Statistical Analysis and Reporting

A Jupyter Book to help you find and run statistical tests in both R and Python.

Using your data, find the test you want to run (proportion, assumption, distribution, effect, etc.) and which language you want to run this test in. The code snippet provided with each test is just an example, Code recipes only get one so far. Please do not blindly throw code snippets at every problem you encounter. In reality, there’s sometimes more to be done.

Tests of Proportion Index

Samples	Response Categories	N	Test in R	Test in Python
1	2	≤200	Binomial Test	Binomial Test
1	≥2	≤200	Multinomial Test	Multinomial Test
1	≥2	>200	One-Sample Pearson Chi-Squared Test	One-Sample Pearson Chi-Squared Test
2	≥2	≤200	Fisher’s Exact Test	Fisher’s Exact Test
2	≥2	>200	G-Test	G-Test
2	≥2	>200	Two-Sample Pearson Chi-Squared Test	Two-Sample Pearson Chi-Squared Test

Tests of Assumption Index

Assumption	Context of Use	Test in R	Test in Python
Normality	t-test, ANOVA, LM, LMM	Shapiro-Wilk Test (on responses)	Shapiro-Wilk Test (on responses)
Normality	t-test, ANOVA, LM, LMM	Shapiro-Wilk Test (on residuals)	Shapiro-Wilk Test (on residuals)
Normality	t-test, ANOVA, LM, LMM	Anderson-Darling Test (on responses)	Anderson-Darling Test (on responses)
Normality	t-test, ANOVA, LM, LMM	Anderson-Darling Test (on residuals)	Anderson-Darling Test (on residuals)
Homoscedasticity (Homogeneity of Variance)	t-test, ANOVA, LM, LMM	Levene’s Test	Levene’s Test
Homoscedasticity (Homogeneity of Variance)	t-test, ANOVA, LM, LMM	Brown-Forsythe Test	Brown-Forsythe Test
Sphericity	Repeated Measures ANOVA	Mauchly’s Test of Sphericity	Mauchly’s Test of Sphericity

Tests of Distributions Index

Distribution	Parameterization	Test in R	Test in Python
Normal	mean (μ): mean, standard deviation (σ): sd	KS Test for Normal Distribution	KS Test for Normal Distribution
Lognormal	mean (μ): meanlog, standard deviation (σ): sdlog	KS Test for Lognormal Distribution	KS Test for Lognormal Distribution
Poisson	lambda (λ): lambda	KS Test for Poisson Distribution	KS Test for Poisson Distribution
Negative Binomial	theta (θ): theta, mu (μ): mu	KS Test for Negative Binomial Distribution	KS Test for Negative Binomial Distribution
Exponential	rate (λ): rate	KS Test for Exponential Distribution	KS Test for Exponential Distribution
Gamma	shape (α): shape, rate (β): rate	KS Test for Gamma Distribution	KS Test for Gamma Distribution

Parametric Tests of Effect Index

Samples	Levels	Between or Within Subjects	Test in R	Test in Python
1	2	Between	Independent-Samples t-test	Independent-Samples t-test
1	2	Within	Paired-Samples t-test	Paired-Samples t-test
1	≥2	Between	One-Way ANOVA	One-Way ANOVA
1	≥2	Within	One-Way Repeated Measures ANOVA	One-Way Repeated Measures ANOVA
≥2	≥2	Between	Factorial ANOVA	Factorial ANOVA
≥2	≥2	Between	Linear Model (LM)	Linear Model (LM)
≥2	≥2	Within	Factorial Repeated Measures ANOVA	Factorial Repeated Measures ANOVA
≥2	≥2	Within	Linear Mixed Model (LMM)	Linear Mixed Model (LMM)

Nonparametric Tests of Effect Index

Samples	Levels	Between or Within Subjects	Test in R	Test in Python
1	2	Between	Mann-Whitney U test	Mann-Whitney U test
1	2	Within	Wilcoxon Signed-Rank Test	Wilcoxon Signed-Rank Test
1	≥2	Between	Kruskal-Wallis Test	Kruskal-Wallis Test
1	≥2	Within	Friedman Test	Friedman Test
≥2	≥2	Between	Aligned Rank Transform for Between Subjects (ART)	Aligned Rank Transform for Between Subjects (ART)
≥2	≥2	Between	Generalized Linear Model (GLM)	Generalized Linear Model (GLM)
≥2	≥2	Within	Aligned Rank Transform for Within Subjects (ART)	Aligned Rank Transform for Within Subjects (ART)
≥2	≥2	Within	Generalized Linear Mixed Model (GLMM)	Generalized Linear Mixed Model (GLMM)

