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A Probability Method for Comparing Varieties against Checks

USDA-ARS, Forage and Range Res. Lab., Utah State Univ., Logan, UT 84322-6300

Combining results of tests conducted over a period of years is desirable when the tests are conducted at a single location or across locations known not to exhibit large nonrandom, predictable genotype x location interactions. But when cumulative reports across tests are attempted, complications arise because of unbalanced structure. The objective of this work was to derive a method to compare varieties against checks using accumulated data in the usual situation, where varieties are changing over the years the accumulated tests are conducted. The resultant probability method is easy to use, easy to present in an extension publication, and easy to interpret by the extension audience. It tests the null hypothesis that a variety equals a check in performance and permits calculation of the probability that the variety equals a check in performance when the null hypothesis is rejected (type 1 error). Calculations are simplified data are coded and standardized for each test year. The method was used on an unbalanced data set yield of 23 varieties and 35 test years of alfalfa (Medicago sativa L.) grown near Ames, IA. Probability of one-tailed Type I erroranged from 0.47 to near 0.00 when data were coded on a test-year mean basis, and from 0.86 to near 0.00 when data were coded on the basis of the mean of ‘Saranac’ and ‘Vernal’. The probability method determined that no more than seven test years were necessary to evaluate these varieties.

Received for publication December 21, 1987.

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