# Student's t-test

The t-test is a term used in mathematical statistics, he refers to a group hypothesis tests with t- distributed Testprüfgröße. Often, however, is meant by the t- test of the one-sample or two-sample t-test.

- The One-Sample t- test (also Simple t-test; . Engl One -sample t-test) checked against the mean of a sample, whether the mean of a population is different from a predetermined target value. It is assumed that the data of the sample of a normal population originate or there is a sufficiently large sample size, so that the central limit theorem is satisfied.

- The two-sample t- test (also Double t-test; . Engl Two -sample t-test) verified on the means of two independent samples behave as the means of two populations from each other. It is assumed that the data of samples of a normal population originate or there are sufficiently large sample sizes so that the central limit theorem is satisfied. The classic t-test assumes that both samples come from populations with the same variance. Test or Welch 's t-test Satterthwaite is a variant which does not require the equality of variances.

- The dependent t- test (also pair differences test; . Engl Paired t-test ) tests for two related (dependent) samples, if the average difference between the measurements is different. It is assumed that the differences are normally distributed.

- The t-test of the regression coefficient examined in the linear regression of the normally distributed interference if a regression coefficient is zero.

- Steiger's Z- test checks whether the Bravais -Pearson correlation coefficient is equal to a predetermined value (eg zero). It is assumed that the data of samples of a bivariate normal population originate.

## History

The t-statistic was introduced in 1908 by William Sealy Gosset. He worked as a chemist for the Guinness brewery in Dublin ( Ireland) and developed the t-test as a cheap way to monitor the quality of the stout. Guinness prohibited its employees, results to be published, therefore Gosset published his work under the pseudonym Student.