statistical-reporting

name statistical-reporting description Statistical test selection, assumption checking, and APA-formatted reporting. Use when analyzing experimental results or writing results sections. metadata {"category":"writing","trigger-keywords":"statistic,hypothesis test,p-value,regression,ANOVA,t-test,effect size,confidence interval","applicable-stages":"14,17","priority":"3","version":"1.0","author":"researchclaw","references":"adapted from K-Dense-AI/claude-scientific-skills"} Statistical Reporting Best Practice Test Selection Quick Reference Comparing two groups (independent, normal) : Independent t-test Comparing two groups (independent, non-normal) : Mann-Whitney U test Comparing two groups (paired, normal) : Paired t-test Comparing two groups (paired, non-normal) : Wilcoxon signed-rank test Comparing 3+ groups (independent, normal) : One-way ANOVA + post-hoc Comparing 3+ groups (non-normal) : Kruskal-Wallis test Relationship between continuous variables : Pearson or Spearman correlation Categorical outcomes : Chi-square or Fisher's exact test Predicting continuous outcome : Linear regression Predicting binary outcome : Logistic regression Assumption Checking Normality : Shapiro-Wilk test (n < 50) or visual Q-Q plots Homogeneity of variance : Levene's test before t-tests and ANOVA Independence : Verify study design ensures independent observations Linearity : Scatter plots and residual plots for regression Multicollinearity : VIF < 5 for multiple regression predictors When assumptions are violated, use non-parametric alternatives or robust methods APA Reporting Format t-test : t(df) = X.XX, p = .XXX, d = X.XX ANOVA : F(df_between, df_within) = X.XX, p = .XXX, eta-squared = .XX Correlation : r(df) = .XX, p = .XXX [95% CI: .XX, .XX] Chi-square : chi-square(df, N = XXX) = X.XX, p = .XXX Regression : beta = X.XX, SE = X.XX, t = X.XX, p = .XXX Always report exact p-values (not "p < .05") unless p < .001 Use leading zero for values that can exceed 1 (e.g., t = 0.50) but not for those bounded by 1 (e.g., p = .032, r = .45) Effect Sizes ALWAYS report effect sizes alongside p-values Cohen's d for group comparisons: small = 0.2, medium = 0.5, large = 0.8 Eta-squared for ANOVA: small = .01, medium = .06, large = .14 R-squared for regression: report adjusted R-squared for multiple predictors Odds ratios for logistic regression with 95% confidence intervals Distinguish statistical significance from practical significance Common Mistakes to Avoid Never say "the results were not significant, therefore there is no effect" Do not confuse correlation with causation in observational data Apply multiple comparison corrections (Bonferroni, FDR) when running many tests Report confidence intervals, not just point estimates State whether tests are one-tailed or two-tailed and justify the choice