TY - JOUR

T1 - Multiple comparisons in model I one-way ANOVA with unequal variances

AU - Tamhane, A.

PY - 1977

Y1 - 1977

N2 - A fixed effects one-way layout model of analysis of variance is considered where the variances are taken to be possibly unequal. Conservative single-stage procedures based on Banerjee’s method for the solution of the Behrens-Fisher problem are proposed for the following multiple comparisons problems: 1) all pairwise comparisons with a control population mean, and 2) all pairwise comparisons and all linear contrasts among the means. Since these procedures are likely to be very conservative in practice, approximate procedures based on Welch’s method for the solution of the Behrens-Fisher problem are suggested as alternatives. Monte Carlo studies indicate that the latter are much less conservative and hence may be better in practice. Both these sets of procedures need only the tables of the Student’s t-distribution for their application and are very simple to use. Exact two-stage procedures are proposed for the following multiple comparisons problems: 1) all pairwise comparisons and all linear contrasts among the means, and 2) all linear combinations of the means.

AB - A fixed effects one-way layout model of analysis of variance is considered where the variances are taken to be possibly unequal. Conservative single-stage procedures based on Banerjee’s method for the solution of the Behrens-Fisher problem are proposed for the following multiple comparisons problems: 1) all pairwise comparisons with a control population mean, and 2) all pairwise comparisons and all linear contrasts among the means. Since these procedures are likely to be very conservative in practice, approximate procedures based on Welch’s method for the solution of the Behrens-Fisher problem are suggested as alternatives. Monte Carlo studies indicate that the latter are much less conservative and hence may be better in practice. Both these sets of procedures need only the tables of the Student’s t-distribution for their application and are very simple to use. Exact two-stage procedures are proposed for the following multiple comparisons problems: 1) all pairwise comparisons and all linear contrasts among the means, and 2) all linear combinations of the means.

U2 - 10.1080/03610927708827466

DO - 10.1080/03610927708827466

M3 - Article

VL - 6

SP - 15

EP - 32

JO - Communications in Statistics - Theory and Methods

JF - Communications in Statistics - Theory and Methods

SN - 0361-0926

ER -