A proposal to make the correlated t-test less conservative #1
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dpaetzel
requested changes
Jul 3, 2024
| rho = self.fraction_test | ||
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| sigma_2_hat = ((x - x_over) ** 2).sum() / (n - 1) | ||
| corrected_sigma_2_hat = (1 / n + rho / (1 - rho)) * sigma_2_hat # Corrected variance using Nadeau-Bengio's correction |
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Note that it makes the tests more conservative for variances < 1 (which would be quite common for losses or other error metrics, especially on standardized datasets) and only less conservative on higher values. However, from my testing of this PR, the results feel more 'correct' for the smaller values. In the sense that they align better with my visual interpretations of plotting the runs individually |
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In the correlated t-test, the squared variance should be used as the scale parameter, as the scipy.stats.t expects the standard deviation.
See: https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.t.html