Classical inferential test statistics for two-group comparisons, like the t-test, often face the problem of small effect size or borderline significance. Moreover, the issue is not so clear when we cannot reject the null.

Here I would like to discuss the following paper: Wetzels et al. How to quantify support for and against the null hypothesis: a flexible WinBUGS implementation of a default Bayesian t test, Wetzels R, Raaijmakers JG, Jakab E, Wagenmakers EJ. *Psychonomic Bulletin & Review* (2009) 16 (4): 752-60.

We propose a sampling-based Bayesian t test that allows researchers to quantify the statistical evidence in favor of the null hypothesis. This Savage-Dickey (SD) t test is inspired by the Jeffreys-Zellner-Siow (JZS) t test recently proposed by Rouder, Speckman, Sun, Morey, and Iverson (2009). The SD test retains the key concepts of the JZS test but is applicable to a wider range of statistical problems. The SD test allows researchers to test order restrictions and applies to two-sample situations in which the different groups do not share the same variance.

The paper from Rouder et al., Bayesian t tests for accepting and rejecting the null hypothesis, is also available as PDF.

Oups, it looks like this has yet to be written.

To my knowledge, no implementation of the SD test is available in R.

#### See Also

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High-dimensional data analysis in cancer research
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Permutation vs. bootstrap test of hypothesis
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Bayesian analysis with R
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Bayesian analysis with Python
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Multiple comparisons and p-value adjustment