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Guides and worked analyses on choosing, running and reporting statistics, grouped by topic.
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Not sure which test fits your data? Start with How to choose a statistical test for your data.
Topics
Choosing a test, 1 article
- How to choose a statistical test for your data
Pick a test from four facts about your study: the question, the outcome type, how observations are linked, and how many groups. With a decision table.
Guide
P-values and inference, 6 articles
- P-values and confidence intervals: report both
What a p value and a confidence interval each tell you, how they relate, how to read p = 0.06, and how to report both, with a worked example in R.
Blog post, 24 min read
- How to find a p-value from a test statistic
Blog post, 11 min read
- How to write a confidence interval conclusion
Blog post, 10 min read
- Multiple comparisons: Bonferroni, Holm, or BH
Guide
- Standard error vs margin of error vs SD, explained
Blog post, 12 min read
- Type I and type II errors in hypothesis testing
Blog post, 10 min read
Effect sizes, 5 articles
- Effect sizes: Cohen's d, eta squared, OR and r
What an effect size is, which one goes with which test, the SD each version of Cohen's d uses, and a worked R example with d and its 95% interval.
Blog post, 27 min read
- Cohen's d vs Hedges' g vs Glass's delta
Blog post, 13 min read
- Cramer's V and phi: effect sizes for chi-square
Blog post, 11 min read
- Effect sizes for Mann-Whitney and Wilcoxon tests
Blog post, 9 min read
- Eta squared vs partial eta squared: which to report
Blog post, 5 min read
Assumptions and diagnostics, 8 articles
- Parametric test assumptions: checks and fallbacks
The assumptions behind t-tests, ANOVA and regression, how to check each without the pre-test traps, and what to do when one fails, with a worked Welch ANOVA.
Blog post, 26 min read
- Breusch-Pagan test in R: what it tells you
Blog post, 5 min read
- Do you need to test for normality before a t-test?
Blog post, 7 min read
- Heteroscedasticity: how to detect it and fix it
Blog post, 7 min read
- Homogeneity of variance and what to do about it
Blog post, 9 min read
- Linear regression assumptions and how to check them
Blog post, 16 min read
- Logistic regression assumptions, real and invented
Blog post, 13 min read
- The independence assumption: clustered data
Blog post, 10 min read
Data cleaning and missing data, 4 articles
- Data cleaning checklist before a statistical test
An ordered data cleaning checklist for statistical analysis: structure, codes, duplicates, ranges, units, missing data and outliers, run on R's airquality data.
Blog post, 26 min read
- How to analyse values below the detection limit
Guide
- How to handle outliers before a statistical test
Blog post, 13 min read
- The IQR rule: upper and lower fences for outliers
Blog post, 10 min read
Comparing groups, 14 articles
- T-tests explained: one-sample, paired and Welch
What a t-test does, how to choose the one-sample, paired, Student or Welch version, and a worked Welch example in R with Cohen's d and its interval.
Blog post, 25 min read
- ANCOVA (analysis of covariance): a practical guide
Guide
- ANOVA post hoc tests: Tukey, Games-Howell, Dunn
Blog post, 8 min read
- ANOVA test explained: one-way, Welch and two-way
Blog post, 16 min read
- Dunn's test after Kruskal-Wallis, explained
Blog post, 5 min read
- F-test vs t-test: what each one compares
Blog post, 11 min read
- One-sample t-test: comparing a mean to a reference
Blog post, 8 min read
- One-way ANOVA, Welch ANOVA or Kruskal-Wallis?
Guide
- Paired t-test or Wilcoxon signed-rank test?
Guide
- Paired vs unpaired t-test: which design you have
Blog post, 13 min read
- T-test or Mann-Whitney U test: which to use?
Guide
- Two-sample t-test: formula, assumptions, example
Blog post, 9 min read
- Two-way ANOVA: interaction, main effects, post hoc
Guide
- Welch's t-test: when to use it instead of Student's
Blog post, 8 min read
Categorical data, 4 articles
- Chi-square test explained, with a worked R example
What the chi-square test of independence computes, how to read expected counts, Cramer's V and residuals, and a worked R example on real survey data.
Blog post, 15 min read
- Chi-square or Fisher's exact test: which to use?
Guide
- McNemar's test for paired proportions
Guide
- Odds ratio or relative risk: which to report?
Guide
Regression models, 9 articles
- Multiple linear regression, and when to switch
Choosing a regression model from your outcome type (linear, logistic, Poisson, negative binomial or ordinal), with a multiple linear regression worked in R.
Blog post, 14 min read
- Confounding variables and how adjustment works
Blog post, 13 min read
- Correlation matrix in R with p-values and intervals
Blog post, 11 min read
- Correlation vs causation in research reports
Blog post, 9 min read
- Logistic regression: odds ratios and separation
Guide
- Multicollinearity and VIF: a worked example in R
Blog post, 7 min read
- Ordinal or multinomial logistic regression?
Guide
- Poisson or negative binomial regression?
Guide
- Residual standard error: how to read it in R
Blog post, 10 min read
Repeated measures and mixed models, 1 article
- Repeated-measures ANOVA or a linear mixed model?
Repeated-measures ANOVA drops anyone with a missing visit; a linear mixed model keeps every observation. When each fits, shown on one dataset run both ways.
Guide
Survival analysis, 4 articles
- Survival analysis: Kaplan-Meier, Cox and AFT in R
Survival analysis in R on public lung cancer data: censoring, Kaplan-Meier, log-rank, Cox regression with its proportional hazards check, and AFT.
Blog post, 15 min read
- Cox regression in R: coxph() with the exact script
Blog post, 14 min read
- How to interpret a hazard ratio in Cox regression
Blog post, 3 min read
- Kaplan-Meier and Cox regression for survival data
Guide
Agreement and diagnostic accuracy, 3 articles
- Bland-Altman plot: agreement between two methods
How to make and read a Bland-Altman plot: bias, limits of agreement with their confidence intervals, a proportional-bias check, sample size and R code.
Guide
- Inter-rater reliability: kappa and alternatives
Blog post, 13 min read
- Sensitivity vs specificity in a diagnostic study
Blog post, 11 min read
Reporting results in APA style, 3 articles
- APA style statistics reporting: every common test
The APA 7 rules for reporting statistics (italics, leading zeros, p values, degrees of freedom, intervals) and a fill-in template for each common test.
Blog post, 19 min read
- How to report a t-test in APA style, with examples
Blog post, 12 min read
- How to report chi-square test results in APA style
Blog post, 10 min read
Reproducible analysis, 1 article
- Reproducible statistical analysis: the rerun test
What a reviewer needs to rerun your analysis: the data, one script, the seed, package versions, session info and a decision record, shown on a seeded R example.
Guide
Statistics for a thesis or dissertation, 4 articles
- Dissertation statistics: a design-first guide
Choose the statistics for a thesis from the study design: five common designs, the test, the assumption checks and the effect size to report for each.
Blog post, 21 min read
- Analysing Likert scale data: items and scales
Blog post, 12 min read
- Pretest posttest design: change scores or ANCOVA?
Blog post, 10 min read
- Regression to the mean in pre-post studies
Blog post, 5 min read
Latest
- Confounding variables and how adjustment works
October 23, 2026, 13 min read
- Correlation matrix in R with p-values and intervals
October 23, 2026, 11 min read
- Correlation vs causation in research reports
October 23, 2026, 9 min read
- Cox regression in R: coxph() with the exact script
October 23, 2026, 14 min read
- How to interpret a hazard ratio in Cox regression
October 23, 2026, 3 min read
- Inter-rater reliability: kappa and alternatives
October 23, 2026, 13 min read