Event Title

Generalized Two-Sample t-Test for Box-Cox Transformations of the Sample Means

Research Mentor(s)

Kimihiro Noguchi

Description

Many fields of experimental sciences are suffering from a widespread reproducibility issue of published results. It has been suggested that this issue stems primarily from an overreliance of hypothesis testing at a significance level of α=0.05 and comparison of p-values as the sole criteria for statistical significance. Replacing these oversimplified methods with more powerful and robust test statistics, combined with meaningful effect size measures and a more stringent significance level of α=0.005, may help to remedy this issue. In this study, we consider a generalization of Welch's two-sample t-test statistic based around transformations of the sample means as a potentially highly robust statistic. Particularly, we have considered Box-Cox type power transformations with the power parameter values k∈[-2,2]. We then performed a simulation study using the gamma, exponential, and chi-squared distributions with various sample sizes to investigate the robustness and power, using α=0.005 as our nominal significance level. We observed that choices of the power parameter values k∈[-1,0] typically provided the most robust statistic with either k=0 or k=-0.5 being the optimal choice considering the balance between power and robustness.

Document Type

Event

Start Date

May 2018

End Date

May 2018

Department

Mathematics

Rights

Copying of this document in whole or in part is allowable only for scholarly purposes. It is understood, however, that any copying or publication of this document for commercial purposes, or for financial gain, shall not be allowed without the author’s written permission.

Language

English

Format

application/pdf

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May 17th, 12:00 PM May 17th, 3:00 PM

Generalized Two-Sample t-Test for Box-Cox Transformations of the Sample Means

Many fields of experimental sciences are suffering from a widespread reproducibility issue of published results. It has been suggested that this issue stems primarily from an overreliance of hypothesis testing at a significance level of α=0.05 and comparison of p-values as the sole criteria for statistical significance. Replacing these oversimplified methods with more powerful and robust test statistics, combined with meaningful effect size measures and a more stringent significance level of α=0.005, may help to remedy this issue. In this study, we consider a generalization of Welch's two-sample t-test statistic based around transformations of the sample means as a potentially highly robust statistic. Particularly, we have considered Box-Cox type power transformations with the power parameter values k∈[-2,2]. We then performed a simulation study using the gamma, exponential, and chi-squared distributions with various sample sizes to investigate the robustness and power, using α=0.005 as our nominal significance level. We observed that choices of the power parameter values k∈[-1,0] typically provided the most robust statistic with either k=0 or k=-0.5 being the optimal choice considering the balance between power and robustness.