Skill: Statistical Distribution Analysis

Use When

• User wants to understand the distribution of a numeric variable before choosing a statistical test
• User needs to check whether data is approximately normally distributed
• User wants summary statistics (mean, median, variance, skewness, kurtosis) for one or more columns
• User is preparing an EDA (exploratory data analysis) report

Inputs

• Required:
  • Data table (CSV or TSV) with at least one numeric column
• Optional:
  • Column(s) to analyze (default: all numeric columns)
  • Normality test method: shapiro (default, n ≤ 5000) or anderson (Anderson-Darling, recommended for larger samples)
  • Output directory (default: ./dist_output)

Workflow

1. Read the data file; identify numeric columns to analyze (or use user-specified subset).
2. For each target column, compute summary statistics: mean, median, standard deviation, variance, min, max, 25th/75th percentiles, skewness, kurtosis.
3. Run normality test:
   • Shapiro-Wilk when n ≤ 5000
   • Anderson-Darling when n > 5000 Report test statistic, p-value (or significance level where applicable), and sample size.
4. Classify each variable as approximately_normal or non_normal using both test output and Q-Q plot inspection (do not classify from hypothesis-test p-value alone).
5. Generate plots for each variable: histogram with density overlay, Q-Q plot.
6. If multiple variables, produce a summary table across all variables.
7. Write summary statistics table (TSV) and plots (PDF) to output directory.
8. Save an executable analysis script (analysis_code.py or analysis_code.R) and software version manifest (session_info.txt) used to produce results.
9. Report which variables appear normally distributed and suggest appropriate downstream tests.

Output Contract

• Summary statistics table (TSV): variable, n, mean, median, sd, variance, skewness, kurtosis, normality_test, test_statistic, p_value_or_significance, normality_call
• Histogram + density plot per variable (PDF)
• Q-Q plot per variable (PDF)
• Reproducibility artifacts: analysis_code.py or analysis_code.R, plus session_info.txt

Limits

• Shapiro-Wilk test is unreliable for very large n; use Anderson-Darling and visual diagnostics instead.
• Avoid one-sample KS tests against a fitted normal distribution unless a corrected procedure is explicitly implemented.
• Normality tests have low power for small samples (n < 20); visual inspection of Q-Q plot is recommended.
• Does not handle categorical or date columns; these are silently skipped.
• Common failure: non-numeric columns passed explicitly cause an error — pre-filter if needed.