Discussion: Research Design and t Tests: How Are They Connected?

The t Test for Independent Samples

The t Test for Independent Samples Program Transcript

MATT JONES: The independent samples t-test is a comparison of means test that compares two means across an independent categorical variable. Let's go to SPSS to see how we conduct this procedure. In my independent sample t-test, I would like to test for any possible differences between socioeconomic status and respondent's race. In SPSS in my Variable View for the race variable, with the label "What is respondent's race of first mention?," I can click on the values. The reason I'm doing this is because an independent sample t-test can only test for differences in two means at one time. Therefore, I can only choose two races for this test. I can see in the race variable that there are a number of races present within this variable.

For this test, I will choose respondents that self-identified as white, which is denoted as 1, and respondents to self-identified as black or African American, denoted as 2. I'll need to remember those for the next procedure. To perform this procedure, Analyze, Compare Means, independent sample t-test. My test variable is my dependent variable for the variable of which a mean is calculated on. Therefore, it is that metric level variable, or any other variable where it makes sense to calculate a mean. In this case, it's the socioeconomic status index of the respondent.

Click on that. Move it over to the test variable. The grouping variable is my categorical variable. And in this case, it is the respondent's race. I move respondents race over to the grouping variable. Right away, behind the variable name, you will see a set of parentheses with two question marks. This is SPSS's prompt to tell me what races I should enter. SPSS knows that it can only calculate two means and therefore is asking me to define groups. So I must click on the define groups, group 1 and group 2. For group 1, I'm going to enter the value number of 1, which were those respondents that self-identified as white. For group 2, I'm going to enter 2, which for those respondents that self-identified as black or African American. Click Continue, and once I click OK, I will receive the output for my independent sample t-test.

The first piece of output I'm provided are the group statistics. I could look at the N and get an idea of the sample that ended up in the test. There are 1,094 white respondents and 191 black or African American respondents. I can see from the descriptive statistics that the mean socioeconomic status index score for whites is 50.99, and for black or African Americans it's 44.96. I'm also provided with standard deviations for each mean, as well as the standard error of the mean.

Before I interpret the independent sample t-test, I must first examine the Levene's test for equality of variances. An assumption of the independent samples t-test is that variances are equal across the two groups. SPSS, by default, provides you with this test to test for equality of variances. There's an F

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The t Test for Independent Samples

statistic, an associated p value with it. The Levene's test tests the null hypothesis that variances are equal. As you can see, the p value is 0.059, which is slightly above the conventional 0.050 threshold. In this case, you have to make a decision whether you reject or retain this null. If you set your level of significance at 0.050, and since 0.0059 is slightly above that, you would fail to reject the null, and assume equal variances.

Another option you might have is since this is so close to being statistically significant, you could also assume unequal variances, especially since you have an imbalance in the sample size above. For this specific test, I'm going to choose to interpret equal variances not assumed. As such, I interpret the bottom row. Here, I have a t statistic of 4.216, an associated p value of 0.000, which means the results are statistically significant at the 0.001 level. The mean difference between white and black or African Americans, on average, is 6.02, with a 95% confidence interval of the difference being between 3.21 and 8.84. Therefore, I can safely reject the null hypothesis and conclude that there is a significant difference in socioeconomic status between those who identify as white and those who identify as black or African American.

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