327Chapter 13 :: Paired- and Independent-Samples t Tests
Step 3: This step uses the “Independent Samples Test” output box, which appears on a computer
screen as a single long box but has been broken in two parts to better fit in Figure 13.6. But this box
contains two lines of results for the independent-samples t test. There are two values for the t statis-
tic, for degrees of freedom, and for the significance level. Step 3 for the independent-samples t tests
includes an additional decision because you must decide which result line is the correct one to use.
The reason for two sets of results is that there are two ways of estimating the standard error of
the sampling distribution for independent-samples t tests. One method assumes that the variance
in the male population on number of hours worked is exactly equal to the variance in the female
population on number of hours worked. The other method does not assume the population vari-
ances are equal. Whether the variances in the two populations are the same or different affects the
calculation of the standard error, the value of the t statistic, the degrees of freedom, and the prob-
ability or significance level.
To reach a conclusion about whether the variances are or are not equal, an entirely separate
hypothesis test is done with the null hypothesis that the variances are equal. What appears in the
output under the heading “Levene’s Test for Equality of Variances” are the results of that separate
hypothesis test. If the significance level (“Sig.”) of Levene’s test is .05 or less, use the second line of
t test results, the “Equal variances not assumed” line. If the significance level of Levene’s test is
greater than .05, use the first line of t test results, the “Equal variances assumed” line.
Sometimes the two methods of estimating the standard error give you almost identical results
(as they do in Figure 13.6), and sometimes they do not. Always check the significance of Levene’s
test and then use the correct line of t test results.
In Figure 13.6, the significance level of Levene’s test is .668. Since this is greater than .05, the
first line of results is used. The two-tailed significance level for the t test for equality of means is
.041. Since this is a one-tailed hypothesis, we want the one-tailed significance level, which is .041/2
or .0205. (Make sure you leave Step 3 with the significance level for the t test for equality of means.
Do not leave Step 3 with the significance for Levene’s test. Once the significance of Levene’s test
tells you which row of output to use, you are done with it.)
How degrees of freedom are calculated for independent-samples t tests depends on whether
equal variances are or are not assumed. When equal variances are assumed, degrees of freedom are
simply N minus 2. A more complex formula is used when equal variances are not assumed.
The “Independent Samples Test” box also shows you the mean difference, the standard error of
the difference, and the 95% confidence interval of the difference. The mean difference is always
calculated by subtracting the sample mean for Group 2 from the sample mean for Group 1. If Group
1 has the higher mean, the mean difference will be positive; if Group 2 has the higher mean, the
mean difference will be negative. In the sample data, employed males report an average of 3.902
more hours of work per week than employed females.
Step 4: Since the probability is .0205, we reject the null hypothesis. Among the 1980 GSS young
adults, employed males did work significantly more hours per week than employed females.
A Second Example
“Was there a significant difference between the employed 1980 GSS young adults and the employed
1980 GSS middle-age adults in the number of hours worked per week?”