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Evaluation of Cluster Analysis for Comparing Treatment Means¹

Univariate cluster analysis of treatment means is considered as an alternative to the least significant difference for those experiments where painvise multiple comparisons are applicable. Although cluster analysis procedures produce distinct, non-overlapping groupings of the treatments, little previous study has been made of their statistical behavior. The objective of the present research was to examine statistical properties of four clustering algorithms in terms of their power and Type I and I11 error rates for several patterns of homogeneity among breatment means. The Scott-Knott (SK) divisive procc dure and three agglomerative procedures based on single linkage (SL), complete linkage (a), and unweighted pair group averages (UPG), respectively, were compared to the least significant difference (FLSD) when a preliminary F test of overall treatment effects is performed.

Results of simulation studies indicate that the overlapping nature of the groupings of treatments obtained with the FLSD provides considerable protection against Type I and Type III errors. Both types of errors occurred with higher frequencies for all four clustering algorithms than for the FLSD. Furthermore, comparisonwise Type I error rates for the FLSD are determined by the researcher's choice of significance level, while the rates for cluster analysis are dependent on both the significance level and the degree of precision of the experiment. Consequently, researchers should contemplate with caution any possible adoption of cluster analysis as a replacement for a pairwise multiple comparison procedure such as the FLSD.

Key Words: Least significant difference • Multiple comparisons • Scott-Knott procedure • Statistical analysis

² Former graduate research assistant (now graduate assistant in statistics, Ohio State Univ.), professor of biometry, and professor of biometry and soil fertility, Dep. of Agron., Univ. of Illinois.

Received for publication May 31, 1979.

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