Generalized Linear (Mixed) Models Index

Distribution	Typical Uses	Between or Within Subjects	Test in R	Test in Python
Normal	Linear Regression: equivalent to linear (mixed) model (lm / lmm)	Between	GLM for Normal Distribution Data	GLM for Normal Distribution Data
Normal	Linear Regression: equivalent to linear (mixed) model (lm / lmm)	Within	GLM for Normal Distribution Data	GLM for Normal Distribution Data
Binomial	Logistic Regression: dichotomous responses (e.g. nominal responses with two categories)	Between	GLM for Binomial Distribution Data	GLM for Binomial Distribution Data
Binomial	Logistic Regression: dichotomous responses (e.g. nominal responses with two categories)	Within	GLM for Binomial Distribution Data	GLM for Binomial Distribution Data
Multinomial	Multinomial Logistic Regression: polytomous responses (i.e. nominal responses with more two categories)	Between	GLM for Multinomial Distribution Data	GLM for Multinomial Distribution Data
Multinomial	Multinomial Logistic Regression: polytomous responses (i.e. nominal responses with more two categories)	Within	GLM for Multinomial Distribution Data	GLM for Multinomial Distribution Data
Ordinal	Ordinal Logistic Regression: ordinal responses (i.e. Likert scales)	Between	GLM for Ordinal Distribution Data	GLM for Ordinal Distribution Data
Ordinal	Ordinal Logistic Regression: ordinal responses (i.e. Likert scales)	Within	GLM for Ordinal Distribution Data	GLM for Ordinal Distribution Data
Poisson	Poisson Regression: counts, rare events (e.g. gesture recognition errors, 3-pointers per quarter, number of “F” grades)	Between	GLM for Poisson Distribution Data	GLM for Poisson Distribution Data
Poisson	Poisson Regression: counts, rare events (e.g. gesture recognition errors, 3-pointers per quarter, number of “F” grades)	Within	GLM for Poisson Distribution Data	GLM for Poisson Distribution Data
Zero-Inflated Poisson	Zero-Inflated Poisson Regression: counts, rare events with a large portion of zeroes	Between	GLM for Zero-Inflated Poisson Distribution Data	GLM for Zero-Inflated Poisson Distribution Data
Zero-Inflated Poisson	Zero-Inflated Poisson Regression: counts, rare events with a large portion of zeroes	Within	GLM for Zero-Inflated Poisson Distribution Data	GLM for Zero-Inflated Poisson Distribution Data
Negative Binomial	Negative Binomial Regression: same as Poisson but for use in the presence of overdispersion	Between	GLM for Negative Binomial Distribution Data	GLM for Negative Binomial Distribution Data
Negative Binomial	Negative Binomial Regression: same as Poisson but for use in the presence of overdispersion	Within	GLM for Negative Binomial Distribution Data	GLM for Negative Binomial Distribution Data
Zero-Inflated Negative Binomial	Zero-Inflated Negative Binomial Regression: same as Zero-Inflated Poisson but for use in the presence of overdispersion	Between	GLM for Zero-Inflated Negative Binomial Distribution Data	GLM for Zero-Inflated Negative Binomial Distribution Data
Zero-Inflated Negative Binomial	Zero-Inflated Negative Binomial Regression: same as Zero-Inflated Poisson but for use in the presence of overdispersion	Within	GLM for Zero-Inflated Negative Binomial Distribution Data	GLM for Zero-Inflated Negative Binomial Distribution Data
Gamma and Exponential	Gamme and Exponential Regression: exponentially distributed responses (e.g. income, wait times)	Between	GLM for Gamme and Exponential Distribution Data	GLM for Gamma and Exponential Distribution Data
Gamma and Exponential	Gamme and Exponential Regression: exponentially distributed responses (e.g. income, wait times)	Within	GLM for Gamme and Exponential Distribution Data	GLM for Gamma and Exponential Distribution Data