probe, and 82% more than probe number 7 (Table 16). The rank of the probes in order of decreasing accuracy was 2, 7, 6, hand grabbing, 4, 3, 1 and 5. Probe number 6 was most precise, followed by probe numbers 1, 2, 5, 7, 3, 4 and hand grabbing. Table 15. Performance of various probes and hand sampling on colored perennial ryegrass seed. Probe Expected Found Bias Precision MSE 98 (Number of swds) (%) Hand 331 351 6.0 656 1056 11" l 331 359 8.5 179 963 11.3" 2 330 327 -0.8 275 284 2.6 3 331 356 7.6 431 1056 11.6" 4 330 353 7.0 623 1152 12.3Ml 5 330 367 11.2 322 I691 19.1""I 6 330 349 5.8 38 399 4.6 7 330 340 3.0 419 519 4.8 Expected = sample weight (g) x seeds/g x colored seeds (%); Found = number of colored seeds in the sample; Bias % = (Found - Expected) x lOO‘Vo/Expected; Precision = Variance within individual laboratories; MSE = Mean Square Error = Precision + (Found - Expected)2; ‘,"Significantly different from expected colored swds at 5% and 1% levels, respectively. Chi-square tests showed that the colored seed detected with probe numbers 2, 6, and 7 was not significantly different from the expected values, while those from other probes and hand grabbing were significantly different at 69 either the 5% or 1% levels of confidence. Although probe number 1 was relatively precise, it was. not very accurate. Table 16. Relative efficiency (R.E.%) of probes for detecting colored seeds of perennial ryegrass. Probe 6 7 1 Hand 3 4 5 2 38 82 243 270 275 308 490 6 32 148 168 171 195 326 7 88 103 106 124 224 1 8 9 19 72 Hand 1 10 59 3 9 57 4 45 Note: R.E % of a probe in a row over a probe in a column = (the MSE of the probe in the column - the MSE of the probe in the row) x 100% / the MSE of the probe in the column. Purity components of Kentucky bluegrass/perennial ryegrass/red fescue mixture The Chi-square test showed that proportions of the purity components detected with all probes were not significantly different from those expected (Table 17). However, it was important to note that all probes (probes 1-8) resulted in consistent over-estimation of Kentucky bluegrass by 4.47 to 12.68% and perennial ryegrass by 2.74 to 10.66% except probe number 5 (a 305-mm probe) which resulted in an under-estimation for perennial ryegrass of 0.6%. All probes resulted in a consistent under-estimation of red fescue by 6.20 to 18.04%. None of the probes tested provided an unbiased sample for the 70 onHoonm - 655...: + commmooum u “ohm 03:5 :82 H mm: mMateo-Eons 3.63%.: 555 359$ n 36605 mgxmgoe x 63825 - ease ... so 3m 6388 65 E 303 coho—co mo 03:3qu H ex; venom 62$ .285 .55 + .x. 88 .28 + .x. 88 825 -8 c u Axe Beaxm BEe a: 3 n.3- Ea 3 92 5 a." 3 v.2 N;- NE- 2» inn 3%. nun Ea... 823 3! 2. 3.8 no» 3 n: 3 2” 3 «.8. 3- ; QR v.3 can can o ”88... 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In contrast to the various probes, the manual grab method consistently provided samples in which longer more chaffy seeds were over-represented compared to shorter, more free-flowing seeds which tended to be under- represented. Although none of these deviations from expected levels were significant, there was a consistent bias toward certain kinds of seed depending on their flowability characteristics for all sampling methods. Overall, this bias was less pronounced for the 305-mm probe (probe number 5) with the sharpest end and widest opening. Red colored contaminants in the mixture of Kentucky bluegrass/Perennial ryegrass/red fescue Probe number 3 provided the best overall results, with 21% more efficiency than probe number 2 and 31% more than probe number 1 (Table 18). All of the probes were more efficient than hand sampling. However, Chi-square tests showed that the number of colored seeds detected was significantly different from the expected values at the 1% level (Table 19, page 74). Since all contaminants were so greatly under-estimated, we believe that both the accuracy and efficiency, especially for perennial ryegrass, were generally reduced by the analyst's inability to detect slightly-stained seed and that the 72 results of this test did not truly reflect the absolute efficiency of the probes tested. However, the relative efficiency and precision of the various probes (Table 18) should have been unaffected. This also suggests that further research should be done to more definitively test this conclusion. Table 18. Relative efficiency (R.E.%) of probes for detecting colored seeds from the mixture lot. Probe 2 1 4 6 5 7 8 Hand 3 21 31 41 94 167 172 193 294 2 8 17 60 120 125 142 225 1 8 49 104 109 124 202 4 37 88 93 107 179 6 37 40 51 103 5 2 10 48 7 8 45 8 35 Note: R.E % of a probe in a row over a probe in a column = (the MSE of the probe in the column - the MSE of the probe in the row) x 100%/ the MSE of the probe in the column. Wheat with contaminants of red colored wheat All probes provided samples in which the incidence of red-colored wheat seed was over-represented (Table 20, page 75). Some gave reasonable accuracy but were not very precise (e.g., probe number 3), whereas others (e.g., probe number 9) were precise but lacked accuracy. The number of colored seeds obtained with probe numbers 1, 10, 3 and 9 was significantly below that expected at both the 5% or 1% levels of confidence, while the results with other probes were not (Table 20). Probe number 2 was 73 503.8%": ...—961x.— 28 Rh 8 mason Eco—co 363.8 :8... 