How to use the t-Test
1 The Student’s t-test
The Student’s t-test is a robust, well-documented test that compares the means of two sets of
data. The end result of the test is a single value of ‘t’, which is a measure of the extent to
which the two sets of data overlap. Remember, where the data extensively overlap, the
independent variable had little effect on the participants. This is the case if t is small. If t is
large, the two sets of data only partially overlap which means that the independent variable
had a (mathematically) noticeable effect on the participants. Put another way:
•
If t is small, the null hypothesis (of no difference between the participants’
performance in the two conditions) is accepted.
•
If t is large, the null hypothesis is rejected.
Specific values of t are converted into a probability, so that the rather vague phrases about
extensive and partial overlap used above become actual numbers, albeit still only
probabilities. The computation of t is usually left to computer software packages; one such
multimedia package is the t-test calculator available in The OpenScience Lab.
Requirements for doing a t-test
One value that must be known before you can apply a statistical test is the number of degrees
of freedom. Degrees of freedom is an important, if elusive, mathematical term. Usually its
numerical value is one less than the number of participants in each condition and this is the
method of calculation you will use here.
Degrees of freedom are a measure of how many items in a set of data need to be specified
before all the items in that set are known. For example if, in a two-participant trial, the mean
score is 25, and you know that Participant 2 scored 18, then Participant 1 must have scored
32 because no other value would give a mean for the two participants of 25. This trial
therefore has 1 degree of freedom (2 – 1 = 1). In the case of an experiment that has two
groups and the participants in each group are different, the degrees of freedom are calculated
for each group as reported above, and then added together. As an example, consider an
experiment which has seven participants in Group A and eight participants in Group B. In
this case the degrees of freedom would be (7–1) + (8–1) = 13.
When running the t-test calculator software the results that need to be reported are the
degrees of freedom, the value of t, and the p value calculated by the test. Here is a fictitious
example. Let’s imagine an experiment had 24 participants in each group. The degrees of
freedom are therefore (24–1) + (24–1) = 46. The researcher calculates a t value from the data
and the value returned by the calculator is 2.36. They also deduce a p value of 0.003. The
researcher should then report these results in either of the following formats:
