Data Cleaning: Check for missing values, outliers; apply appropriate imputation or sensitivity analyses.
Descriptive Statistics: Summarize patient demographics and baseline characteristics.
2.2 Statistical Methods
Goal Test/Model Rationale
Compare categorical variables (e.g., gender distribution across groups) Chi‑square test / Fisher’s exact test Assess association between group membership and categorical outcomes.
Compare continuous variables (e.g., age, lab values) Independent t‑test or Mann–Whitney U (if non‑normal) Evaluate differences in means/medians between two groups.
Adjust for confounders when assessing the effect of a predictor on outcome Multivariable logistic regression (binary outcomes) / Cox proportional hazards model (time‑to‑event) Estimate adjusted odds ratios or hazard ratios, controlling for covariates such as age, sex, comorbidities.
Validate model assumptions Residual analysis, Hosmer–Lemeshow goodness‑of‑fit test, proportional hazards check Ensure reliability of inference.
Hazard Ratio (HR) >1 indicates higher hazard (risk) over time; <1 indicates lower risk.
Confidence intervals that do not cross 1 and p‑values <0.05 signify statistical significance.
These tools allow researchers to quantify the impact of specific variables on outcomes while controlling for confounding factors, ensuring robust and reproducible conclusions.
4. Practical Take‑away Checklist
Step Action Best Practice
1. Study Design Choose prospective cohort or RCT with adequate sample size. Power calculations, inclusion/exclusion criteria clearly defined.
2. Data Collection Use standardized instruments; train staff on data entry. Pilot test forms; double‑entry for critical variables.
3. Handling Missing Data Document reasons; assess pattern (MCAR, MAR, MNAR). Consider multiple imputation or sensitivity analysis if missing not trivial.
Interpretation: The difference in mean scores between Group A and Group B is statistically significant at α=0.05; there is strong evidence that the two groups differ in their performance on the measure. If we had a directional hypothesis (e.g., Group A expected to score higher), the one‑sided test would yield p≈0.0025, reinforcing the conclusion.
Assumptions & Caveats:
Normality and equal variances were assumed; if violated, consider Welch’s t‑test or non‑parametric alternatives (e.g., Mann–Whitney U).
The test only indicates that means differ; it does not quantify effect size. Computing Cohen’s d would provide additional insight.
Multiple comparisons could inflate Type I error; adjust significance levels accordingly.
Next Steps:
Report the results with 95 % confidence intervals for the mean difference.
Include an effect‑size estimate (Cohen’s d) and its confidence interval.
If sample sizes are unequal or variances differ, re‑run Welch’s t‑test to confirm robustness.
Final Note: The calculation of p‑values in hypothesis testing is a straightforward application of the sampling distribution corresponding to your test statistic. For a two–sided test with a normal approximation and standard errors derived from sample variance, you use the standard normal CDF; for discrete data (counts), you may need Poisson or binomial distributions. The key is to match the null hypothesis distribution with the observed statistic to determine how extreme your result would be under the assumption that the null holds. This procedure yields the p‑value, which quantifies evidence against the null.
