Use this statistical tests cheat sheet to quickly match data types with the right hypothesis test. The guide simplifies choice criteria, assumptions, and interpretation so you can apply tests with confidence.
Each section highlights practical guidance for common research and analytics workflows. You will find decision points, method details, and reminders that keep your analysis rigorous and transparent.
| Test Category | When to Use | Key Assumptions | Typical Output |
|---|---|---|---|
| Compare Means | Compare group averages | Normality, equal variance | t, F statistic, p-value |
| Compare Variances | Check spread equality | Normality, independence | F statistic, p-value |
| Association | Test relationships in tables | Independence, expected counts | Chi-square, odds ratio |
| Correlation & Rank | Monotonic or non-normal relationships | Ordinal or continuous data | Spearman, Kendall tau |
| Survival & Time to Event | Censored time-to-event data | Proportional hazards, non-informative censoring | Hazard ratios, survival curves |
Choosing the Right Statistical Test
This step helps you align research goals with suitable tests based on data structure and distribution.
Define Your Question and Data Type
Start by stating whether you compare groups, assess association, or model time to event. Identify variable types as categorical, continuous, or time-to-event, since this directs method selection.
Check Distribution and Sample Size
Inspect skewness and outliers; approximate normality supports parametric tests. Small or non-normal samples often point to nonparametric alternatives that rely on ranks.
Assumptions and Diagnostics
Verifying core assumptions protects against misleading inference and supports credible conclusions.
Independence and Sampling Design
Ensure observations are independent or apply mixed models for clustered or repeated measures data. Ignoring dependence inflates type I error and invalidates standard errors.
Normality, Variance, and Linearity
Use plots and tests to assess normality, equal variance, and linearity where relevant. Transformations, robust tests, or generalized linear models can address violations.
Parametric Tests Overview
Parametric tests offer strong power when assumptions hold, using mean-based comparisons and known sampling distributions.
t-Tests and ANOVA
Use t-tests to compare two group means and ANOVA for three or more groups under balanced, normal conditions with similar variances.
Linear Regression and Correlation
Apply linear regression and Pearson correlation for continuous outcomes with linear trends, checking residuals and influential points.
Nonparametric and Specialized Alternatives
Nonparametric and robust methods provide flexibility when data violate standard assumptions or ranks better represent effects.
Mann-Whitney, Kruskal-Wallis, and Rank Correlation
Choose Mann-Whitney for two independent samples, Kruskal-Wallis for multiple groups, and Spearman or Kendall tau for monotonic associations with non-normal data.
Survival Analysis and Goodness-of-Fit
Use Kaplan-Meier curves and Cox models for censored time-to-event data, and apply chi-square or exact tests for categorical fit and independence problems.
Best Practices and Next Steps
Adopt consistent habits that improve reliability and communication of your statistical work.
- Clarify research questions and variable types before selecting a test.
- Check assumptions using plots, tests, and robustness checks.
- Document decisions, alternatives considered, and interpretation caveats.
- Report effect sizes and confidence intervals alongside p-values.
- Iterate with visual exploration and consult domain experts as needed.
FAQ
Reader questions
How do I decide between t-test and Mann-Whitney U in the statistical tests cheat sheet?
Prefer t-test when data are approximately normal with similar variances and you care about mean differences; switch to Mann-Whitney for skewed data, outliers, or small samples where ranks are more appropriate.
What should I do if my variances are unequal but groups are normal in this statistical tests cheat sheet?
Use Welch t-test or Welch ANOVA, which do not assume equal variances, and report chosen method transparently alongside classical results if needed.
Can I use chi-square for small sample sizes in this statistical tests cheat sheet?
For small samples, prefer exact tests such as Fisher exact test instead of chi-square to maintain valid type I error rates, especially when expected cell counts are low.
How do I handle repeated measures data in this statistical tests cheat sheet?
For repeated or clustered measures, use mixed-effects models or nonparametric repeated measures alternatives to account for within-subject correlation and avoid biased inference.