Moderated t-test

Moderated t-test based on empirical Bayes techniques to improve statistical power

This packages provides an implementation of the moderated t-test, which utilizes an empirical Bayes method to shrink the sample variances towards a common value and augment the degrees of freedom for the individual variances, resulting in increased statistical power. It includes two functions: 'moderated_ttest' for one-sample or paired t-tests, and 'moderated_ttest2' for two-sample t-tests. For ease of use, these functions closely mirror the input and output structure of MATLAB's ttest and ttest2 functions and can be used interchangeably. The implementation is inspired from R's limma package and applies the techniques outlined in the Smyth (2004) paper.

Example Use:

% Load the example dataset
load('examgrades.mat');
x = grades(:, 1);
y = grades(:, 2);
% Perform the test
[h,p,ci,stats] = moderated_ttest2(x, y)

h = 0

p = 0.9867

ci = 2x1

-1.9438

1.9771

stats = struct with fields:

tstat: 0.0167

df: 238

sd: 7.7084

mean: 0.0167

sd_prior: 7.7084

df_prior: 0

When performing a single test, moderated t-test is equivalent to the standard t-test.

Perform tests for each row:

X = grades(:, 1:2);
Y = grades(:, 3:4);
% Compare results of first exam with 3rd and second with 4th
[h,p,ci,stats] = moderated_ttest2(X, Y, 'Dim', 2);

% Convert to table and display the first 3 results
T = struct2table(struct('Passed', h, 'PValue', p, 'CI', ci, ...
    'TStat', stats.tstat, 'DF', stats.df, 'SD', stats.sd));
disp(T(1:3, :));

Passed PValue CI TStat DF

______ _________ __________________ ________ ___

false 1 -8.5232 8.5232 0 360

false 0.90822 -9.0232 8.0232 -0.11537 360

false 0.17917 -2.6899 14.357 1.3459 360