Multiple comparison inference is simultaneous inference ona comparison of the treatment means. The focus of this research was to develop simultaneous confidence interval methods for different types of multiple comparison inference when the equality of variances can not be assumed and when prior knowledge of the ratios of variance is available.
Under the usual normality and equal variance assumptions,
Dunnet's (1955) method provided the simultaneous inference on the difference between each new treatment mean and the control mean, which is useful for estimating the minimum effective dose (MED) and
the maximum safe dose (MSD) in does-response studies. In practice, however, homogeneity of variances is seldom satisfied. In this research, an exact method for multiple comparisons with a control
was developed when prior knowledge of the ratios of variance among treatments is available but without equal variance assumption. An example was considered and a simulation study on error rate was conducted. The results indicated that Dunnet's method has inflated error rate and may lead to erroneous inference when the equal variance assumption is not satisfied. In addition, robustness of the exact method was also examined through a simulation study.
Tamhane and Logan (2003) proposed a simultaneous confidence interval method for identifying the MED and MSD, while assuming equal variance. By the same motivation, a method was proposed for
identifying the doses which are both effective and safe when the variances are different among treatments and the ratios of variance are known. We suggested a simulation based approach to estimate the critical values. The power of the approach was estimated using a simulation study.
In addition, all-pairwise comparisons are of interest in many circumstances. Under the unbalanced design, the Tukey-Kramer method provided a set of
conservative simultaneous confidence intervals for all-pairwise differences assuming equal variances and normal distribution. When the variances are different among treatments and previous knowledge of the ratios of variance is available, we proposed an approximate
approach which provides simultaneous inference on all-pairwise differences. A simulation study was conducted to evaluate the error rate of the Tukey-Kramer method and the proposed method. The results
showed that the error rates of the Tukey-Kramer method are excessive and much larger than the nominal level when the equal variance assumption is invalid. The error rates of the proposed approach were all within the normal level.
Similarly, Hsu's (1984) multiple comparisons with the best (MCB) is a good choice when it is of interest to compare each treatment with the
best of the other treatments. We extended Hsu's constrained MCB to the unequal variance case and assumed known ratios of variance in this dissertation.
When there is no information on the ratios of variances and the equality of variances can not be assumed, we proposed some approximate approaches for difference types of multiple comparison procedures in the last part of this dissertation.