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Optimal Significance Levels for Application of the Least Significant Difference in Crop Performance Trials¹

Studies in the context of crop performance trials were undertaken to determine the effects of the frequencies of three types of statistical errors, the relative scriousness of these errors, and the frequency distribution of true differences between means in the application of the least significant difference (L.S.D.) for pairwise multiple comparisons. The results indicate that the optimal choice of significance level, , for the L.S.D. depends on the seriousness of type I and type III errors relative to type II errors. Arguments are presented supporting the use of significance levels in the range = 0.20 to 0.40 for the L.S.D. when making pairwise multiple comparisons between observed means from crop performance trials.

Key Words: Multiple comparisons • Statistical analysis • Statistical methods

² Professor of biometry, Dep. of Agronomy, Univ. of Illinois, Urbana-Champaign.

Received for publication November 23, 1974.