Study Notes on Statistical Analysis

Overview

Statistical analysis provides quantitative foundations for research projects, utilizing tools like R, SAS, and SPSS to reduce errors and ensure replication. It is especially useful for retrospective data interpretation.

Key Concepts

• Significance Level ($\alpha$): The risk of a Type I error (false positive).

• Beta ($\beta$): The risk of a Type II error (false negative).

• Power ($1 - \beta$): The probability of detecting an effect that exists. While increased sample sizes improve power, they must be balanced against potential bias and cost.

• Effect Size: Indicates the practical magnitude of results beyond simple statistical significance.

Variable Classification

• Categorical: Mutually exclusive groups (e.g., gender, smoking status).

• Quantitative: Numerical measurements (e.g., age, BMI).

• Predictor vs. Response: Predictor (independent) variables explain changes in Response (dependent/outcome) variables.

Statistical Testing

• T-tests: Compare quantitative averages between $2$ categorical groups.

• ANOVA: Evaluates mean variations across $3$ or more groups.

• Chi-square Tests: Assess associations between $2$ categorical variables.

• Multiple Regression: Controls for multiple predictors to isolate effects on a response.

  • Linear Regression: Predicts continuous outcomes.

  • Logistic Regression: Predicts binary/categorical outcomes (e.g., readmission vs. no readmission).

Best Practices in Interpretation

• Report test statistics, p-values, and confidence intervals.

• Significant results (p < 0.05) identify differences unlikely due to chance.

• Findings should include both significant and non-significant results to avoid selection bias.