# Statistics

## Parametric methods

#### One-sided t-test

• Difference between a sample mean and a (known) population mean).
• Difference between two paired samples (the population mean is 0 in this case).

#### Two-sided t-test

• Compare the difference between two sample means.
• i.e. test whether the two samples came from the same population.

## Non-parametric methods

#### Fisher's exact test

Calculates exact probability that two groups are different based on a contingency table.

#### Wilcoxon signed rank test

• Non-parametric equivalent of a one-sided t-test.
• Has more power than the sign test.

#### Kruskal-Wallis test

• Non-parametric equivalent of ANOVA.

## Correlations

#### Pearson correlation (R)

• Measures linear correlation between two variables.
• Square root of the R2 measure of the goodness of fit.

#### Spearman's correlation (ρ)

• Extension of Pearson's R to ordinal values.
• Captures the amount of variance that is explained by the other parameter.

#### Kendall rank correlation (τ)

• Correlation between two ordinal values.
• Based on the difference between the number of concordant and discordant pairs.
• Should be preferred over Spearman's ρ.

## Other tests

#### Dunnett test

Dunnett's test for comparing several treatments with a control.

## Distributions

Information retrieval

• Kolmogorov–Smirnov test — Nonparametric test of the equality of continuous, one-dimensional probability distributions that can be used to compare a sample with a reference probability distribution (one-sample K–S test), or to compare two samples (two-sample K–S test).
• Kullback–Leibler divergence — Measure of simmilarity between two probability distributions.
• Jensen–Shannon divergence — Symmetric version of the Kullback–Leibler divergence.