chi2_test_BFF

chi2_test_BFF constructs BFFs based on the t test. BFFs depend on hyperparameters r and tau^2 which determine the shape and scale of the prior distributions which define the alternative hypotheses.
By setting r &gt; 1, we use higher-order moments for replicated studies. Fractional moments are set with r &gt; 1 and r not an integer.
All results are on the log scale.

Bayes factors represent the ratio of probabilities assigned to data by competing scientific hypotheses. However, one drawback of Bayes factors is their dependence on prior specifications that define null and alternative hypotheses. Additionally, there are challenges in their computation. To address these issues, we define Bayes factor functions (BFFs) directly from common test statistics. BFFs express Bayes factors as a function of the prior densities used to define the alternative hypotheses. These prior densities are centered on standardized effects, which serve as indices for the BFF. Therefore, BFFs offer a summary of evidence in favor of alternative hypotheses that correspond to a range of scientifically interesting effect sizes. Such summaries remove the need for arbitrary thresholds to determine "statistical significance." BFFs are available in closed form and can be easily computed from z, t, chi-squared, and F statistics. They depend on hyperparameters "r" and "tau^2", which determine the shape and scale of the prior distributions defining the alternative hypotheses. Plots of BFFs versus effect size provide informative summaries of hypothesis tests that can be easily aggregated across studies.

Rachael Shudde

Bayes Factor Functions

František Bartoš

Saptati Datta

Riana Guha

Sandy Pramanik

Valen Johnson

chi2_test_BFF function

<dl><dt>chi2_stat</dt>
<dd>chi-square statistic</dd>
<dt>n</dt>
<dd>sample size (if one sample test)</dd>
<dt>df</dt>
<dd>degrees of freedom</dd>
<dt>LRT</dt>
<dd>should LRT be performed? Default is FALSE</dd>
<dt>omega</dt>
<dd>standardized effect size. For the chi^2-test, this is often called Cohen's w (can be a single entry or a vector of values)</dd>
<dt>omega_sequence</dt>
<dd>sequence of standardized effect sizes. If no omega is provided, omega_sequence is set to be seq(0.01, 1, by = 0.01)</dd>
<dt>r</dt>
<dd>variable controlling dispersion of non-local priors. Default is 1. r must be &gt;= 1</dd></dl>

Arguments

chi2_test_BFF — chi2_test_BFF

<dl>

<dt>chi2_stat</dt>
<dd>chi-square statistic</dd>


<dt>n</dt>
<dd>sample size (if one sample test)</dd>


<dt>df</dt>
<dd>degrees of freedom</dd>


<dt>LRT</dt>
<dd>should LRT be performed? Default is FALSE</dd>


<dt>omega</dt>
<dd>standardized effect size. For the chi^2-test, this is often called Cohen's w (can be a single entry or a vector of values)</dd>


<dt>omega_sequence</dt>
<dd>sequence of standardized effect sizes. If no omega is provided, omega_sequence is set to be seq(0.01, 1, by = 0.01)</dd>


<dt>r</dt>
<dd>variable controlling dispersion of non-local priors. Default is 1. r must be &gt;= 1</dd>

</dl>

chi2_test_BFF: chi2_test_BFF

Description

Usage

Value

Arguments

Examples