A t-test is any statistical hypothesis test in which the test statistic follows a Student's t distribution if the null hypothesis is supported.

[A "null' hypothesis is when you assume at the outset there is "no difference" between the two populations.]

A t-test  is used in three types of statistical questions:

 

1. Comparing a single value with  sample, to check whether that particular individual could come from that sample population. This is a single sample t rest.

2. If there are two independent  groups we wish to compare  two means to check if there is a difference between the two groups.

3. To compare two matched (or paired) samples to check if they are different. In this case we look at the differences between the pairs as there is a  paired or 'design' element in the experiment.

To undertake a t test, it is necessary to estimate the mean values, their standard errors, and to calculate a t statistic.

 

This requires the values of n (the sample size), the means, or for a matched pairs  the difference between the pairs of means, and the standard error of the estimates.

 

The matched pairs could be used for a "before and after" study (looking at an individuals marks of students after undertaking some training).

Another example would be applying two eye medicines, on to the left eye and one to the right eye of an individual, in this case the individual is like a block, as we compare two treatments on one individual.