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

Algina, James; Oshima, T. C.; Lin, Wu

doi:10.2307/1165297

Cited by 30 publications

(22 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The Type I error rates of the omnibus Welch test became liberal when distributions were skewed, and the KruskalWallis test had liberal Type I error rates when variances were unequal (specifically when sample sizes and variances were negatively paired). These results concerning the liberal Type I error control of the Welch test with skewed and heteroscedastic data, and the Kruskal-Wallis procedure with unequal variances are consistent with previous reports (e.g., Algina, Oshima & Lin, 1994;Zimmerman & Zumbo, 1993a, 199b). With respect to power, there was very little difference between the procedures when the distributions were normal, although the power rates of the Welch test on ranks, the Brunner heteroscedastic nonparametric procedure, and the KruskalWallis procedure were generally the largest.…”

Section: Resultssupporting

confidence: 92%

Tests for Treatment Group Equality When Data are Nonnormal and Heteroscedastic

Cribbie

Wilcox

Bewell

et al. 2007

J. Mod. App. Stat. Meth.

View full text Add to dashboard Cite

Several tests for group mean equality have been suggested for analyzing nonnormal and heteroscedastic data. A Monte Carlo study compared the Welch tests on ranked data and heterogeneous, nonparametric statistics with previously recommended procedures. Type I error rates for the Welch tests on ranks and the heterogeneous, nonparametric statistics were well controlled with a slight power advantage for the Welch tests on ranks.

show abstract

Section: Resultssupporting

confidence: 92%

Tests for Treatment Group Equality When Data are Nonnormal and Heteroscedastic

Cribbie

Wilcox

Bewell

et al. 2007

J. Mod. App. Stat. Meth.

View full text Add to dashboard Cite

show abstract

“…The Welch (1938) approximate test is the most popular alternative to take care of heterogeneous variances. However, it can be liberal if the underlying distribution is non-normal (Algina et al, 1994). In addition, nonparametric methods are not suitable for the Behrens± Fisher problem (Fligner & Policello II, 1981;Pratt, 1964).…”

Section: Introductionmentioning

confidence: 99%

Johnson's transformation two-sample trimmed t and its bootstrap method for heterogeneity and non-normality

Luh

Guo²

2000

Journal of Applied Statistics

View full text Add to dashboard Cite

The present study investigates the performance of Johnson's transformation trimmed t statistic, Welch's t test, Yuen's trimmed t , Johnson's transformation untrimmed t test, and the corresponding bootstrap methods for the two-sample case with small/unequal sample sizes when the distribution is non-normal and variances are heterogeneous. The Monte Carlo simulation is conducted in two-sided as well as one-sided tests. When the variance is proportional to the sample size, Yuen's trimmed t is as good as Johnson's transformation trimmed t . However, when the variance is disproportional to the sample size, the bootstrap Yuen's trimmed t and the bootstrap Johnson's transformation trimmed t are recommended in one-sided tests. For two-sided tests, Johnson's transformation trimmed t is not only valid but also powerful in comparison to the bootstrap methods.

show abstract

“…A related issue is what effect nonnormal distributions will have on the Schuirmann and SchuirmannÁ Welch tests of equivalence. Although a full treatment of this topic is beyond the scope of this article, previous evidence has indicated that the modified Welch statistics have reasonable Type I error rates when distributions are slightly to moderately skewed and sample sizes and variances are unequal (e.g., Algina, Oshima, & Lin, 1994). However, when distributions become very asymmetric, Welch statistics no longer produce accurate Type I error rates when sample sizes and variances are unequal.…”

Section: Establishing An Equivalence Intervalmentioning

confidence: 96%

Evaluating clinical significance through equivalence testing: Extending the normative comparisons approach

Cribbie

Arpin-Cribbie

2009

Psychotherapy Research

View full text Add to dashboard Cite

The field of psychology, as with many other disciplines, has been increasingly interested in being able to measure the effectiveness of behavioral interventions. This trend has led to a number of different approaches for measuring clinical significance, each addressing a slightly different aspect of the clinical outcome. Recently, clinical psychologists (and clients) have supported the contention that one of the most important therapeutic questions is whether clients are functioning equivalently to normal controls following an intervention. To address this question, Kendall, Marrs-Garcia, Nath, and Sheldrick (1999) presented an approach to measuring clinical significance that utilizes tests of equivalence. The present study clarifies the nature of the hypotheses being conducted in measuring clinical significance with tests of equivalence and extends the approach by incorporating recent advances in equivalence testing. A revised approach for evaluating clinical significance via equivalence testing is proposed, and an empirical example demonstrating this approach is provided.

show abstract

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

Cited by 30 publications

References 0 publications

Tests for Treatment Group Equality When Data are Nonnormal and Heteroscedastic

Tests for Treatment Group Equality When Data are Nonnormal and Heteroscedastic

Johnson's transformation two-sample trimmed t and its bootstrap method for heterogeneity and non-normality

Evaluating clinical significance through equivalence testing: Extending the normative comparisons approach

Contact Info

Product

Resources

About