Hypothesis Testing

Definition

Hypothesis testing is a formal procedure for deciding between two competing statements — the null hypothesis and the alternative hypothesis — using sample data. A test statistic is computed and compared to its distribution under the null; if the resulting p-value falls below a pre-specified significance level, the null is rejected.

Why It Matters

Hypothesis testing provides the logical backbone of empirical research, from clinical trials to policy evaluation. Without it, researchers would have no rigorous way to distinguish genuine effects from random noise. Understanding Type I and Type II errors, significance levels, and p-values is essential for designing studies that produce credible, reproducible results and for interpreting the findings of others with appropriate scepticism.

Example

A school district wants to test whether a new reading programme improves literacy scores. The null hypothesis states that the programme has no effect (mean difference = 0). After randomly assigning 200 students to the programme or a control group, the district conducts an independent-samples t-test. The p-value is 0.01, which falls below the 5% significance threshold. The district rejects the null hypothesis and concludes there is statistically significant evidence that the programme improves literacy.

Related Terms

• Null Hypothesis
• P-Value
• Statistical Significance
• Type I Error
• Type II Error
• Statistical Power
• Effect Size

Software Notes

• SPSS: All standard test procedures are under Analyze > Compare Means (t-tests, ANOVA) and Analyze > Nonparametric Tests. Set the significance level before analysis; SPSS reports exact p-values.
• R: t.test(), aov(), chisq.test(), wilcox.test(), and many others. Most return a p-value and a confidence interval automatically.
• Stata: ttest, anova, prtest, ranksum, and signrank cover the most common parametric and non-parametric tests.