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Essen. n. m x n. m x u. m v. mm x n. m x n. .296 mm: SE8... 35 28”. 8325 Ben. .2338 CV gov-o. .m 25 E. 329». .n. .0: 889...: 3. ..o 288 8.630 95022. .6. wooed .o cocascotod .3 can... 74 most efficient, with 16% and 28% greater efficiency than probe numbers 4 and 5, respectively (Table 21). Probe number 3 was the least efficient among all probes tested. Table 20. Performance of various probes for detecting colored wheat seeds. 2 Probe Expected Found Bias MSE Precision x (number of seeds) (%) 1 137.1 120.9 -11.8 391.8 129.4 10.46“ 2 137.1 124.0 -9.6 252.6 81.0 6.79 3 137.1 134.6 -1.8 802.1 795.9 17.60" 4 137.1 123.5 -9.9 293.4 108.4 7.78 5 137.1 130.4 -4.9 324.2 279.3 7.43 9 137.1 114.2 -l6.7 570.3 45.9 16.36" 10 137.1 125.2 -8.7 350.1 208.5 8.73“ Expected = sample weight (g) x seeds/g x colored seeds (%); Found = number of colored seeds in the sample; Bias % = (Found - Expected) x 100%/Expected; Precision = Variance within individual laboratories; MSE = Mean Square Error = Precision + (Found - Expected)2; ‘,**Significantly different from expected colored seeds at 5% and 1% levels, respectively. Table 21. Relative efficiency (R.E.%) of probes for detecting colored wheat seeds. Probe 4 5 10 1 9 3 2 16 28 39 55 126 217 4 10 20 33 95 173 5 8 20 76 147 10 l 1 63 128 1 46 105 9 40 Note: R.E % of a probe in a row over a probe in a column = (the MSE of the probe in the column - the MSE of the probe in the row) x 100%/ the MSE of the probe in the column. 75 Soybean with contaminants of green-colored soybeans All probes except probe number 6 were very effective in detecting the level of green-colored soybean seed (Table 22). Only the colored seed detected by using probe number 6 was significantly different from the expected value at the 5% level. Others were not significantly different. Probe number 1 was the best, with 30% more efficiency than probe number 10, followed by probe numbers 5, 2 and 6 (Table 23). Although probe number 6 gave the closest to the expected seed number (Table 22), results among different replications varied greatly, indicating poor repeatability (precision). Among all 5 probes tested, probe number 6 had the smallest opening diameter (Table 14). Table 22. Performance of various probes for detecting colored soybean seeds. Probe Expected Found Bias MSE Precision x2 (number of seeds) (%) 1 36.2 34.0 -6.1 10.7 5.9 1.1 2 36.2 33.9 -6.4 67.4 62.1 7.74 S 36.2 34.7 -4.1 17.8 15.5 1.72 6 36.2 37.3 3.0 108.6 107.4 845* 10 36.2 38.6 6.6 13.6 7.8 1.13 Expected = sample weight (g) x swds/g x colored seeds (%); Found = number of colored seeds in the sample; Bias % = (Found - Expected) x 100%/Expected; Precision = Variance within individual laboratories; MSE = Mean Square Error = Precision + (Found - Expected)2; *Significantly different from expected colored seeds at 5% level. 76 Table 23. Relative efficiency (R.E.%) of probes for detecting colored soybean seeds. Probe 10 5 2 6 1 30 69 540 935 10 29 391 693 5 280 5 l4 2 62 Note: R.E % of a probe in a row over a probe in a column = (the MSE of the probe in the column - the MSE of the probe in the row) x 100% / the MSE of the probe in the column. Stove-piped soybean and ryegrass seed lots The fact that variation was very high in both seed lots indicates that no probe gave a representative sample from extremely heterogeneous seed bags. The colored seeds detected with all probes were significantly different from expected values, and were either over- or under—estimated (Tables 24 and 25). Table 24. Performance of probes on soybean sampling with stove-piped colored seeds. Probe Expected Found Bias MSE Precision xz (number of seeds) (%) 1 80.9 182.4 125.5 10630 328 521.2“ 2 80.9 74.5 -7.9 940.9 900 35.4" 5 80.9 100.5 24.2 5462.2 5078 207.1M 6 80.9 120.9 49.4 3764 2164 159.2" 10 80.9 48.4 -40.2 1763.3 707 78.7" Expected = sample weight (g) x swds/g x colored seeds (%); Found = number of colored seeds in the sample; Bias % = (Found - Expected) x 100%/Expected; Precision = Variance within individual laboratories; MSE = Mean Square Error = Precision + (Found - Expected)2; *Significantly different from expected colored seeds at 5% level. 77 Table 25. Performance of various probes and hand sampling on perennial ryegrass with red colored seed and stove-piped green seed. Probe Expected Found Bias MSE Precision x (number of seeds) (%) Red-colored seed Hand 334.2 270.3 -19.1 4305 222 50.9" 1 334.5 309.3 -7.5 1241 606 13.2" 2 333.4 410.5 23.1 24119 18175 235.8" 3 334.7 323.3 -3.4 967 837 9.0* 4 335.0 262.5 -21.6 10265 5009 108.2" 5 335.8 318.8 -5.1 2182 1893 20.9" 6 333.6 306.3 -8.2 907 162 108* 7 334.8 303.0 -9.5 2652 1641 18.8" Stove-piped green seed Hand 330.1 3048.5 823.5 8581996 1192297 100347 ** 1 330.3 114.8 -65.2 46882 442 567" 2 329.2 449.3 36.5 41675 27251 417.9M 3 330.6 659.5 99.5 266094 157919 2751.6“ 4 330.8 203.8 -38.4 42320 26191 432.7M 5 331.6 257.0 -22.5 75385 69820 698.3" 6 329.5 342.3 3.9 31444 31280 288'” 7 330.7 275.7 -16.6 61923 58876 382.5" Expected = sample weight (g) x seeds/g x colored seeds (%); Found = number of colored swds in the sample; Bias % = (Found - Expected) x 100%/Expected; Precision = Variance within individual laboratories; MSE = Mean Square Error = Precision + (Found - Expected)2; *Significantly different from expected colored seeds at 5% level. 