Hypothesis Testing

Hypothesis testing provides a structured framework for evaluating evidence against null hypotheses—default assumptions that typically assert no effect, no difference, or no relationship. This approach frames scientific questions as statistical tests, allowing us to quantify the strength of evidence and make decisions with explicit consideration of uncertainty. The process begins by formulating precise null and alternative hypotheses that clearly define what constitutes a meaningful finding versus the status quo assumption.

Different tests address specific analytical scenarios: t-tests compare means between groups or against reference values; chi-square tests evaluate relationships between categorical variables; ANOVA assesses differences across multiple groups while controlling for overall error rates; non-parametric alternatives like Wilcoxon and Mann-Whitney tests make fewer distributional assumptions, offering robustness when data doesn't follow normal distributions. The p-value—a commonly used but often misunderstood metric—quantifies the probability of observing results at least as extreme as those found if the null hypothesis were true. While a threshold of p < 0.05 has become a conventional benchmark for 'statistical significance,' thoughtful analysis considers not just statistical significance but also effect sizes, confidence intervals, and practical importance. Understanding statistical power—the probability of detecting an effect when one truly exists—helps design adequately sized studies that don't miss important relationships due to insufficient sample sizes.