statistics

name	statistics
description	null

Statistical Analysis & Quality Control

Overview

Comprehensive statistical methodology for scientific research. Covers test selection, assumption verification, power analysis, effect size reporting, and reporting standards.

Test Selection Guide

Data Type	Groups	Paired?	Normal?	Recommended Test
Continuous	2	No	Yes	Independent t-test
Continuous	2	No	No	Mann-Whitney U
Continuous	2	Yes	Yes	Paired t-test
Continuous	2	Yes	No	Wilcoxon signed-rank
Continuous	3+	No	Yes	One-way ANOVA + post hoc
Continuous	3+	No	No	Kruskal-Wallis + Dunn
Continuous	3+	Yes	Yes	Repeated measures ANOVA
Categorical	2x2	—	—	Chi-square / Fisher's exact
Time-to-event	2+	—	—	Log-rank + KM curves
Time-to-event	Adjusted	—	—	Cox proportional hazards
Continuous	Prediction	—	—	Linear/logistic regression

Assumption Checks

• Normality: Shapiro-Wilk (n < 50), Kolmogorov-Smirnov (n > 50), Q-Q plot visual
• Homoscedasticity: Levene's test, Bartlett's test
• Independence: study design review (not a statistical test)
• Proportional hazards: Schoenfeld residuals, log-log plot

Multiple Comparison Correction

• Bonferroni: conservative, for few comparisons
• Holm-Bonferroni: step-down, less conservative than Bonferroni
• FDR (Benjamini-Hochberg): for many comparisons (e.g., genomics)
• Tukey HSD: for all pairwise comparisons after ANOVA

Effect Size Guidelines

Measure	Small	Medium	Large
Cohen's d	0.2	0.5	0.8
Pearson r	0.1	0.3	0.5
Odds Ratio	1.5	2.5	4.3
R-squared	0.02	0.13	0.26

Reporting Standards

• Always report: test statistic, degrees of freedom, exact p-value, effect size, 95% CI
• Follow STROBE (observational), CONSORT (RCTs), PRISMA (reviews), ARRIVE (animal)
• Never say "trend toward significance" for p > 0.05
• Report non-significant results honestly