Statistics Tutorials
These tutorials provide accessible introductions to the statistical tests and techniques featured on this site. Each tutorial explains what the test does, why it is used, how it works, and what its results mean. They are written for undergraduate students and assume no prior knowledge of statistics.
Comparing Means
Independent Samples T-Test
Comparing the means of two separate groups
Paired Samples T-Test
Comparing means from the same group at two time points
One-Sample T-Test
Testing whether a sample mean differs from a known value
One-Way ANOVA
Comparing means across three or more independent groups
Repeated Measures ANOVA
Comparing means across three or more related conditions
Two-Way ANOVA
Testing the effects of two factors simultaneously
Tukey HSD Post-Hoc Test
Identifying which specific groups differ after ANOVA
Z-Test for a Sample Mean
Testing a sample mean when the population standard deviation is known
Proportions & Categorical Data
Chi-Square Test of Independence
Testing whether two categorical variables are related
Chi-Square Goodness of Fit
Testing whether observed frequencies match expected frequencies
Fisher Exact Test
Exact test for association in small 2x2 tables
Binomial Test
Testing whether an observed proportion differs from an expected proportion
Z-Test for Two Proportions
Comparing proportions between two groups
Correlation
Pearson Correlation
Measuring the linear relationship between two continuous variables
Spearman's Rank Correlation
Rank-based correlation for ordinal or non-normal data
Kendall's Tau
A robust rank correlation using concordant and discordant pairs
Point-Biserial Correlation
Correlation between a binary variable and a continuous variable
Regression
Non-Parametric Tests
Mann-Whitney U Test
Non-parametric alternative to the independent samples t-test
Wilcoxon Signed-Rank Test
Non-parametric alternative to the paired samples t-test
Kruskal-Wallis Test
Non-parametric alternative to one-way ANOVA
Friedman Test
Non-parametric alternative to repeated measures ANOVA
Sign Test
A simple non-parametric test for paired data
Diagnostic & Supplementary Tests
Levene's Test
Testing whether groups have equal variances
Cohen's Kappa
Measuring agreement between two raters
Effect Size (Cohen's d)
Quantifying the magnitude of a difference between groups
Grubbs' Test
Detecting a single outlier in a dataset
Generalized ESD Test
Detecting multiple outliers in a dataset
Kolmogorov-Smirnov Test
Testing whether data follows a particular distribution
