- Imagine you are a researcher interested in sex differences in student’s attitudes toward homosexuals. Specifically, you want to test the idea that women are more accepting of homosexuals and thus have more positive attitudes toward homosexuals than do men. You collect data from 10 men and 10 women using a scale that measures homophobia. Your data looks like this (note: larger scores equal more positive attitudes).
MEN WOMEN 2 5 4 5 6 6 8 8 1 9 2 9 5 4 9 2 10 7 2 6
- Which of the following tests would you use to test your hypothesis?
Pearson’s Correlation Coefficient (r)
Pearson’s correlation is a measure of the linear relationship between two paired variables, and it is not a statistical test of a difference between means. While correlation could be computed and tested for the relationship between a continuous measure and a dichotomous measure, there is a more common approach to test the difference between the means for two groups.
Regression analysis can be used to derive an equation from which we can predict scores on one variable based on scores on another.Regression analysis is not usually used to test hypotheses about the differences between groups (though advanced uses of regression analysis do allow for this option). There is a more direct test for the difference between the means of two groups.
t-test for Independent Samples
The t-test for independent samples is used to compare means derived from unpaired (uncorrelated) samples. We have two independent groups here, women and men. To test a hypothesis regarding the difference in means between the two groups, we can use a t-test for independent samples.
t-test for Paired Data
A paired t-test is appropriate for data which are paired or matched, such as before-after data. In this case, we have two separate groups which we have no reason to believe consist of pairs. Because our groups do not involve pairing of scores from the two groups, they are termed independent.
If, for example, we were interested in how attitudes toward homosexuals might change after contact with a homosexual, and we had data that measured attitudes before (pre) and after (post) contact, then the paired t-test would be the statistical technique of choice.
It is important to distinguish clearly between paired and independent means t-tests as each test rests on different assumptions. The paired test assumes that the variables of interest may be correlated. In this manner each individual’s score on one variable (e.g., pre-test) is compared to their own score on the other variable (e.g., post-test). In this manner, the paired test takes into consideration each individual’s change or difference in scores.
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The Expert says…
The null hypothesis is that there is no difference between men and women in their mean attitude toward homosexuals.
A continuous measure of homophobia was collected from 20 independent people separated into two groups (men and women), so the data are not paired. A t-test for independent samples is appropriate for this situation.
An assumption of the t-test for independent groups is that the distributions of scores within each population are close to normal and that the variances of scores within each population are approximately the same. We should begin our analysis by plotting our data to see if these assumptions are reasonably well met. When we present our results, we should include information on the effect size and the precision of our estimates. Confidence intervals can be very helpful.