The 2012 ASHS Annual Conference

Statistical analysis of continuous data (such as root length or shoot dry weight) in response to classification treatment effects (such as different fertilizer formulations) often requires comparison of multiple treatment means. Several multiple-comparison procedures (MCPs) are available for testing the null hypotheses of no difference between treatment means (pairwise comparisons), while controlling the familywise error rate (FWE; also known as the experimentwise error rate or overall Type I error rate) by providing adjusted P values that account for the multiple, simultaneous comparisons. The Bonferroni adjustment and Tukey's (HSD) test are two commonly used MCPs. Fisher's LSD does not control the FWE, except in the case of Fisher's Protected LSD (when significance is indicated by an overall ANOVA F test and when comparing no more than three treatment means). Without an adjustment for multiple comparisons, the FWE increases as the number of treatments increases. While MCPs control the FWE, these tests can be conservative, with the actual alpha being less than the specified alpha. Newer MCP methods are now available in SAS/STAT procedures that are more powerful in detecting significant differences between treatment means, while still controlling the FWE. Simulation methods use the actual data to represent the data distribution, rather than relying on an assumed distribution (such as the normal distribution), and can provide additional power for running multiple mean comparisons. Stepdown methods can also be used along with MCPs to improve power. Stepdown procedures involve the ordering of the unadjusted P values from smallest to largest, reducing the family size (number of remaining comparisons) for each sequential P value, and adjusting of the P values accordingly. The power of stepdown procedures can be enhanced by taking into account certain logical constraints among the null hypotheses. The GLIMMIX procedure of SAS includes options under the LSMEANS statement to utilize simulation, stepdown, and logical constraint methods for multiple comparisons. Sample code to product Shaffer-Simulated grouping of treatment least-squared means in a simple case is as follows: PROC GLIMMIX DATA=dataset; CLASS trt; MODEL response = trt; LSMEANS trt / ALPHA=0.05 ADJUST=SIMULATE (SEED=1) STEPDOWN (TYPE=LOGICAL) LINES; RUN;