Blog

Worked analyses with the R script and the output shown.

• Dunn's test after Kruskal-Wallis, explained

  What Dunn's test compares after Kruskal-Wallis, how Holm and Bonferroni adjust its p-values, and a worked R example on six insecticides with effect sizes.

  October 22, 2026, Comparing groups, 5 min read

• Effect sizes for Mann-Whitney and Wilcoxon tests

  The rank-biserial correlation for Mann-Whitney and Wilcoxon tests: what it measures, how its interval works, why it is not Z over root N, how to report it.

  October 22, 2026, Effect sizes, 9 min read

• 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.

  October 22, 2026, Effect sizes, 27 min read

• Eta squared vs partial eta squared: which to report

  Eta squared, partial eta squared and omega squared differ only in the denominator. A two-way ANOVA in R shows which to report and the interval to give.

  October 22, 2026, Effect sizes, 5 min read

• F-test vs t-test: what each one compares

  Which F-test you mean decides the answer: the ANOVA F on two groups equals Student's t squared, while the variance-ratio F compares spreads, not means.

  October 22, 2026, Comparing groups, 11 min read

• Heteroscedasticity: how to detect it and fix it

  What non-constant spread does to a regression, how to see it in a residual plot, and when a log transform or robust standard errors is the right fix.

  October 22, 2026, Assumptions and diagnostics, 7 min read

• Homogeneity of variance and what to do about it

  What unequal group variances do to Student's t and classic ANOVA, why Welch beats testing first, and a worked Welch ANOVA in R with effect sizes.

  October 22, 2026, Assumptions and diagnostics, 9 min read

• How to report chi-square test results in APA style

  A complete results paragraph for a chi-square test of independence: counts, expected counts, the statistic, Cramer's V and the odds ratio with intervals.

  October 22, 2026, Reporting results in APA style, 10 min read

• How to report a t-test in APA style, with examples

  Fill-in APA 7 sentences for Welch, Student, paired and one-sample t-tests, the formatting rule behind each symbol, and a worked example from a real R run.

  October 22, 2026, Reporting results in APA style, 12 min read

• The independence assumption: clustered data

  What repeated or clustered observations do to standard errors, shown on real tree growth data in R with and without a random intercept, and how to spot it.

  October 22, 2026, Assumptions and diagnostics, 10 min read