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:

1. 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

1. 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

1. 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]."

1. 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)

Output

A results section ready for incorporation into a paper, with:

• Descriptive statistics table
• Assumption check results
• Main analysis in APA format
• Sensitivity analysis results
• Brief interpretation (supported/not supported, with caveats)

Critical Rules

• Never round p-values to convenient thresholds. Report exact values.
• Never interpret a non-significant result as "no effect." It means "insufficient evidence."
• Always report what you tested, even when results are null.
• If assumptions are violated and no non-parametric alternative is appropriate, state this explicitly rather than proceeding with an invalid test.