Using SPSS to Understand Research and Data Analysis.

Chapter 10

Paired Samples t-Test:
Assessing Differences Between Correlated Group Means

10.1 Introduction to the Paired-Samples t-Test

In the previous chapter we distinguished between two distinct applications of the t-test: the independent samples t-test and the correlated samples t-test. Recall that when a between-subjects design is used, the independent-samples t-test is the appropriate test. This is the procedure introduced in Chapter 9.

Use of a within-subjects design (sometimes called a repeated measures design) or a participant-by-participant matched design requires analysis with the paired samples t-test (also known as the correlated or paired-samples t-test). We turn our attention to this application of the t-test in this chapter.

The differences in these types of designs is both procedural and statistical. In the independent samples design, separate (and independent) groups of participants are compared, and each particpant is measured only once on the dependent variable. The two sets of scores are therefore independent (uncorrelated).

In the correlated samples design, there are still two sets of scores on the dependent variable, but the scores are not independent. There are three ways in which a design can result in correlated scores:

• Repeated Measures are obtained on one group of participants, such as in measuring participants before a treatment is applied and again after the treatment. Thus, each person serves as his/her own control, and because the two sets of scores to be compared are obtained from the same people, the two groups of scores are not independent.
• Groups are established by pairing participants on the basis of some natural relationship between the individuals in each pair. For example, EZ employees' social skills might be compared to those of their fathers. Each person would be paired with his/her father in this design, and because of this natural relationship, the scores are not independent.
• A matched-participant design is employed in which the participants are paired based on receiving similar scores on some pretest. One person in each pair is then assigned to the experimental group (e.g., the group receiving some treatment) and one in each pair is assigned to the control group (which doesn't receive the treatment). This is sometimes done in order to control for some individual difference variable. For example, we might want to control for intelligence in assessing the effects of a drug on memory. We would first measure the participants' IQ and then match them based on their IQ scores before randomly assigning one to the drug and the other to the no-drug condition.

If any of the above three situations exists, the scores in the two groups will be correlated based on the pairing. This intercorrelation must be accounted for statistically when comparing the two groups, and that is what the paired-samples t-test does.

Recall from the EZ Manufacturing project that we do have three repeated-measures variables. Participants' social skills, task skills and performance scores were obtained prior to attending a leadership training workshop, then again after the workshop. The paired-samples t-test is the appropriate statistical test to determine whether or not there was a significant change in scores on these variables after the workshop compared to before participation. We will use social skills for the example in this chapter.