hypotesetest

Hypothesis testing is a formal procedure in statistics used to assess evidence about a population parameter based on sample data. It begins with two competing statements: the null hypothesis H0, which asserts no effect or no difference, and the alternative hypothesis Ha, which posits that an effect or difference exists. A significance level alpha, commonly set at 0.05, defines the threshold for deeming the observed data unlikely under H0.

After data collection, a test statistic is calculated according to the chosen method (for example a t-statistic for a mean, a chi-square statistic for categorical data). The p-value or critical region is used to decide whether to reject H0. If the p-value is less than or equal to alpha, H0 is rejected in favor of Ha; otherwise there is not enough evidence to reject H0. It is important to note that failing to reject H0 does not prove H0 true.

Concepts of error are central: a Type I error occurs if H0 is true but rejected, while a Type II error occurs if H0 is false but not rejected. Power is the probability of rejecting H0 when Ha is true. Valid results rely on appropriate data assumptions, such as random sampling, independence, and distributional requirements specific to the test used.

Tests can be one-sided or two-sided. Common tests include t-tests for means, chi-square tests for independence, analysis of variance for comparing multiple means, and nonparametric alternatives when assumptions are violated. Reporting typically includes the test used, test statistic and degrees of freedom when applicable, the p-value, and an effect size. Researchers should guard against p-hacking and consider multiple testing corrections when relevant.