scholarly journals The variable-criteria sequential stopping rule: Generality to unequal sample sizes, unequal variances, or to large ANOVAs

2010 ◽  
Vol 42 (4) ◽  
pp. 918-929 ◽  
Author(s):  
Douglas A. Fitts
Keyword(s):  
Stopping Rule ◽  
Sample Sizes ◽  
Unequal Variances ◽  
Unequal Sample Sizes

Power of a Test That is Robust against Variance Heterogeneity

1995 ◽  
Vol 77 (1) ◽  
pp. 155-159 ◽  
Author(s):  
John E. Overall ◽  
Robert S. Atlas ◽  
Janet M. Gibson
Keyword(s):  
Type I Error ◽  
T Test ◽  
Type I ◽  
Sample Sizes ◽  
Error Protection ◽  
Unequal Variances ◽  
Main Effect ◽  
Test Of Significance ◽  
The Difference ◽  
Unequal Sample Sizes

Welch (1947) proposed an adjusted t test that can be used to correct the serious bias in Type I error protection that is otherwise present when both sample sizes and variances are unequal. The implications of the Welch adjustment for power of tests for the difference between two treatments across k levels of a concomitant factor are evaluated in this article for k × 2 designs with unequal sample sizes and unequal variances. Analyses confirm that, although Type I error is uniformly controlled, power of the Welch test of significance for the main effect of treatments remains rather seriously dependent on direction of the correlation between unequal variances and unequal sample sizes. Nevertheless, considering the fact that analysis of variance is not an acceptable option in such cases, the Welch t test appears to have an important role to play in the analysis of experimental data.

On Two-Stage Multiple Comparison Procedures When there are Unequal Sample Sizes in the First Stage

1984 ◽  
Vol 9 (3) ◽  
pp. 227-236 ◽  
Author(s):  
Rand R. Wilcox
Keyword(s):  
Type I Error ◽  
Practical Importance ◽  
Multiple Comparison ◽  
Type I ◽  
Sample Sizes ◽  
Two Stage ◽  
Unequal Variances ◽  
Type I Error Probability ◽  
Multiple Comparison Procedures ◽  
Unequal Sample Sizes

A problem of considerable practical importance when applying multiple comparison procedures is that unequal variances can seriously affect power and the probability of a Type I error. A related problem is getting a precise indication of how many observations are required so that the length of the confidence intervals will be reasonably short. Two-stage procedures have been proposed that give an exact solution to these problems, the first stage being a pilot study for the purpose of obtaining sample estimates of the variances. However, the critical values of these procedures are available only when there are equal sample sizes in the first stage. This paper suggests a method of evaluating the experimentwise Type I error probability when the first stage has unequal sample sizes.

Pairwise comparisons of means under realistic nonnormality, unequal variances, outliers and equal sample sizes

2011 ◽  
Vol 81 (2) ◽  
pp. 125-135 ◽  
Author(s):  
Philip H. Ramsey ◽  
Kyrstle Barrera ◽  
Pri Hachimine-Semprebom ◽  
Chang-Chia Liu
Keyword(s):  
Pairwise Comparisons ◽  
Sample Sizes ◽  
Unequal Variances

The fisher-yates exact test and unequal sample sizes

Psychometrika ◽  
1972 ◽  
Vol 37 (1) ◽  
pp. 103-106 ◽  
Author(s):  
Edgar M. Johnson
Keyword(s):  
Sample Sizes ◽  
Exact Test ◽  
Unequal Sample Sizes

Approximating the Probability of Selecting the Best Treatment With A Heteroscedastic Procedure When The First Stage Has Unequal Sample Sizes

1983 ◽  
Vol 8 (1) ◽  
pp. 45-58
Author(s):  
Rand R. Wilcox
Keyword(s):  
Sample Sizes ◽  
Two Stage ◽  
Normal Distributions ◽  
The One ◽  
Unequal Sample Sizes

Consider k normal distributions having means μ1,..., μk and variances σ21,..., σ2 k. Let μ[1]≥...≥ μ[ k] be the means written in ascending order. Dudewicz and Dalai proposed a two-stage procedure for selecting the population having the largest mean μ[ k] where the variances are assumed to be unknown and unequal. This paper considers an approximate but conservative solution for situations where unequal sample sizes are used in the first stage. The paper also considers how to estimate the actual probability of selecting the “best” treatment; that is, the one having mean μ[ k], after a heteroscedastic ANOVA has been performed.

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