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.

Sample (statistics) Digital Object Identifier
759075
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