Choosing the best pairwise comparisons of means from non-normal populations, with unequal variances, but equal sample sizes

2010 ◽  
Vol 80 (6) ◽  
pp. 595-608 ◽  
Author(s):  
Philip H. Ramsey ◽  
Patricia P. Ramsey ◽  
Kyrstle Barrera
Keyword(s):  
Pairwise Comparisons ◽  
Sample Sizes ◽  
Unequal Variances ◽  
Normal Populations

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

Exact Type 1 Error Rates for Robustness of Student's t Test with Unequal Variances

1980 ◽  
Vol 5 (4) ◽  
pp. 337-349 ◽  
Author(s):  
Philip H. Ramsey
Keyword(s):  
Type I Error ◽  
Error Rates ◽  
T Test ◽  
Type I ◽  
Sample Sizes ◽  
Unequal Variances ◽  
Normal Populations ◽  
Type 1 Error ◽  
Student’S T ◽  
Equal Population

It is noted that disagreements have arisen in the literature about the robustness of the t test in normal populations with unequal variances. Hsu's procedure is applied to determine exact Type I error rates for t. Employing fairly liberal but objective standards for assessing robustness, it is shown that the t test is not always robust to the assumption of equal population variances even when sample sizes are equal. Several guidelines are suggested including the point that to apply t at α = .05 without regard for unequal variances would require equal sample sizes of at least 15 by one of the standards considered. In many cases, especially those with unequal N's, an alternative such as Welch's procedure is recommended.

Estimation of the Common Mean of Two Normal Populations Using Two Stage Sampling

1998 ◽  
Vol 48 (1-2) ◽  
pp. 73-82
Author(s):  
Moloy De ◽  
Jyotirmoy Sarkar
Keyword(s):  
Sampling Scheme ◽  
Two Stage ◽  
Unequal Variances ◽  
Common Mean ◽  
Normal Populations ◽  
The Common

We exhibit the superiority of the Graybill- Deal estimator for estimating the common mean of two univariate normal populations with unequal variances, under a two stage sampling scheme. Some properties of the two-stage Graybill-Deal estimator are discussed.

On a Class of Admissible Estimators of the Common Mean of Two Univariate Normal Populations

1995 ◽  
Vol 45 (1-2) ◽  
pp. 103-110
Author(s):  
Moloy De
Keyword(s):  
Two Stage ◽  
Unequal Variances ◽  
Common Mean ◽  
Normal Populations ◽  
The Common

The purpose of this article is to extend a result of Sinha and Mouqadem ( Commun. Stal. Theo. Meth. 11, 1982, 1603-1614), and present a class of admissible estimators of the common mean of two univariate normal populations with unknown unequal variances. An extension of tbis result in the case of two-stage procedures is also briefly discussed.

Sample sizes for comparing means of two multivariate normal populations

1987 ◽  
Vol 16 (4) ◽  
pp. 1207-1218 ◽  
Author(s):  
Paul Speckman ◽  
Sharon Anderson ◽  
John Hewett
Keyword(s):  
Multivariate Normal ◽  
Sample Sizes ◽  
Normal Populations

Type I Error Rates for Welch’s Test and James’s Second-Order Test Under Nonnormality and Inequality of Variance When There Are Two Groups

1994 ◽  
Vol 19 (3) ◽  
pp. 275-291 ◽  
Author(s):  
James Algina ◽  
T. C. Oshima ◽  
Wen-Ying Lin
Keyword(s):  
Degrees Of Freedom ◽  
Type I Error ◽  
Total Sample ◽  
Error Rates ◽  
Second Order ◽  
T Test ◽  
Type I ◽  
Sample Sizes ◽  
Unequal Variances ◽  
Type I Error Rates

Type I error rates were estimated for three tests that compare means by using data from two independent samples: the independent samples t test, Welch’s approximate degrees of freedom test, and James’s second-order test. Type I error rates were estimated for skewed distributions, equal and unequal variances, equal and unequal sample sizes, and a range of total sample sizes. Welch’s test and James’s test have very similar Type I error rates and tend to control the Type I error rate as well or better than the independent samples t test does. The results provide guidance about the total sample sizes required for controlling Type I error rates.

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