78 CONCLUSIONS Based on the result of this study, the following conclusions are drawn: 1. The performance of probes with different physical features varied among crops and sampling situations. 2. For perennial ryegrass seed, only probe numbers 2, 6 and 7 performed well. They provided samples from which the number of the stained components was not significantly different than expected. Use of the other probes resulted in samples that varied from expected levels by varying amounts. 3. For the mixture of Kentucky bluegrass, perennial ryegrass and red fescue, all probes as well as the hand grab method, provided representative samples. However, only probe number 5 provided consistently unbiased samples. All other probes provided consistently biased samples although the bias was not statistically significant for any probe. Smaller and more free-flowing components (Kentucky bluegrass and perennial ryegrass) were more likely to be sampled than longer and narrower, more chaffy seed types (e.g., red fescue). On the other hand, the hand grab method provided samples in which the longer, chaffier seed (red fescue) was consistently over-represented and the shorter, more free-flowing components were consistently under-represented. The best probe for sampling from this mixture was probe number 5 a 305-mm (12-inch) probe with the sharpest end and a wide (8-21 mm) opening. It is likely (though not proven) that this probe would also be best for other seed mixtures containing both shorter, more free-flowing seeds and longer less free-flowing seed. 4. For wheat (middle-sized seed) probe numbers 2, 4 and 5 provided 79 representative samples. However, probe number 2 was the most efficient. 5. For soybean seed, all probes except probe number 6 were very efficient in providing representative samples. Probe number 6 was the only one with openings less than 10 mm in diameter. This indicates that all probes with large openings (diameter) should provide representative samples, although probe number 1 was the most precise in sampling soybeans. Since soybean has a rather large seed, probes with relatively small openings (less than 15 mm diameter) should be avoided. 6. For the extremely heterogeneous stove-piped soybean and perennial ryegrass seed lots, all probes as well as the hand grab method failed to provide a representative sample. The numbers of colored seeds detected varied greatly above or below expected values, showing the difficulty in obtaining a representative sample from extremely heterogeneous containers with any sampling method. 7. It should be expected that similar results would be obtained in sampling from other species and/or mixtures of species with similar characteristics. 8. Finally, the overall conclusion of this research is that all of the probes tested will provide a statistically representative sample if properly used for appropriate seed types and sampling situations. 80 SUMMARY The performance of probes with different physical features varied among crops and sampling situations. Representative samples are unlikely to be obtained by any probe from heterogeneous seed containers. On the other hand, with certain exceptions, most probes and sampling methods should provide a representative seed sample from a homogeneous seed lot if properly used. However, some seed lots, e.g., those containing blends of varieties or mixtures of contaminants with different seed size and flow characteristics, can not be sampled accurately with certain probes. Probes with smaller openings tended to provide samples that under-represented the longer, more chaffy seed types, while over-representing the shorter, more free-flowing components. We believe that the diameter of the opening is the most important feature of a probe that will enable it to provide a representative sample from such lots. Furthermore, all probes should be long enough to reach across the entire width or length of the container. Finally, regardless of the sampling instrument used, it is very important to follow proper sampling procedures. 81 REFERENCES Bean, J. E. (1970). Seed trier efficiency trial. Proc. of ISTA 35(3): 673681. Debney, E. W. (1960). Dynamic seed sampling spears in the United Kingdom. Proc. of ISTA 25: 174-181. Grisez, J. P. and E. E. Hardin. (1972). A comparison of four methods of sampling small seeds. Proc. of ISTA 37(3): 661-667. Leggatt, C. W. (1938). A new sampler for sampling seed in the sack. Proc. of AOSA 1938: 192-195. Mullin, J. F. (1965). Investigation into some common methods of lot sampling. Proc. of ISTA 30(2): 207-213. Munn, M. T. (1935). Observations upon the movement of seeds in bags when sampled with instmments. Proc. of ISTA 7: 15-18. Nees, L. W. (1990). Seed inspector's qualification and training committee report. AASCO, 1990. ISTA. (1938). lntemational Rules for Seed Testing. Proc. of ISTA 10: 408-410. 82 APPENDIX A FIGURES FOR GERMINATION, VIGOR AND SEED COUNT TESTS 83 ..umfiEEE 88> Emu .mcato on. .0 «$5 $2.53 8-3m. 5 Eco co 2321on $6.8 cozmcfitom .mco_.co>coo comm-co. co. c2633 Becca.» 6cm 88238 .0 69:5: 5923 95:25.61 ._.-.< 239“. 3. 5.85.58. .2 68m (ll/(ll. Joe/x/oé/z/o/e/e/(éeéé/e/z %%%%%%%%%%%%%%%@ . e»... 90.6% T T I j 1 GQNOIDQMNFO T 1 82 SEEN“ M" 88 mobs-PDT. ca 88 ask-l. .« up. 2.0. I. «N “013911199 91390338 84 .FQmEEE 2o; Emu 6596 on. .0 $0M: 22:33 8-3m. 5 536m co 2.0-611086228 co_.mc_E._mm .mcozcoEoo comm-8.. co. c2833 uumucmfi ucm 3.62.69. .0 cones: comics aEmcozflmm .N.