Teststatistikat

Teststatistikat, often translated as "test statistics," are values calculated from sample data during hypothesis testing. Their primary purpose is to summarize the information in the sample in a way that allows us to decide whether to reject or fail to reject a null hypothesis. Each type of hypothesis test, such as a t-test, z-test, chi-squared test, or F-test, uses a specific test statistic.

The calculation of a test statistic typically involves the difference between an observed sample value and a hypothesized population value, often normalized by a measure of variability from the sample. For example, a t-statistic measures the difference between a sample mean and a hypothesized population mean, scaled by the sample standard error. A chi-squared statistic, on the other hand, assesses the discrepancy between observed frequencies and expected frequencies in categorical data.

Once calculated, the test statistic is compared to a critical value from a probability distribution (e.g., the t-distribution, standard normal distribution, chi-squared distribution). Alternatively, a p-value, which represents the probability of observing a test statistic as extreme as, or more extreme than, the one calculated, is determined. If the test statistic falls into the rejection region (beyond the critical value) or if the p-value is less than the chosen significance level, the null hypothesis is rejected. Conversely, if the test statistic does not fall into the rejection region or the p-value is greater than the significance level, the null hypothesis is not rejected. Test statistics are therefore central to the inferential process in statistical hypothesis testing, providing a quantitative basis for making decisions about population parameters.