statistical-analysis

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:

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."

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

• 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