< 8:9". 3. 585.55. .2 use 0 & 019.919.9110 ( A. 60%60@Qéaéwéaéaéaéwéwéaaweaweaw «me/o 1.- or 82 Ben. E l- a. mam. 68.:- D 1- cm 8.2 95%. l. .N 62 6:0 I I. «N uormmp mapums 85 .53 :_ Eco no 83. 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Emacmfi ucm 380:8. .o .onEzc .5023 3:25:23. .o.< 2:9“. .... .26. 32>. .o. .88 3...... :82 8:. 68.. 682 .88 6me am: :38 can 28.. :88 :m.« 8.. 1 r VOCD‘DNCOIDVWNx-O x-x- N "ODBMPP marinas lOV'm v-Fx— So”. a E i 0.5-PI i eco- 89 ..usmséa 28, E8 3598 as .o s«. .3 22.3. 8-82 s 88.8 co e8. 28 comm-co. .o. c2532. Emacflm can 360:3. .o .095: 5923 322.286”. ....< 2:9". 3.. .26. .85. .2 68m 6%. E... 652 cam .88 8: 88 88 A8... 88 :88 as. l...— l .... . .« .m ... m o . m m 2 .. «. 2 ... 2 2 t 2 2 5.2.0me ON fl 82... .« i 02;.- NN ii 2.0. mm ..« 8 uormgaep pmpuezs 90 tandard deviation (%) 1.4 1.2 * 0.8 4 0.6 - 0.4 l 0.2 1 Sample size I One rep I Two reps El Three reps Four reps I Five reps I Six reps 375g Figure A-8. Standard deviation for electronic counts as a function of sample sizes and number of replicates on soybean in 1995-96. 91 1.6 I One rep 1.4 — ITwo reps *— El Three reps 1.2 _ Four reps .3 O l Standard deviation (%) o o '0) oo .0 A l 0.2 - 0.0 - 1 00 200 300 400 Sample size (seeds/test) Figure A-9. Standard deviation for manual counts as a function of sample sizes and number of replicates for soybean tested in 1996-97. 92 Standard deviation (%) I One rep I Two reps ElThree reps # Four reps I Five reps E Six reps 1259 2509 3759 5009 Sample size Figure A-10. Standard deviation for electronic counts as a function of sample sizes and number of replicates for soybean tested in 1996-97. 93 1.4 HOne rep ITwo reps 1-2 ‘ ClTree reps T IFour reps 0:; 1.0 _ Z .2 *5 0.8 ~ '5 a: 'o 'E 0.6 A a 'u E m 0.4 J 0.2 ~ 0.0 - 1259 2509 3759 5009 Sample size Figure A-11. Standard deviation for electronic counts as a function of sample sizes and number of replicates for seed lot 1 (6240 seeds/kg) of soybean tested in 1998. 2.5 B One rep I Two reps D Three reps Four reps T 2.0 ~ .3 01 1 Standard deviation (%) 8 0.5 ~ 0.0 _ .1 if? 1259 2509 3759 5009 Sample size Figure A-12. Standard deviation for electronic counts as a function of sample sizes and number of replicates for seed lot 2 (5199 seeds/kg) of soybean tested in 1998. 95 1.8 B One rep 1-5 ITwo reps _ EIThree reps 1.4 Four reps 5}: 1.2 l c .2 E 1.0 — > 0 1: 'E 0.8 — I! 1:: S a 0.6 ~ 0.4 ~ 0.2 - 0.0 — 1259 2509 3759 5009 Sample size Figure A-13. Standard deviation for electronic counts as a function of sample sizes and number of replicates for seed lot 3 (7610 seeds/kg) of soybean tested in 1998. APPENDIX B STATISTICAL ANALYSIS TABLES The relationship between germination (or vigor) levels and standard deviation Model: model I Dependent variable = Standard deviation Table A-1. Regression analysis for corn CGR tests. (1) Number of replication = 1 Sum of Mean Source DF Squares Square F Value Prob>F Model 1 23.55322 23.55322 438.114 0.0001 Error 22 1.18273 0.05376 C Total 23 24.73595 Root MSE 0.23186 R-square 0.9522 Dep Mean 2.37607 Adj R-sq 0.9500 C.V. 9.75826 Parameter Standard T for H0: Variable DF Estimate Error Parameter=0 Prob > |T| INTERCEP 1 29.433683 129356096 22.754 0.0001 MEAN 1 -0.286132 0.01367016 -20.931 0.0001 (2) Number of replication = 2 Sum of Mean Source DF Squares Square FValue Prob>F Model 1 21.57545 21.57545 512.119 0.0001 Error 22 0.92685 0.04213 C Total 23 22.50230 Root MSE 0.20526 R-square 0.9588 Dep Mean 1.97456 Adj R-sq 0.9569 C.V. 10.39498 Parameter Standard T for H0: Variable DF Estimate Error Parameter=0 Prob > |T| INTERCEP 1 27.868511 1.14499499 24.339 0.0001 MEAN 1 0273831 0.01210034 -22.630 0.0001 (3) Number of replications = 3 Sum of Mean Source DF Squares Square F Value Prob>F Model 1 21.20799 21.20799 459.967 0.0001 Error 22 1.01437 0.04611 C Total 23 22.22236 97 Root MSE 0.21473 R-square 0.9544 Dep Mean 1.82175 Adj R-sq 0.9523 C.V. 11.78684 Parameter Standard T for H0: Variable DF Estimate Error Parametemo Prob > |T| INTERCEP 1 27.417933 1.19427507 22.958 0.0001 MEAN 1 -0.270675 0.01262073 -21.447 0.0001 (4) Number of replications = 4 Sum of Mean Source DF Squares Square FValue Prob>F Model 1 20.14405 20.14405 391.786 0.0001 Error 22 1.13115 0.05142 C Total 23 21.27520 Root MSE 0.22675 R-square 0.9468 Dep Mean 1.74278 Adj R-sq 0.9444 C.V. 13.01087 Parameter Standard T for H0: Variable DF Estimate Error Parameter=0 Prob > |T| INTERCEP 1 26.660040 1.25970624 21.164 0.0001 MEAN 1 0263493 0.01331206 -19.794 0.0001 Table A-2. Regression analysis for soybean CGR tests. (1) Number of replications = 1 Sum of Mean Source DF Squares Square FValue Prob>F Model 1 24.29208 24.29208 151.851 0.0001 Error 22 3.51941 0.15997 0 Total 23 27.81149 Root MSE 0.39997 R-square 0.8735 Dep Mean 3.12150 Adj R-sq 0.8677 C.V. 12.81327 Parameter Standard T for H0: Variable DF Estimate Error ParameteFO Prob > |T| INTERCEP 1 19.758398 1.35255851 14.608 0.0001 MEAN 1 -0.181765 0.01475032 42.323 0.0001 (2) Number of replications = 2 Sum of Mean Source DF Squares Square F Value Prob>F Model 1 22.06183 22.06183 135.390 0.0001 Error 22 3.58490 0.16295 C Total 23 25.64673 98 Root MSE 0.40367 R-square 0.8602 Dep Mean 2.67461 Adj R-sq 0.8539 C.V. 15.09269 Parameter Standard T for H0: Variable DF Estimate Error Parameter=0 Prob > |T| INTERCEP 1 18.553511 1.36715228 13.571 0.0001 MEAN 1 -0. 