Blog

Worked analyses with the R script and the output shown.

• Standard error vs margin of error vs SD, explained

  Standard deviation, variance, standard error, margin of error and IQR: what each measures, how they connect, and which to report, with a worked example.

  October 23, 2026, P-values and inference, 12 min read

• Type I and type II errors in hypothesis testing

  Null and alternative hypotheses, alpha, type I and type II errors and power, shown by counting false positives and misses across 2,000 seeded studies.

  October 23, 2026, P-values and inference, 10 min read

• ANOVA test explained: one-way, Welch and two-way

  What an ANOVA test does, how to choose one-way, Welch, two-way or repeated-measures ANOVA, and a worked Welch example in R with eta squared and its interval.

  October 22, 2026, Comparing groups, 16 min read

• Breusch-Pagan test in R: what it tells you

  How the Breusch-Pagan test checks a regression for non-constant spread, how to read it in R, and why large samples flag changes that may not matter.

  October 22, 2026, Assumptions and diagnostics, 5 min read

• 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.

  October 22, 2026, Categorical data, 15 min read

• Cohen's d vs Hedges' g vs Glass's delta

  Which standardised mean difference to report, Cohen's d, Hedges' g or Glass's delta, by sample size, unequal spread and purpose, with a worked R example.

  October 22, 2026, Effect sizes, 13 min read

• How to write a confidence interval conclusion

  What a correct confidence interval conclusion says, built from one worked example in R, with common incorrect wordings side by side and how to fix each.

  October 22, 2026, P-values and inference, 10 min read

• Cramer's V and phi: effect sizes for chi-square

  What Cramer's V and phi measure, why their small, medium and large cut-offs depend on table size, the bias-corrected V, and a worked example in R.

  October 22, 2026, Effect sizes, 11 min read

• 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.

  October 22, 2026, Data cleaning and missing data, 26 min read

• 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.

  October 22, 2026, Statistics for a thesis or dissertation, 21 min read