Statistical Analysis Skill

Purpose: Structured pipeline for statistical analysis deliverables. Prevents assumption violations, missed effect sizes, and uninterpretable output. Origin: Created ahead of Assignment 19 (SPSS, Siva, $250, deadline Mar 8). No protocol coverage existed for this domain.

The 5-Step Pipeline

Step 1: DATA AUDIT

• Load dataset (CSV, SPSS .sav, Excel)
• Profile: N, variable types (nominal/ordinal/interval/ratio), missing data %, outliers
• Check for:
  • Missing data pattern (MCAR/MAR/MNAR) — Little's MCAR test if available
  • Outliers (z-score > 3 or IQR method)
  • Variable coding (reverse-coded items, string-to-numeric conversion)
  • Sample size adequacy per planned test (rule of thumb: 10–15 observations per predictor for regression)

Step 2: ASSUMPTION MATRIX

[!IMPORTANT] Every statistical test has assumptions. Violating them invalidates results. Check BEFORE running.

Step 3: TEST EXECUTION

For each test in the scope:

1. State the hypothesis (H₀ and H₁) explicitly
2. Run the test — output test statistic, df, p-value, effect size
3. Effect size (mandatory — p-value alone is insufficient):
   • Cohen's d (t-test)
   • η² or partial η² (ANOVA)
   • r or R² (correlation/regression)
   • Cramér's V (chi-square)
   • Cronbach's α (reliability — this IS the effect)
4. Decision: Reject/Fail to reject H₀ at α = 0.05 (unless specified otherwise)

Step 4: INTERPRETATION

For each test result, produce a 3-part interpretation:

1. Statistical statement: "A Pearson correlation revealed a significant positive relationship between X and Y, r(183) = .42, p < .001."
2. Effect size interpretation: "This represents a medium effect (Cohen, 1988)."
3. Practical meaning: "Workers who received more safety training hours reported higher safety compliance scores, explaining approximately 18% of the variance."

Step 5: CLIENT-READY REPORT

Structure the output document:

1. Introduction (research context, variables, hypotheses)
2. Methodology (sample, measures, statistical tests used)
3. Results
   3.1 Reliability Analysis
   3.2 Chi-Square Tests
   3.3 Correlation Analysis
   3.4 Regression Analysis
4. Discussion (interpret findings, connect to research questions)
5. Limitations
6. References
Appendix: SPSS Output Tables (screenshots or formatted tables)

• Use APA 7th edition reporting standards for statistical notation
• Include assumption check results in methodology or as footnotes
• Tables formatted per APA: no vertical lines, horizontal rules at top/bottom/below header only

Assignment 19 Quick Reference

Exit Gate

• All assumption checks documented
• Every test has: hypothesis, test statistic, df, p-value, effect size
• APA-compliant statistical notation
• Practical interpretation (not just "significant/not significant")
• Client-ready formatted output document