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: 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 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