hypothesistesting

Hypothesis testing is a statistical method used to assess evidence from data about a population parameter. It centers on two competing statements: the null hypothesis (H0), which expresses a default position or no effect, and the alternative hypothesis (H1 or Ha), which represents what the researcher aims to support. The process evaluates whether observed data are unlikely under H0.

The procedure typically proceeds as follows: a significance level alpha is chosen (commonly 0.05); a test statistic is computed from the data (for example, a z, t, chi-square, or F statistic); a p-value or critical value is obtained; and H0 is rejected if the p-value is at most alpha or the statistic falls in the predesignated rejection region. Otherwise, H0 is not rejected. Tests can be one-tailed (testing for an effect in a specific direction) or two-tailed (testing for any deviation from H0). They can be one-sample or two-sample, and are extended in form to proportions, variances, regressions, and more.

Key concepts include Type I and Type II errors. A Type I error occurs when H0 is true but is rejected, with probability alpha. A Type II error occurs when H0 is false but is not rejected, with probability beta; the power of a test is 1 - beta. Power increases with larger sample size and larger true effects, while alpha controls the rate of false positives. Assumptions about data—such as randomness, independence, and distributional form—underlie many tests (z, t, chi-square, ANOVA, regression). When assumptions fail, nonparametric methods or resampling can be used. Interpretation emphasizes that a p-value measures compatibility with H0, not the probability that H0 is true, and that statistical significance does not necessarily imply practical significance.