Statistical Recipes in Python

Descriptive Statistics

1. Arithmetic mean
2. Geometric mean
3. Harmonic mean
4. Maximum
5. Minimum
6. Moment
7. Kurtosis
8. Sample standard deviation
9. Sample standard error
10. Sample variance
11. Skew

Normality Tests

Examine whether a set of values are normally distributed.

1. Kurtosis test
2. Jarque-Bera test: normality test for large sample size
3. Shapiro-Wilk test for normality
4. Skew test

Equal Variance Tests

Examine whether two or more sets of values have the same variance (or standard deviation).

1. Bartlett's test
2. Fligner-Killeen test
3. Levene's test

Parametric and Nonparametric Correlations

Examine the trend of 2 sets of values.

1. Kendall's tau: correlation measure for ordinal data
2. Pearson's correlation coefficient: correlation measure for normally distributed data
3. Point biserial correlation coefficient: correlation measure between a binary variable and a continuous variable
4. Somer's D: asymmetric measure of ordinal association
5. Spearman's rank correlation coefficient: correlation measure for ranked data

Parametric Tests

1. Alexander Govern test
2. ANOVA - One-way
3. t-test - 2-samples (independent samples) assuming equal variance
4. t-test - 2-samples (independent samples) assuming unequal variance
5. t-test - paired (dependent samples)

Nonparametric Tests

1. Brunner-Munzel test
2. Chi-Square test
3. Kruskal-Wallis H-test
4. Mann-Whitney U test
5. Wilcoxon rank-sum test
6. Wilcoxon signed-rank test