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t-test

(NL: t-toets)

The t-test is a statistical hypothesis test that is used as an alternative to the z-test when the population standard deviation \(\sigma\) is unknown or when the sample size is too small (\(n<30\)). The test is also used to determine whether the mean of two samples is equal.

The conditions for the t-test are:

  • the sample must be random
  • the investigated stochastic variable must be normally distributed

one sample t-test

The procedure of the t-test for one sample is almost identical to that of the z-test, with the only difference that you use the Student-t distribution with \(n-1\) degrees of freedom instead of the normal distribution. The standard deviation of the sample is used as an estimator of the population standard deviation \(\sigma\).

two sample t-test

The t-test can also be used to determine the difference in means of two samples. We distinguish two cases:

  • Independent samples: the two samples are taken separately and the test assesses whether the means of the two samples are equal or not.
  • Paired samples: for each observation in the first sample, there is a corresponding observation in the second sample (for example, once before and once after a certain intervention). The test assesses whether or not the mean of the differences between the two measurements is equal to zero.