When samples are dependent, each case consists of a pair of data points, one data point from each of two samples. In dependent samples, also called paired samples, the data points may be paired in a variety of ways. One pairing, called a repeated-measures design, means the same participants provide data at two points in time. (This is also called longitudinal research because it follows participants over time or a pre-post design as participants are measured on the outcome variable before and after an intervention.) An example of a repeated-measures design would be measuring the level of anxiety in people before and after learning relaxation techniques.

Another type of pairing, called a within-subjects design, involves the same participants being measured in two different situations or under two different conditions. For example, a cognitive psychologist might measure how much information people retain when studying in silence and then measure information retention for the same participants when they study while listening to music.

Repeated-measures and within-subjects designs involve one sample of cases measured at two points in time or under two conditions. Find this confusing. “Why,” they ask, “is it called a two-sample test when there is just one sample of cases?” Unfortunately, this is statistical terminology that just needs to be learned. To a statistician, each condition in a dependent samples study is considered a “sample.”

294

Repeated-measures and within-subjects designs have a significant advantage over independent-samples designs. These dependent-samples designs control for individual differences, attributes that vary from case to case. Because the same participants are in both groups, the researcher can be sure that the two samples are comparable in terms of background characteristics. As a result of this, the researcher can be more confident that any observed difference between the groups on the outcome variable is due to the explanatory variable and not some confounding variable.

In an attempt to derive this benefit, researchers have developed a number of other paired-samples techniques in which different participants are in two conditions. In one, the pairs have some similarity because of some connection, either biological (such as that between two siblings), or formed (such as that between a romantic couple). Another is called matched pairs. In matched pairs, participants are grouped, by the researcher, into sets of two based on their being similar on potential confounding variables. For example, if a dean were comparing the GPAs of male and female students, she might want to match them, based on IQ, into male–female pairs. That way, a researcher couldn’t argue that intelligence was a confounding variable if one sex had a higher GPA.

Because there are so many different types of paired samples, the paired-samples t test has more names than any other test in statistics. But, whether it is called a paired-samples t test, dependent-samples t test, correlated-samples t test, related-samples t test, matched-pairs t test, within-subjects t test, or repeated-measures t test, it is all the same test.

The wide number of different names reflects how commonly used the paired-samples t test is. It is a commonly used test for several reasons. One reason is that many experimental situations are of a pre-post design where the outcome variable is measured before and after the explanatory variable is applied. Another reason is that controlling individual differences makes studies that use paired samples more powerful than studies that use independent samples. In a statistical sense, being more powerful means that the probability of being able to reject the null hypothesis, when it is false, is higher. As a result, a researcher needs a smaller sample size for a paired-samples t test than for an independent-samples t test. This is a big advantage of paired-samples t tests. If a researcher is studying a rare phenomenon or one where participants are hard to come by, a dependent-samples design is the way to go.

Here is an example of research that used paired samples to investigate how stress affects recovery from a physical wound (Kiecolt-Glaser et al., 1995). One sample, the people who were under stress, consisted of women who were caring for a husband or mother with Alzheimer’s disease. Because the researchers believed that age and socioeconomic status might influence physical recovery, they matched each caregiver with a control participant of the same sex, age, and family income who was not a caregiver. So, the participants were matched pairs of women, one a caregiver (the experimental group) and one a control.

Using a dermatology procedure, the researchers made a small wound on each participant’s forearm and timed how long it took to heal. The wound took almost 10 days longer on average to heal in the caregivers (M = 48.7) than in the controls (M = 39.3), and this difference was statistically significant. Why did this difference exist? Well, because the pairs were matched on age and socioeconomic status, it can’t be argued that the caregivers were older or poorer. With these confounding variables removed, it seems more plausible that it is the stress of caring for someone who is deteriorating with a chronic illness that affects how quickly one heals from a physical wound.

295

Now, having seen paired-samples in action and observed their advantages, it’s time to learn how to perform a paired-samples t test.