statistical-analysis

Statistical Analysis Skill

Use when running statistical analyses. Validates assumptions, runs tests, produces APA-formatted results.

When to Activate

• User asks to "analyse data", "run a test", or "check significance"
• The /analyse command is invoked
• User provides a dataset and a hypothesis

Process

1. Identify the appropriate test. Based on:

   • Number of groups/conditions (2 vs 3+)
   • Type of variables (continuous, categorical, ordinal)
   • Design (between-subjects, within-subjects, mixed)
   • Sample size (parametric vs non-parametric)
   • Independence of observations

   Common mappings:

   Question	Test
   Two group means	Independent t-test (or Mann-Whitney U)
   Paired means	Paired t-test (or Wilcoxon)
   3+ group means	One-way ANOVA (or Kruskal-Wallis)
   Relationship between continuous vars	Pearson r (or Spearman rho)
   Predicting from multiple vars	Multiple regression
   Categorical association	Chi-square test

2. Check assumptions. For each test, verify:

   • Normality — Shapiro-Wilk test, Q-Q plot description, skewness/kurtosis values
   • Homogeneity of variance — Levene's test
   • Independence — Design-based assessment
   • Linearity — Scatterplot inspection for correlations/regression
   • No multicollinearity — VIF values for regression

3. Run the analysis. Execute the test and capture:

   • Test statistic and degrees of freedom
   • Exact p-value (to 3 decimal places, or "< .001")
   • Effect size with confidence interval
   • Sample sizes per group

4. Format results in APA style.

   Examples:

   • "An independent samples t-test revealed a significant difference between groups, t(48) = 2.34, p = .023, d = 0.67, 95% CI [0.09, 1.24]."
   • "There was no significant correlation between X and Y, r(98) = .12, p = .231, 95% CI [-.08, .31]."

5. Sensitivity check. Run at least one robustness check:

   • Non-parametric equivalent if assumptions are marginal
   • Analysis with and without outliers
   • Alternative operationalisation of key variables (if available)