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

Many books on statistical methods advocate a 'conditional decision rule' when comparing two independent group means. This rule states that the decision as to whether to use a 'pooled variance' test that assumes equality of variance or a 'separate variance' Welch t test that does not should be based on the outcome of a variance equality test. In this paper, we empirically examine the Type I error rate of the conditional decision rule using four variance equality tests and compare this error rate to the unconditional use of either of the t tests (i.e. irrespective of the outcome of a variance homogeneity test) as well as several resampling-based alternatives when sampling from 49 distributions varying in skewness and kurtosis. Several unconditional tests including the separate variance test performed as well as or better than the conditional decision rule across situations. These results extend and generalize the findings of previous researchers who have argued that the conditional decision rule should be abandoned.

Section: Resultssupporting

confidence: 90%

Further evaluating the conditional decision rule for comparing two independent means

Hayes¹,

Cai²

2007

“…In this case, μ gh should be subtracted from ɛ ij before multiplying by σ j . When dealing with trimmed means, the data generation can be referred to Luh and Guo (2000). Based on the size of the trimmed sample needed under the specific condition, the generated data were first tested to investigate the empirical Type I error (setting d = d t =0) of the corresponding Welch's t and Yuen's t w , respectively.…”

Section: Simulation Design and Resultsmentioning

confidence: 99%

“…Her simulation results showed that her test performed better than Welch's (1938) approximate test. Luh and Guo (2000) and Guo and Luh (2000) extended Yuen's method in conjunction with Johnson (1978) or Hall's (1992) transformation to deal with heterogeneity and non‐normality. Although trimmed mean methods are becoming popular, and statistical packages such as SAS have included them in their subroutines, the gaps in the availability of sample size determination procedures are most notable in robust statistics (Adcock, 1997).…”

Section: Introductionmentioning

confidence: 99%

Approximate sample size formulas for the two‐sample trimmed mean test with unequal variances

Luh

Guo²

2007

Self Cite

Yuen's two-sample trimmed mean test statistic is one of the most robust methods to apply when variances are heterogeneous. The present study develops formulas for the sample size required for the test. The formulas are applicable for the cases of unequal variances, non-normality and unequal sample sizes. Given the specified alpha and the power (1-beta), the minimum sample size needed by the proposed formulas under various conditions is less than is given by the conventional formulas. Moreover, given a specified size of sample calculated by the proposed formulas, simulation results show that Yuen's test can achieve statistical power which is generally superior to that of the approximate t test. A numerical example is provided.

“…Moreover, trimmed means may provide a relatively small standard error (Staudte & Sheather, 1990; Wilcox, 2004). Luh and Guo (2000) and Guo and Luh (2000) extended Yuen's (1974) trimmed t test in conjunction with Johnson's (1978) or Hall's (1992) transformation to deal with severe heterogeneity as well as asymmetry. Luh, Olejnik, and Guo (2009) have already developed sample size formulas for the one‐ and two‐sample trimmed mean tests with homogeneous variances.…”

Section: Introductionmentioning

confidence: 99%

Optimum sample size allocation to minimize cost or maximize power for the two‐sample trimmed mean test

Guo¹,

Luh²

2009

Self Cite

When planning a study, sample size determination is one of the most important tasks facing the researcher. The size will depend on the purpose of the study, the cost limitations, and the nature of the data. By specifying the standard deviation ratio and/or the sample size ratio, the present study considers the problem of heterogeneous variances and non-normality for Yuen's two-group test and develops sample size formulas to minimize the total cost or maximize the power of the test. For a given power, the sample size allocation ratio can be manipulated so that the proposed formulas can minimize the total cost, the total sample size, or the sum of total sample size and total cost. On the other hand, for a given total cost, the optimum sample size allocation ratio can maximize the statistical power of the test. After the sample size is determined, the present simulation applies Yuen's test to the sample generated, and then the procedure is validated in terms of Type I errors and power. Simulation results show that the proposed formulas can control Type I errors and achieve the desired power under the various conditions specified. Finally, the implications for determining sample sizes in experimental studies and future research are discussed.