Discriminability Testing

If you have repeated measures from the same subject, and want to see if these are different than those from other subjects. Let's look at the mathematical formulations:

With \(D_x\) as the sample discriminability of \(x\), one sample test performs the following test:

\[\begin{split}H_0 &: D_x = D_0 \\ H_A &: D_x > D_0\end{split}\]

where \(D_0\) is the discriminability that would be observed by random chance.

This can also be formulated as a two-sample test. Let \(\hat{D}_x\) denote the sample discriminability of one approach, and \(\hat{D}_y\) denote the sample discriminability of another approach. Then,

\[\begin{split}H_0 &: D_x = D_y \\ H_A &: D_x > D_y\end{split}\]

Alternative tests can be done for \(D_x < D_y\) and \(D_x \neq D_y\).

Like all the other tests within hyppo, each method has a statistic and test method. The test method is the one that returns the test statistic and p-values, among other outputs, and is the one that is used most often in the examples, tutorials, etc. The p-value returned is calculated using a permutation test.

Discrimnability one-sample and Discrimnability two-sample are time series tests of independence. More details can be found in hyppo.discrim.DiscrimOneSample and hyppo.discrim.DiscrimTwoSample.

Each class has a is_dist parameter that indicates whether or not inputs are distance matrices. These distances must be Euclidean distance. Also, remove_isolates indicates whether or not to remove measurements with a single instance. Otherwise, these tests runs like any other test.

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Conditional Independence Testing