Hypothesis Testing

In statistics, hypothesis testing is a method used to determine whether a specific hypothesis is true. This technique helps verify if a given sample originates from a particular population and assesses whether observed differences are significant enough to conclude they are unlikely to occur by random chance. Typically, hypothesis testing involves formulating two competing hypotheses: the null hypothesis (H₀) and the alternative hypothesis (H₁). The null hypothesis represents the default assumption we aim to test, while the alternative hypothesis is what we seek to demonstrate as true.

By comparing sample data with population parameters, we compute a test statistic (e.g., t-value, z-score, or F-statistic) that quantifies the deviation between observed and expected results. This statistic is then evaluated against a critical value or p-value threshold to decide whether to reject or fail to reject the null hypothesis. In computational implementations, this process often involves: - Defining hypothesis parameters using statistical libraries (e.g., SciPy's `scipy.stats` module in Python) - Calculating test statistics through functions like `ttest_ind()` for t-tests or `chi2_contingency()` for chi-square tests - Determining significance levels (commonly α=0.05) and critical regions - Interpreting p-values where p < α indicates statistical significance

Rejecting the null hypothesis supports the alternative hypothesis, while failing to reject it suggests insufficient evidence against the null. Thus, hypothesis testing serves as a fundamental statistical tool for scientific research, enabling data-driven conclusions with measurable confidence levels. Code implementations typically include steps for data preprocessing, assumption checks (e.g., normality via Shapiro-Wilk test), and post-hoc analysis when multiple comparisons are involved.