173487 0.01490987 -11.636 0.0001 (3) Number of replications = 3 Sum of Mean Source DF Squares Square FValue Prob>F Model 1 21.80926 21.80926 127.321 0.0001 Error 22 3.76847 0.17129 C Total 23 25.57773 Root MSE 0.41388 R-square 0.8527 Dep Mean 2.52712 Adj R-sq 0.8460 C.V. 16.37744 Parameter Standard T for H0: Variable DF Estimate Error Parameter=0 Prob > |T| INTERCEP 1 18.321119 1.40227284 13.065 0.0001 MEAN 1 -0.172572 0.01529398 -11.284 0.0001 (4) Number of repliwtions = 4 Sum of Mean Source DF Squares Square F Value Prob>F Model 1 21.86639 21.86639 133.564 0.0001 Error 22 3.60172 0.16371 C Total 23 25.46811 Root MSE 0.40462 R-square 0.8586 Dep Mean 2.43801 Adj R-sq 0.8522 C.V. 16.59619 Parameter Standard Tfor H0: Variable DF Estimate Error Parameter=0 Prob > |T| INTERCEP 1 18.275546 1.37287152 13.312 0.0001 MEAN 1 -0.173035 0.01497231 -11.557 0.0001 99 Table A-3. Regression analysis for corn BGR tests. (1) Number of replicates = 1 Sum of Mean Source DF Squares Square F Value Prob>F Model 1 3.58116 3.58116 5.890 0.0936 Error 3 1.82404 0.60801 C Total 4 5.40520 Root MSE 0.77975 R-square 0.6625 Dep Mean 4.97803 Adj R-sq 0.5501 C.V. 15.66384 Parameter Standard Tfor H0: Variable DF Estimate Error Parameter=0 Prob > |T| INTERCEP 1 14.318206 3.86433312 3.705 0.0342 MEAN 1 —0.111360 0.04588513 -2.427 0.0936 (2) Number of replicates = 2 Sum of Mean Source DF Squares Square F Value Prob>F Model 1 2.63021 2.63021 5.24 0.1064 Error 3 1.51058 0.50353 C Total 4 4.14079 Root MSE 0.70960 R-square 0.6352 Dep Mean 3.98775 Adj R-sq 0.5136 C.V. 17.79437 Parameter Standard T for H0: Variable DF Estimate Error Parameter=0 Prob > |Tj INTERCEP 1 12.106574 3.56643590 3.395 0.0426 MEAN 1 0096811 0.04235847 -2.286 0.1064 (2) Number of replicates = 3 Sum of Mean Source DF Squares Square F Value Prob>F Model 1 2.21012 2.21012 4.739 0.1177 Error 3 1 .39902 0.46634 C Total 4 3.60914 Root MSE 0.68289 R-square 0.6124 Dep Mean 3.63045 Adj R-sq 0.4832 C.V. 18.81011 100 Parameter Standard Tfor H0: Variable DF Estimate Error Parameter=0 Prob > |T| INTERCEP 1 11.006631 3.40198713 3.235 0.0480 MEAN 1 -0.088010 0.04042720 -2. 177 0.1 177 (4)Number of replicates = 4 Sum of Mean Source DF Squares Square F Value Prob>F Model 1 2.14372 2.14372 4.444 0.1256 Error 3 1.44710 0.48237 C Total 4 3.59082 Root MSE 0.69453 R-square 0.5970 Dep Mean 3.44191 Adj R-sq 0.4627 C.V. 20.17850 Parameter Standard Tfor H0: Variable DF Estimate Error Parameter=0 Prob > |T| INTERCEP 1 10.693882 3.45400937 3.096 0.0535 MEAN 1 -0.086554 0.04105740 -2.108 0.1256 (5) Number of replicates = 5 Sum of Mean Source DF Squares Square FValue Prob>F Model 1 1.87104 1.87104 3.574, 0.1551 Error 3 1.57049 0.52350 C Total 4 3.44153 Root MSE 0.72353 R-square 0.5437 Dep Mean 3.32410 Adj R-sq 0.3916 C.V. 21.76621 Parameter Standard T for H0: Variable DF Estimate Error Parameter=0 Prob > |T| INTERCEP 1 10.093916 3.59548686 2.807 0.0674 MEAN 1 0080794 0.04273600 -1.891 0.1551 (6) Number of replicates = 6 Sum of Mean Source DF Squares Square FValue Prob>F Model 1 2.03458 2.03458 3.598 0.1541 Error 3 1.69625 0.56542 C Total 4 3.73083 Root MSE 0.75194 R-square 0.5453 Dep Mean 3.27472 Adj R-sq 0.3938 C.V. 22.96206 101 Parameter Standard Tfor H0: Variable DF Estimate Error Parametemo Prob > |T| INTERCEP 1 10.350957 3.74547492 2.764 0.0699 MEAN 1 0084437 0.04451232 -1.897 0.1541 (7) Number of replicates = 7 Sum of Mean Source DF Squares Square FValue Prob>F Model 1 1.95608 1.95608 3.349 0.1647 Error 3 1 .75220 0.58407 C Total 4 3.70828 Root MSE 0.76424 R-square 0.5275 Dep Mean 3.22047 Adj R-sq 0.3700 C.V. 23.73078 Parameter Standard Tfor H0: Variable DF Estimate Error Parameter-=0 Prob > |T| INTERCEP 1 10.156553 3.80549887 2.669 0.0758 MEAN 1 -0.082762 0.04522414 -1.830 0.1647 (8) Number of replicates = 8 Sum of Mean Source DF Squares Square F Value Prob>F Model 1 1.67501 1.67501 2.560 0.2079 Error 3 1 .96285 0.65428 C Total 4 3.63786 Root MSE 0.80888 R-square 0.4604 Dep Mean 3.13672 Adj R-sq 0.2806 C.V. 25.78742 Parameter Standard T for H0: Variable DF Estimate Error Parametemo Prob > |T| INTERCEP 1 9.569640 4.03676430 2.371 0.0984 MEAN 1 -0.076749 0.04796728 -1.600 0.2079 Table A-4. Regression analysis for soybean BGR tests. (1) Number of replicates = 1 Sum of Mean Source DF Squares Square F Value Prob>F Model 1 11.53389 11.53389 137.021 0.0013 Error 3 0.25253 0.08418 C Total 4 11.78642 102 Root MSE 0.29013 R-square 0.9786 Dep Mean 5.10477 Adj R-sq 0.9714 C.V. 5.68353 Parameter Standard T for H0: Variable DF Estimate Error Parameter-=0 Prob > |T| INTERCEP 1 21.904900 1.44107673 15.200 0.0006 MEAN 1 0200228 0.01710538 -11.706 0.0013 (2) Number of replicates = 2 Sum of Mean Source DF Squares Square F Value Prob>F Model 1 7.29431 7.29431 354.535 0.0003 Error 3 0.06172 0.02057 C Total 4 7.35604 Root MSE 0.14344 R—square 0.9916 Dep Mean 4.16870 Adj R-sq 0.9888 C.V. 3.44082 Parameter Standard T for H0: Variable OF Estimate Error Parameter=0 Prob > |T| INTERCEP 1 17.804472 0.72702103 24.490 0.0001 MEAN 1 0162574 000863420 -18.829 0.0003 (3) Number of replicates = 3 Sum of Mean Source DF Squares Square FValue Prob>F Model 1 6.72516 6.72516 384.960 0.0003 Error 3 0.05241 0.01747 C Total 4 6.77757 Root MSE 0.13217 R-square 0.9923 Dep Mean 3.77308 Adj R-sq 0.9897 C.V. 3.50306 Parameter Standard T for H0: Variable DF Estimate Error Parameter-=0 Prob > |T| INTERCEP 1 16.825381 0.66786205 25.193 0.0001 MEAN 1 0155646 0.00793288 -19.620 0.0003 (4) Number of