Permutationtilastot

Permutationtilastot, also known as permutation tests or randomization tests, are a class of non-parametric statistical hypothesis tests. They are used to determine the significance of observed data by comparing it to a distribution of values that could arise by chance. Unlike traditional parametric tests that rely on assumptions about the underlying distribution of the data (e.g., normality), permutation tests are distribution-free.

The core idea behind permutation testing is to generate a null distribution by repeatedly permuting the observed data. Under the null hypothesis, the labels or group assignments of the data are considered exchangeable. Therefore, by shuffling these labels and recalculating the test statistic for each permutation, one can estimate the probability of observing a test statistic as extreme as, or more extreme than, the one calculated from the original, unpermuted data.

To perform a permutation test, one first calculates a test statistic of interest from the observed data. Then, the data points are randomly shuffled many times (typically thousands or tens of thousands). For each shuffled dataset, the same test statistic is recalculated. The collection of these recalculated test statistics forms the empirical null distribution. The p-value is then the proportion of permuted test statistics that are as extreme as or more extreme than the observed test statistic.

Permutation tests are particularly useful when sample sizes are small, when parametric assumptions are violated, or when the exact distribution of the test statistic under the null hypothesis is unknown. They can be applied to a wide range of statistical problems, including comparing means, medians, correlations, and for evaluating the performance of machine learning models. While computationally intensive, advances in computing power have made permutation tests a practical and powerful tool in statistical analysis.