t test

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The t -test is a term from mathematical statistics , it describes a group of hypothesis tests with a t-distributed test test variable . Often, however, the t-test means the one-sample or two-sample t test for a mean difference.

  • The Einstichproben- t test (also easier t test; engl one-sample. T -test) checks on the basis of the mean value of a sample , whether the mean of a population differs from a predetermined desired value. It is assumed that the sample data come from a normally distributed population or that there is a sufficiently large sample size so that the central limit theorem is fulfilled.
  • The Zweistichproben- t test (also Double t test; engl two-sample. T -test) checks on the basis of two mean values independent samples, as the means of two populations relate to each other. It is assumed that the sample data come from a normally distributed population or that the sample sizes are large enough so that the central limit theorem is met. The classic t test assumes that both samples come from populations with the same variance . The Welch test or Satterthwaite's t test is a variant that does not require the variances to be equal.
  • The dependent t test (also paired t test) checks for two connected (dependent) samples whether the mean difference between the measured values ​​differs. It is assumed that the differences are normally distributed.
  • The t test of the regression coefficient checks in linear regression under the assumption of normally distributed disturbance variables whether a regression coefficient is zero.
  • Steiger's Z-test checks whether the Bravais-Pearson correlation coefficient is equal to a predetermined value (e.g. equal to zero). It is assumed that the data of the samples come from a bivariate normally distributed population.

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 forbade its employees to publish results, so Gosset published his work under the pseudonym Student .

Individual evidence

  1. ↑ for further information on the economist Mark Satterthwaite and his equation of variance see the English lemma
  2. ^ Student: The Probable Error of a Mean . In: Biometrika . tape 6 , no. 1 , March 1908, p. 1-25 , doi : 10.1093 / biomet / 6.1.1 , JSTOR : 2331554 .