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Approximate sample size formula for testing group mean differences when variances are unequal in one-way anova.
| Content Provider | CiteSeerX |
|---|---|
| Author | Guo, Jiin-Huarng Luh, Wei-Ming |
| Abstract | This paper is published in Educational and Psychological Measurement (Impact factor 0.831, ranked 19 out of 38 Educational Psychology Journals in 2007 JCR). The one-way fixed-effect ANOVA is one of the most common statistical methods used in scientific research. Because of the adverse consequences of insufficient sample size, a more practical sample size calculation is worth developing in heterogeneous ANOVA. Some researchers have developed algorithms and computer programs for sample size determination by specifying a lower bound for the difference between the maximum and the minimum effects to be tested (Schwertman, 1987). However, the approximate test, Welch’s F test (1951), with the degrees of freedom estimated from the sample variances, has been used widely and is increasingly recognized as the most practical solution to the Behrens-Fisher problem. Therefore, the present study proposes a sample size determination for Welch’s F test when unequal variances are expected. Given a certain maximum deviation in population means and using the quantile of F and t distributions, there is no need to specify a non-centrality parameter, and it is easy to estimate the approximate sample size needed for heterogeneous one-way ANOVA. For the comparison of the mean differences of two independent groups with heterogeneous variances, Mace (1974, p. 81-84) already developed formulas by using Welch’s t (1938) test for the sample size needed. It should be noted that the optimal sample sizes roughly satisfy the condition of n1/n2=σ1/σ2 (Lee, 1992). As demonstrated by Schwertman (1987), the largest mean difference can be tested as where ∆=μmax-μmin, and σ2 is the common variance. Then the sample size needed can be written as |
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| Access Restriction | Open |
| Subject Keyword | Group Mean Difference One-way Anova Approximate Sample Size Formula Sample Size Sample Size Determination Mean Difference Non-centrality Parameter Insufficient Sample Size Welch Test Impact Factor Computer Program Sample Variance Approximate Sample Size Heterogeneous One-way Anova Approximate Test Practical Solution Max Min N1 N2 Adverse Consequence Educational Psychology Journal Common Statistical Method One-way Fixed-effect Anova Certain Maximum Deviation Practical Sample Size Calculation Common Variance Heterogeneous Variance Behrens-fisher Problem Population Mean Minimum Effect Present Study Scientific Research Heterogeneous Anova Psychological Measurement Optimal Sample Unequal Variance Independent Group |
| Content Type | Text |
| Resource Type | Article |
