8.1 Types of Two-Sample t Tests
Two-sample t tests are used to compare the mean of one population to the mean of another population. To conduct a two-sample t test, a researcher needs two samples of cases and an interval- or ratio-level dependent variable. Many experiments in psychology follow this format. For example, a group of researchers was interested in seeing how stereotypes affect behavior (Bargh, Chen, & Burrows, 1996). They divided undergraduate students into two groups, a control group and an experimental group. Both groups were given words that they had to put into sentences. The control group received neutral words and the experimental group was given words like Florida, wrinkle, and forgetful—words that were meant to prime a stereotype of elderly people. When the participants thought the experiment was over, they exited through a hallway and the experimenters secretly timed how long each person took to walk down the hall. The experimenters believed that being primed with words that are associated with the elderly would lead participants to act like elderly people and walk more slowly.
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The results showed that the control group walked down a 30-foot hall, on average, 1 second faster than the experimental group. One second does not sound like much of a difference, but when the experimenters analyzed the data using a two-sample t test, they found that the difference was a statistically significant one.
The difference meant that by the time an average person in the control group reached the end of the hall, an average person in the experimental group wasn’t yet 90% of the way down the hall (Figure 8.1). The experimental group averaged 2.6 mph compared to 2.9 mph in the control group. Being primed with an elderly stereotype did lead participants to act more like elderly people and a two-sample t test helped the researchers reach this conclusion.
There are two different types of two-sample t tests, the independent-samples t test (the focus of this chapter) and the paired-samples t test (see Chapter 9). Obviously, they differ in terms of the samples being analyzed, whether the samples are independent or paired. What’s the difference between independent samples and paired samples?
With independent samples, how cases are selected for one sample has no influence on (is independent of) the case selection for the other sample. Each sample could be a random sample from its population. With paired samples, often called dependent samples, the cases selected for one sample are connected to (depend on) the cases in the other sample. The cases in the samples are pairs of cases, yoked together in some way.
To clarify the difference between independent samples and paired samples, here is an example of two different ways to compare the intelligence of men and women to see which sex is smarter:
Dr. Smith obtains a random sample of men from the population of men in the world and a random sample of women from the population of women. Each person in the samples takes an IQ test, and Dr. Smith compares the mean of the men to the mean of the women.
Dr. Jones gets a random sample of married heterosexual couples. Each man and each woman takes an IQ test, and Dr. Jones compares the mean of the men to the mean of the women.
In the first example, the cases selected for one group have no influence on the cases selected for the other group, so that is an example of independent samples. In the second scenario, who the women are is dependent on the men, so that is an example of paired samples.
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It is important to know if the two samples being analyzed are independent or paired so that the researcher can choose the right two-sample test. The example above is one way that subjects can be paired. Table 8.1 contains some guidelines for determining if subjects are paired.
Practice Problems 8.1
Apply Your Knowledge
8.01 A gym owner is offering a strength training course for women. Eight women have signed up. The gym owner measures how many pounds they can bench press at the first class. He plans to measure this again, 12 weeks later, at the last class, in order to see if their strength has changed. Should he use an independent-samples t test or a paired-samples t test?
8.02 A public health researcher wants to compare the rate of cigarette smoking for a sample of eastern states vs. a sample of western states. Should she use an independent-samples t test or a paired-samples t test?
8.03 A nutritionist wants to compare calories for meals at restaurants with tablecloths to restaurants without tablecloths. He gets a sample of each type of restaurant and finds out the calorie count for the most popular meal at each restaurant. Should he use an independent-samples t test or a paired-samples t test?