replicates = 4 Sum of Mean Source DF Squares Square F Value Prob>F Model 1 6.01871 6.01871 374.221 0.0003 Error 3 0.04825 0.01608 C Total 4 6.06696 103 Root MSE 0.12682 R-square 0.9920 Dep Mean 3.61822 Adj R-sq 0.9894 C.V. 3.50504 Parameter Standard T for H0: Variable DF Estimate Error Parameter=0 Prob > |T| INTERCEP 1 15.982001 0.64163826 24.908 0.0001 MEAN 1 -0.147413 0.00762028 -19.345 0.0003 (5) Number of replicates = 5 Sum of Mean Source DF Squares Square F Value Prob>F Model 1 5.91554 5.91554 662.957 0.0001 Error 3 0.02677 0.00892 C Total 4 5.94231 Root MSE 0.09446 R-square 0.9955 Dep Mean 3.48279 Adj R-sq 0.9940 C.V. 2.71223 Parameter Standard T for H0: Variable DF Estimate Error Parameter=0 Prob > |T| INTERCEP 1 15.748692 0.47825294 32.930 0.0001 MEAN 1 -0.146190 0.00567775 -25.748 0.0001 (6) Number of replicates = 6 Sum of Mean Source DF Squares Square F Value Prob>F Model 1 5.56865 5.56865 536.417 0.0002 Error 3 0.03114 0.01038 C Total 4 5.59979 Root MSE 0.10189 R-square 0.9944 Dep Mean 3.40285 Adj R-sq 0.9926 C.V. 2.99420 Parameter Standard T for H0: Variable DF Estimate Error Parameter=0 Prob > |T| INTERCEP 1 15.330835 0.51702211 29.652 0.0001 MEAN 1 -0.142152 000613763 -23.161 0.0002 (7) Number of replicates = 7 Sum of Mean Source DF Squares Square F Value Prob>F Model 1 5.15431 5.15431 528.848 0.0002 Error 3 0.02924 0.00975 C Total 4 5.18355 104 Root MSE 0.09872 R-square 0.9944 Dep Mean 3.35319 Adj R-sq 0.9925 C.V. 2.94416 Parameter Standard T for H0: Variable DF Estimate Error Parameter=0 Prob > |T| INTERCEP 1 14.875355 0.50297678 29.575 0.0001 MEAN 1 -0.137310 0.00597087 -22.997 0.0002 (8) Number of replicates = 8 Sum of Mean Source DF Squares Square F Value Prob>F Model 1 4.81536 4.81536 753.145 0.0001 Error 3 0.01918 0.00639 C Total 4 4.83454 Root MSE 0.07996 R-square 0.9960 Dep Mean 3.31041 Adj R-sq 0.9947 C.V. 2.41543 Parameter Standard T for H0: Variable DF Estimate Error Parametemo Prob > |T| INTERCEP 1 14.465820 0.40805661 35.451 0.0001 MEAN 1 -0.132953 0.00484460 -27.443 0.0001 Table A-5. Regression analysis for corn vigor tests with 50 seeds per replicate_ (1) Number of replicates = 1 Sum of Mean Source DF Squares Square F Value Prob>F Model 1 69.01359 69.01359 125.276 0.0001 Error 7 3.85625 0.55089 C Total 8 72.86984 Root MSE 0.74222 R-square 0.9471 Dep Mean 5.18249 Adj R-sq 0.9395 C.V. 14.32172 Parameter Standard T for H0: Variable DF Estimate Error Parameter=0 Prob > |T| INTERCEP 1 29.110613 2.15210624 13.527 0.0001 MEAN 1 -0.271870 0.02429001 -11.193 0.0001 105 (2) Number of replicates = 2 Sum of Mean Source DF Squares Square F Value Prob>F Model 1 73.79827 73.79827 192.801 0.0001 Error 7 2.67938 0.38277 CTotal 8 76.47765 Root MSE 0.61868 R-square 0.9650 Dep Mean 4.28103 Adj R—sq 0.9600 C.V. 14.45172 Parameter Standard Tfor H0: Variable DF Estimate Error Parameter=0 Prob > |T| INTERCEP 1 28.386096 1.74822027 16.237 0.0001 MEAN 1 -0.274000 0.01973310 -13.885 0.0001 (3) Number of replicates = 3 Sum of Mean Source DF Squares Square F Value Prob>F Model 1 71.20864 71.20864 188.097 0.0001 Error 7 2.65001 0.37857 CTotal 8 73.85865 Root MSE 0.61528 R-square 0.9641 Dep Mean 3.75437 Adj R-sq 0.9590 C.V. 16.38847 Parameter Standard Tfor H0: Variable DF Estimate Error Parameter=0 Prob > |T| INTERCEP 1 27.675578 1.75619879 15.759 0.0001 MEAN 1 0271684 0.01980948 -13.715 0.0001 (4) Number of replicates = 4 Sum of Mean Source DF Squares Square FValue Prob>F Model 1 70.30120 70.30120 152.355 0.0001 Error 7 3.23001 0.46143 CTotal 8 73.53122 Root MSE 0.67929 R-square 0.9561 Dep Mean 3.46292 Adj R-sq 0.9498 C.V. 19.61602 Parameter Standard Tfor H0: Variable DF Estimate Error Parameter=0 Prob > |T| INTERCEP 1 27.383161 1.95111028 14.035 0.0001 MEAN 1 -0.271494 0.02199539 -12.343 0.0001 106 Table A-6. Regression analysis for com vigor tests with 100 seeds per replicate. (1) Number of replicates = 1 Sum of Mean Source DF Squares Square FValue Prob>F Model 1 17.87761 17.87761 53.233 0.0001 Error 12 4.03004 0.33584 C Total 13 21.90765 Root MSE 0.57951 R-square 0.8160 Dep Mean 4.14165 Adj R-sq 0.8007 C.V. 13.99236 Parameter Standard Tfor H0: . Variable DF Estimate Error Parameter=0 Prob > |T| INTERCEP 1 13.465483 1.28727235 10.460 0.0001 MEAN 1 -0.107215 0.01469485 -7.296 0.0001 (2) Number of replicates = 2 Sum of Mean Source DF Squares Square F Value Prob>F Model 1 14.89389 14.89389 44.165 0.0001 Error 12 4.04677 0.33723 C Total 13 18.94066 Root MSE 0.58072 R-square 0.7863 Dep Mean 3.79510 Adj R-sq 0.7685 C.V. 15.30175 Parameter Standard Tfor H0: Variable DF Estimate Error Parameter-'0 Prob > |T| INTERCEP 1 12.273223 1.28513879 9.550 0.0001 MEAN 1 -0.097476 0.01466750 -6.646 0.0001 (3) Number of replicates = 3 Sum of Mean Source DF Squares Square F Value Prob>F Model 1 18.16749 18.16749 49.029 0.0001 Error 12 4.44660 0.37055 C Total 13 22.61409 Root MSE 0.60873 R-square 0.8034 Dep Mean 3.64113 Adj R-sq 0.7870 C.V. 16.71809 107 Parameter Standard T for H0: Variable DF Estimate Error Parameter=0 Prob > |T| lNTERCEP 1 12.957105 1.34037601 9.667 0.0001 MEAN 1 -0.107094 0.01529472 -7.002 0.0001 (4) Number of replicates = 4 Sum of Mean Source DF Squares Square F Value Prob>F Model 1 17.44496 17.44496 41.670 0.0001 Error 12 5.02377 0.41865 C Total 13 22.46873 Root MSE 0.64703 R-square 0.7764 Dep Mean 3.57527 Adj R-sq 0.7578 C.V. 18.09735 Parameter Standard T for H0: Variable DF Estimate Error Parametemo Prob > |T| INTERCEP 1 12.768073 1.43454946 8.900 0.0001 MEAN 1 0105663 0.01636860 -6.455 0.0001 Table A-7. Regression analysis for soybean vigor tests with 50 seeds per replicate. (1) Number of replicates = 1 Sum of Mean Source DF Squares Square F Value Prob>F Model 1 4.10031 4.10031 0.778 0.3965 Error 1 1 57.95594 5.26872 C Total 12 62.05625 Root MSE 2.29537 R-square 0.0661 Dep Mean 8.63806 Adj R-sq -0.0188 C.V. 26.57275 Parameter Standard T for H0: Variable DF Estimate Error ParametemO Prob > |T| INTERCEP 1 10.894987 2.63638249 4.133 0.0017 MEAN 1 -0.030122 0.03414554 -0.882 0.3965 (2) Number of replicates = 2 Sum of Mean Source DF Squares Square F Value Prob>F Model 1 5.36635 5.36635 1.436 0.2560 Error 1 1 41.10408 3.73673 C Total 12 46.47043 108 Root MSE 1.93306 R-square 0.1155 Dep Mean 7.72139 Adj R-sq 0.0351 C.V. 25.03517 Parameter Standard T for H0: Variable DF Estimate Error Parameter=0 Prob > |T| INTERCEP 1 10.313233 2.22825376 4.628 0.0007 MEAN 1 -0.034560 0.02883868 -1.198 0.2560 (3) Number of replicates = 3 Sum of Mean Source DF Squares Square F Value Prob>F Model 1 2.98246 2.98246 0.719 0.4147 Error 1 1 45.65890 4.15081 C Total 12 48.64136 Root MSE 2.03735 R-square 0.0613 Dep Mean 7.45758 Adj R-sq -0.0240 C.V. 27.31924 Parameter Standard T for H0: Variable DF Estimate Error Parameter=0 Prob > |T| INTERCEP 1 9.379082 2.33620272 4.015 0.0020 MEAN 1 0025591 0.03018994 -0.848 0.4147 (4) Number of replicates = 4 Sum of Mean Source DF Squares Square F Value Prob>F Model 1 5.72736 5.72736 1.336 0.2722 Error 1 1 47.16021 4.28729 C Total 12 52.88757 Root MSE 2.07058 R-square 0.1083 Dep Mean 7.36010 Adj R-sq 0.0272 C.V. 28.13245 Parameter Standard Tfor H0: Variable DF Estimate Error Parameter=0 Prob > |T| INTERCEP 1 10.037556 2.38664227 4.206 0.0015 MEAN 1 -0.035619 0.03081700 -1.156 0.2722 109 Table A-8. Regression analysis for soybean vigor tests with 100 seeds per replicate. (1) Number of replicates = 1 Sum of Mean Source DF Squares Square F Value Prob>F Model 1 17.40599 17.40599 13.307 0.0045 Error 10 13.08045 1.30804 C Total 11 30.48644 Root MSE 1.14370 R-square 0.5709 Dep Mean 5.28506 Adj R-sq 0.5280 C.V. 21.64019 Parameter Standard T for H0: Variable DF Estimate Error Parameter=0 Prob > |T| INTERCEP 1 32.850054 7.56369316 4.343 0.0015 MEAN 1 0334168 0.09160667 -3.648 0.0045 (2) Number of replicates = 2 Sum of Mean Source DF Squares Square FValue Prob>F Model 1 16.85334 16.85334 9.226 0.0125 Error 10 18.26751 1.82675 C Total 11 35.12085 Root MSE 1.35157 R-square 0.4799 Dep Mean 4.56606 Adj R-sq 0.4279 C.V. 29.60042 Parameter Standard T for H0: Variable DF Estimate Error ParameteFO Prob > |T| INTERCEP 1 31.235613 8.78902686 3.554 0.0052 MEAN 1 0323516 0.10651046 -3.037 0.0125 (3) Number of replicates = 3 Sum of Mean Source DF Squares Square F Value Prob>F Model 1 16.18786 16.18786 6.968 0.0247 Error 10 23.23094 2.32309 CTotal 11 39.41879 Root MSE 1.52417 R-square 0.4107 Dep Mean 4.36607 Adj R-sq 0.3517 C.V. 34.90946 110 Parameter Standard Tfor H0: Variable DF Estimate Error Parametemo Prob > |T| INTERCEP 1 30.783044 10.01708030 3.073 0.0118 MEAN 1 -0.320411 0.12137984 -2.640 0.0247 (4) Number of replicates = 4 Sum of Mean Source DF Squares Square F Value Prob>F Model 1 17.21996 17.21996 7.156 0.0233 Error 10 24.06415 2.40641 CTotal 11 41.28411 Root MSE 1.55126 R-square 0.4171 Dep Mean 4.29162 Adj R-sq 0.3588 c.v. 36.14633 Parameter Standard TforHO: Variable DF Estimate Error Parameter=0 Prob > |T| INTERCEP 1 31.337402 10.12032127 3.096 0.0113 MEAN 1 -0.328178 0.12268125 -2.675 0.0233 111 APPENDIX C SAS CODE FOR MAJOR STATISTICAL PROCEDURES 1. To generate data from original data sheet provided by AOSA/SCST. data new; set raw ; array a{4} abnl-abn4; array d{4} dedl-ded4; do rep = l to reps; abnorm = a{rep}; dead = d{rep}; /* Use "0" to replace "." values. */ if a{rep} =. then a{rep} =0; if d{rep} =. then d{rep} =0; germten = 100-a{rep}-d{rep}; output; end; run; data selected; set new; if germten < 100; run; proc sort data=selected; by lotid labid; run; data selec; set selected; by lotid labid; if firstJabid then nn= 1; else nn+1; if last.labid and (nn=4) then output; run; 2. Use Miles (1963) method to eliminate outliers which are four standard deviations away from the seed lot mean /* Following procedures are created for statistical analysis of both germination and vigor test results */ proc sort data=import1; by lotid labid ; run; 112 proc means data=importl; var germten; by lotid labid ; output out=0ne mean=germ; I'll“; proc univariate data=one; var germ; output out=med mean=mean; by lotid ; run; data selec; merge one med; d=germ~mean; sigma=sqrt(mean*(100—mean)/400); l' for 50-seed four replicate test, 400 is replaced with 200 ‘/ ratio=dlsigma; by lotid; run; proc sort data=selec; by lotid; run; data three; set selec; if rati0= <4 and ratio: > -4; by lotid ; run; data outliers; set selec; if ratio > 4 or ratio <-4; by lotid; title 'Outliers from loo-seed corn vigor tests in 1993-96' ;run; data two ; merge three importl; if ratio ne . then output; by lotid labid;run; proc sort data=tw0; by lotid ;run; 3. Generate random data to construct subset data of different sizes of replicate /‘ To generate standard deviation for each subset data *I /* -----For more than one rcplicate---------*/ %macro samplcsi(num,r); 113 data simu; set two; ran=ranuni(&num); by lotid ; run; proc sort data=simu; by lotid labid ran;run; data simu; set simu; by lotid labid ; if first.labid then cnt= 1; else cnt+1; run; %macro new1(repl,co); data subset; set simu(where=(cnt < &repl)); by lotid ; run; proc mcans data=subset; var germten; by lotid labid ; output out=one mean = germ; run; proc univariate data=one; var germ; output out=med&repl&oo mean=mean std=std; by lotid ; run; data med&repl&co; set med&repl&oo; n = &repI-l ; t=&oo; run; %mend newl; %newl(5,&r) %newl(4,&r) %newl(3,&r) data medd&r; set med5&r med4&r me03&r; run; %mend samplesi; 114 %samplcsi(1234,01) %samplcsi(2234,02) %samplesi(3234,03) %samplesi(4234,04) %samplcsi(5234,05) %samplcsi(6234,06) %samplesi(7234,07) %samplesi(8234,08) %samplesi(9234,09) %samplesi(2345,10) %samplesi(1234,ll) %samplesi(223,12) %samplcsi(323,13) %samplesi(423,l4) %samplesi(523,15) %samplesi(623,16) %samplesi(723,l7) %samplesi(823,18) %samplesi(923,l9) %samplesi(2340,20) %samplesi(l4,21) %samplesi(24,22) %samplesi(34,23) %samplesi(44,24) %samplesi(54,25) %samplcsi(64,26) %samplcsi(74,27) %samplesi(84,28) %samplesi(94,29) %samplcsi(104,30) data final; set meddOl medd02 medd03 medd04 meddOS medd06 meddO7 medd08 meddO9 medle meddll medd12 meddl3 medd14 medd25 medd16 meddl7 medd18 meddl9 medd20 medd21 medd22 medd23 medd24 medd25 medd26 medd27 medd28 medd29 medd30; run; /* --~--- for one rep */ %macro onerep(num,r); data simu; set two; ran=ranuni(&num); by lotid; run; proc sort data=simu; by lotid labid ran; run; data simu; set simu; by lotid labid; if firstJabid then cnt= 1; else cnt+1; run; data subset; set simu(wbere=(cnt < 2)); by lotid; run; proc means data=subset; var germten; by lotid; output out=one&r mean= germ std=std; run; %mend onerep; %onerep(12,l) %onerep(13,2) %onerep(l4,3) %onerep(15,4) %onerep(16,5) %onerep( 17,6) %onerep(l8,7) %onerep(l9,8) %onerep(20,9) %onerep(234,10) 115 %onerep(235,l l) %onerep(236,12) %onerep(237,l3) %onerep(238,l4) %onerep(239,15) %onerep(232,l6) %onerep(231,17) %onerep(233,18) %onerep(240, 19) %onerep(24l,20) %onerep(512,21) %onerep(513,22) %onerep(514,23) %onerep(5134,24) %onerep(5121,25) %onerep(5123,26) %onerep(2234,27) %onerep(5424,28) %onerep(5554,29) %onerep(5234,30) data fina12; set onel one2 one3 one4 ones one6 one7 one8 one9 onelO onell one12 onel3 one14 one15 one16 onel7 one18 onel9 one20 oneZl one22 one23 one24 one25 one26 on827 one28 one29 one30; run; data out; set final fina12; run; /*========== fortheaveragesofSTD andMEANS =========*/ data new; set import; proc sort; by lotid n; run; proc mcens data=neww; var mcan; by lotid 11; output out=mean mcan=mean; run; proc means data=neww; var std; by lotid 11; output out=stand mcan=stand; run; data newww; merge mcen stand; by lotid n; proc print; run; data new; set new; proc sort; by n; proc print; run; proc reg; model stand=mcan; by n; . titlel 'The relationship between vigor levels and standard deviation'; 116 title2 'SO-swd (30 samples) vigor test on soybean without outliers in 1994—96'; run; 4. To calculate the variation among and within laboratories of seed counts. (The part to construct subset data of different replicate sizes was similar to that of germination and vigor tests, thus not given below) data new; set import; proc sort data=new; by lotid size labid ; run; proc univariate plot data= new ; var counts; by lotid size; output out=one mcan=means std=std; title 'Seed count data from 1998 referee without me adj. '; run; proc mixed data=new; class rep labid; model oounts=; random labid; make out=vl oovparms; by lotid size; run; data four; set one v1; proc print data=four; title 'Tcst variation from soybean seed count referee in 1998'; run; 117 5. Calculation of correlation coefficient among replications within individual laboratories data raw; set soySO; gt=(gl + g2+ g3 +g4)/400;run; data soyeSO; set raw; vb=50*(gt)*(l-gt); /* For lOO-swd test replace 50 with 100*/ vo=((gl-g2)**2+(gi-g3)**2+(gl-g4)**2+ (2283)”2 + (32847“? + (g3 '84)**2)/6; rho = l-(VO/(2*vb)); “111; data firsquar; set soye50 (where=(gt<0.25 or gt=0.25 )); if rho < (-gt)/(1—gt) then rho=(-gt)/(1-gt); run; data secoquar; set soye50 (where=(gt<0.5 and gt>0.25 or gt=0.5)); if rho < (5/6—(4/3)*gt—(l-gt)**2)/(gt*(l-gt)) then rho=(5/6-(4/3)*gt-(l-gt)**2)/(gt*(l-gt)); run; data thirquar; set soyc50 (where=(gt<0.75 and gt>0.5 or gt=0.75)); if rho <((3/4)*gt-0.5-gt**2)/gt*(l-gt) then rho=((3/4)*gt-0.5-gt**2)/gt*(l-gt); run; data fortquar; set soyeSO (where=(gt>0.75 or gt=1)); if rho <-(l-gt)/gt then rho=—(l-gt)/gt; run; data soyeeSO; set firsquar secoquar thirquar fortquar;run; /* Prepare a graph of the correlation coefficients against labid separately for each seediot */ proc plot data=soyee50; plot rho*labid/vref=0; run; /* Test the hypothesis that the average coefficients are not significantly different from 0. */ proc univariate data=soyee50; var rho; output out=mcan mcan=mean n=n signrank=signrank; 118 title 'Soybean vigor SO—seed test '; title2 'Use the lower bound equations by Dr. Gilliland'; run; /*By simulation of random binomial sampling, if z> = 1.65, accept Hn,otherwise accept Ho */ data simui; set mcan; z=(man-0)/(sqrt((2(4*100)**2)/((4*100-1)**2)(4-1))/(sqrt(n))); if z> = 1.65 then sign='*'; else sign= 'n’; proc print; run; /* Test that coefficients are as likely to be positive as they are to be negative*/ data si; set soyeeSO; if rho>0 then rhh= 'p';eise rhh= 'n'; proc freq data=si; tables rhh/testp=(0.5,0.5); run; 119