| name | statistical-analysis |
| description | Structured pipeline for statistical analysis deliverables — SPSS, R, Python. Covers reliability, chi-square, correlation, regression, assumption checking, and client-ready reporting. |
| version | 1.0.0 |
| created | 2026-03-06T00:00:00.000Z |
| cluster | 13 (Build Lifecycle) |
| triggers | ["SPSS","statistics","regression","chi-square","correlation","reliability","Cronbach","hypothesis test","p-value","survey analysis"] |
| context_trigger | SPSS, statistics, regression, chi-square, correlation, reliability, Cronbach, hypothesis test, p-value, survey analysis, t-test, ANOVA |
Statistical Analysis Skill
Purpose: Structured pipeline for statistical analysis deliverables. Prevents assumption violations, missed effect sizes, and uninterpretable output.
Origin: Created ahead of a client SPSS assignment. 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.
| Test Family | Assumptions | Check Method |
|---|
| Reliability (Cronbach's α) | Unidimensionality, interval/ratio data, ≥3 items per scale | Factor analysis / item-total correlations |
| Chi-Square (χ²) | Independence, expected frequency ≥ 5 in 80%+ cells, categorical variables | Expected frequency table |
| Pearson Correlation | Linearity, normality (both vars), no significant outliers, interval/ratio | Scatter plot, Shapiro-Wilk |
| Spearman Correlation | Monotonic relationship, ordinal or non-normal interval | Scatter plot (monotonic check) |
| Multiple Regression | Linearity, independence (Durbin-Watson), homoscedasticity, normality of residuals, no multicollinearity (VIF < 10) | Residual plots, VIF table, Durbin-Watson |
| Independent t-test | Normality, homogeneity of variance (Levene's), interval/ratio DV | Shapiro-Wilk, Levene's |
| One-way ANOVA | Normality, homogeneity (Levene's), independence, interval/ratio DV | Same as t-test + post-hoc if significant |
Step 3: TEST EXECUTION
For each test in the scope:
- State the hypothesis (H₀ and H₁) explicitly
- Run the test — output test statistic, df, p-value, effect size
- 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)
- 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:
- Statistical statement: "A Pearson correlation revealed a significant positive relationship between X and Y, r(183) = .42, p < .001."
- Effect size interpretation: "This represents a medium effect (Cohen, 1988)."
- Practical meaning: "Workers who received more safety training hours reported higher safety compliance scores, explaining approximately 18% of the variance."
| Effect Size | Small | Medium | Large |
|---|
| Cohen's d | 0.2 | 0.5 | 0.8 |
| r | 0.1 | 0.3 | 0.5 |
| R² | 0.01 | 0.09 | 0.25 |
| η² | 0.01 | 0.06 | 0.14 |
| Cramér's V (df=1) | 0.1 | 0.3 | 0.5 |
| Cronbach's α | < 0.6 poor | 0.7–0.8 acceptable | > 0.9 excellent |
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
Example Scope Reference
| Component | Count | Details |
|---|
| Reliability (Cronbach's α) | 5 | One per scale/construct |
| Chi-Square (χ²) | 4 | Independence tests (demographic × outcome) |
| Correlation | 4 | Bivariate (IV-DV pairs) |
| Regression | 1 | Multiple regression (4 IVs → 1 DV) |
| Total tests | 14 | |
| Topic | Safety Training in SG Construction | |
| N | 185 survey responses | |
| IVs | 4 (to be identified from data) | |
| DV | 1 (to be identified from data) | |
Exit Gate
