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
1---2name: statistical-analysis3description: Structured pipeline for statistical analysis deliverables — SPSS, R, Python. Covers reliability, chi-square, correlation, regression, assumption checking, and client-ready reporting.4---56# Statistical Analysis Skill78> **Purpose**: Structured pipeline for statistical analysis deliverables. Prevents assumption violations, missed effect sizes, and uninterpretable output.9> **Origin**: Created ahead of a client SPSS assignment. No protocol coverage existed for this domain.1011## The 5-Step Pipeline1213### Step 1: DATA AUDIT1415- Load dataset (CSV, SPSS .sav, Excel)16- Profile: N, variable types (nominal/ordinal/interval/ratio), missing data %, outliers17- Check for:18 - Missing data pattern (MCAR/MAR/MNAR) — Little's MCAR test if available19 - Outliers (z-score > 3 or IQR method)20 - Variable coding (reverse-coded items, string-to-numeric conversion)21 - Sample size adequacy per planned test (rule of thumb: 10–15 observations per predictor for regression)2223### Step 2: ASSUMPTION MATRIX2425> [!IMPORTANT]26> Every statistical test has assumptions. Violating them invalidates results. Check BEFORE running.2728| Test Family | Assumptions | Check Method |29|---|---|---|30| **Reliability (Cronbach's α)** | Unidimensionality, interval/ratio data, ≥3 items per scale | Factor analysis / item-total correlations |31| **Chi-Square (χ²)** | Independence, expected frequency ≥ 5 in 80%+ cells, categorical variables | Expected frequency table |32| **Pearson Correlation** | Linearity, normality (both vars), no significant outliers, interval/ratio | Scatter plot, Shapiro-Wilk |33| **Spearman Correlation** | Monotonic relationship, ordinal or non-normal interval | Scatter plot (monotonic check) |34| **Multiple Regression** | Linearity, independence (Durbin-Watson), homoscedasticity, normality of residuals, no multicollinearity (VIF < 10) | Residual plots, VIF table, Durbin-Watson |35| **Independent t-test** | Normality, homogeneity of variance (Levene's), interval/ratio DV | Shapiro-Wilk, Levene's |36| **One-way ANOVA** | Normality, homogeneity (Levene's), independence, interval/ratio DV | Same as t-test + post-hoc if significant |3738### Step 3: TEST EXECUTION3940For each test in the scope:41421. **State the hypothesis** (H₀ and H₁) explicitly432. **Run the test** — output test statistic, df, p-value, effect size443. **Effect size** (mandatory — p-value alone is insufficient):45 - Cohen's d (t-test)46 - η² or partial η² (ANOVA)47 - r or R² (correlation/regression)48 - Cramér's V (chi-square)49 - Cronbach's α (reliability — this IS the effect)504. **Decision**: Reject/Fail to reject H₀ at α = 0.05 (unless specified otherwise)5152### Step 4: INTERPRETATION5354For each test result, produce a **3-part interpretation**:55561. **Statistical statement**: "A Pearson correlation revealed a significant positive relationship between X and Y, r(183) = .42, p < .001."572. **Effect size interpretation**: "This represents a medium effect (Cohen, 1988)."583. **Practical meaning**: "Workers who received more safety training hours reported higher safety compliance scores, explaining approximately 18% of the variance."5960| Effect Size | Small | Medium | Large |61|---|---|---|---|62| Cohen's d | 0.2 | 0.5 | 0.8 |63| r | 0.1 | 0.3 | 0.5 |64| R² | 0.01 | 0.09 | 0.25 |65| η² | 0.01 | 0.06 | 0.14 |66| Cramér's V (df=1) | 0.1 | 0.3 | 0.5 |67| Cronbach's α | < 0.6 poor | 0.7–0.8 acceptable | > 0.9 excellent |6869### Step 5: CLIENT-READY REPORT7071Structure the output document:7273```741. Introduction (research context, variables, hypotheses)752. Methodology (sample, measures, statistical tests used)763. Results77 3.1 Reliability Analysis78 3.2 Chi-Square Tests79 3.3 Correlation Analysis80 3.4 Regression Analysis814. Discussion (interpret findings, connect to research questions)825. Limitations836. References84Appendix: SPSS Output Tables (screenshots or formatted tables)85```8687- Use APA 7th edition reporting standards for statistical notation88- Include assumption check results in methodology or as footnotes89- Tables formatted per APA: no vertical lines, horizontal rules at top/bottom/below header only9091## Example Scope Reference9293| Component | Count | Details |94|---|---|---|95| Reliability (Cronbach's α) | 5 | One per scale/construct |96| Chi-Square (χ²) | 4 | Independence tests (demographic × outcome) |97| Correlation | 4 | Bivariate (IV-DV pairs) |98| Regression | 1 | Multiple regression (4 IVs → 1 DV) |99| **Total tests** | **14** | |100| Topic | Safety Training in SG Construction | |101| N | 185 survey responses | |102| IVs | 4 (to be identified from data) | |103| DV | 1 (to be identified from data) | |104105## Exit Gate106107- [x] All assumption checks documented108- [x] Every test has: hypothesis, test statistic, df, p-value, effect size109- [x] APA-compliant statistical notation110- [x] Practical interpretation (not just "significant/not significant")111- [x] Client-ready formatted output document
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