The t Test

In many research situations, a mean from one group is compared with a mean from another group to determine the probability that the corresponding population means are different. The most common statistical procedure for determining the level of significance when two means are compared is the t test. The t test is a formula that generates a number, and this number is used to determine the probability level (p level) of rejecting the null hypothesis.

Two different forms of the equation are used in the t test, one for independent samples and one for samples that are paired, or dependent. Independent samples are groups of participants that have no relationship to each other; the two samples have different participants in each group, and the participants are usually either assigned randomly from a common population or drawn from two different populations.

Example

If you are testing the difference between an experimental group and a control group mean in a posttest-only design, the independent samples t test would be the appropriate statistic. Comparing leadership styles of two groups of superintendents would also utilize an independent samples t test.

The second form of the t test can be referred to by several different names, including paired, dependent samples, correlated, or matched t test. This t test is used in situations in which the participants from the two groups are paired or matched in some way.

Example 2

A common example of this case is the same group of participants tested twice, as in a pretest–posttest study. Whether the same or different subjects are in each group, as long as a systematic relationship exists between the groups it is necessary to use the dependent samples t test to calculate the probability of rejecting the null hypothesis.

In the Pascarella and Lunenburg study, elementary school principals from two school districts received leadership training using Hersey and Blanchard’s situational leadership framework. Pretests and posttests were administered to the principals and a sample of their teachers before and after training to determine the effects of training on principals’ leadership effectiveness and style range. The study provided partial support only for Hersey and Blanchard’s situational leadership theory. Using dependent samples t tests, principals were perceived as more effective three years after training than before training: t (principals) = 6.46 (15) < .01 and t (teachers) = 3.73 (59) < .01. However, no significant differences were found in principals’ effectiveness immediately following training, nor in principals’ leadership style range before and after training.