Independent Sample t-Test

If married women are, on the average, two years younger than men at birth of first child, can we conclude that this is also true in our population?  Can we make an inference about the population (all people) from our sample (about 2,800 people selected from the population)?  To answer this question we need to perform a t-test.  This will test the null hypothesis that men and women in the population do not differ in terms of their mean age at the birth of their first child.  The particular version of the t test that we will be using is called the independent-samples t test since our two samples are completely independent of each other.  In other words, the selection of cases in one of the samples does not influence the selection of cases in the other sample.  We'll look later at a situation where this is not true.

We want to compare our sample of men with our sample of women and then use this information to make an inference about the population.  Click on "Analyze", then point your mouse at "Compare Means" and then click on "Independent-Samples T Test".  Find AGEKDBRN in the list of variables on the left and click on it to highlight it, and then click on the arrow to the left of the Test Variable box.  This is the variable we want to test so it will go in the Test Variable box.  Now click on the list of variables on the left and use the scroll bar to find the variable SEX.  Click on it to highlight it and then click on the arrow to the left of the Grouping Variable box.  SEX defines the two groups we want to compare so it will go in the Grouping Variable box. Now we want to define the groups so click on the "Define Groups" button.  This will open the Define Groups box.  Since males are coded 1 and females 2, type 1 in the Group 1 box and 2 in the Group 2 box.  (You will have to click in each box before typing the value.)  This tells SPSS what the two groups are we want to compare.  (If you don't know how males and females are coded, click on “Options", then on "Variables" and scroll down until you find the variable SEX and click on it.  The box to the right will tell you the values for males and females.  Be sure to close this box.)  Now click on "Continue" and on "OK" in the Independent-Samples t-test box. 

The output table shows that the mean age at birth of first child for men (25.17) and women (22.58) which is a mean difference of 2.41.  It also shows us the results of two t tests.  Remember that this tests the null hypothesis that men and women have the same mean age at the birth of their first child in the population.  There are two versions of this test.  One assumes that the populations of men and women have equal variances (for AGEKDBRN), while the other doesn't make any assumption about the variances of the populations.  The table also gives you the values for the degrees of freedom and the observed significance level.  The significance value is .000 for both versions of the t test.  Actually, this means less than .0005 since SPSS rounds to the nearest third decimal place. This significance value is the probability that the t value would be this big or bigger simply by chance if the null hypothesis was true.  Since this probability is so small (less than five in 10,000), we will reject the null hypothesis and conclude that there probably is a difference between men and women in terms of average age at the birth of their first child in the population.  Notice that this is a two-tailed significance value.  If we want the one-tailed significance value, we can just divide the two-tailed value in half.

Let's work another example.  This time we will compare males and females in terms of average years of school completed (EDUC).  Click on "Analyze", point your mouse at "Compare Means", and click on "Independent-Samples T Test".  Click on "Reset" to get rid of the information you entered previously. Move EDUC into the Test Variable box and SEX into the Grouping Variable box.  Click on "Define Groups" and define males and females as you did before.  Click on "Continue" and then on "OK" to get the output window.  There is not much of a difference between men and women in terms of years of school completed, but we still reject the null hypothesis since the observed significance level is less than .05.  By the way, this is because we have such large samples.  When the samples are large, it is easier to reject the null hypothesis.