Student's t-Test for dependent samples

Comparison of two means from dependent samples.

Examples for dependence:

Repeated measure, parallelized samples, virtual dependence (e.g. twins)

Requirements:

Dependent variable is at least interval scaled and normal distributed.

Hypothesis:

Nondirectional:                                       Directional (example):

H0:                           H0:

H1:                            H1:

The dependence of two measures from the two samples is gathered from the differences of the measurement pairs.

Mean and standard deviation of these differences are defined as follows:

Whereas n is the number of pairs.

The decision between the hypothesis is made according to the sample distribution of .

If both populations are normal distributed, the sample distribution is normal, too, with mean

and standard deviation

If is estimated from the sample, we get the following t-distributed equation:

with degree of freedom df = n-1.