Analysis of Variance (ANOVA)

In this section we have compared two groups (males and females).  What if we wanted to compare more than two groups?  For example, we might want to see if age at the birth of their first child (AGEKDBRN) varies by educational level.  This time let's use the respondent's highest degree (DEGREE) as our measure of education.  To do this we will use One-Way Analysis of Variance (often abbreviated ANOVA).  Click on "Analyze", then point your mouse at "Compare Means", and then click on "Means".  Click on "Reset" to get rid of what is already in the box.  Click on AGEKDBRN to highlight it and then move it to the Dependent List box by clicking on the arrow to the left of the box.  Then scroll down the list of variables on the left and find DEGREE.  Click on it to highlight it and move it to the Independent List box by clicking on the arrow to the left of this box.   Click on the "Options" button and this will open the Means: Options box.  Click on the box labeled "Anova table and etc.  This should put a check mark in this box indicating that we want SPSS to do a One-Way Analysis of Variance.  Click on "Continue" and then on "OK" in the Means box.

 

In this example, the independent variable has five categories: less than high school, high school, junior college, bachelor, and graduate. The output shows the mean age at birth of first child for each of these groups and their standard deviations, as well as the Analysis of Variance table including the sum of squares, degrees of freedom, mean squares, the F-value and the observed significance value.  The significance value for this example is the probability of getting a F-value of 68.266 or higher if the null hypothesis is true.  Here the null hypothesis is that the mean age at birth of first child is the same for all five population groups.  In other words, that the mean age at birth of first child for all people with less than a high school degree is equal to the mean age for all with a high school degree and all those with a junior college degree and all those with a bachelor's degree and all those with a graduate degree.  Since this probability is so low (<.0005 or less than 5 out of 10,000), we would reject the null hypothesis and conclude that these population means are probably not all the same.

There is another procedure in SPSS that does One-Way Analysis of Variance and this is called One-Way ANOVA.  This procedure allows you to use several multiple comparison procedures that can be used to determine which groups have means that are significantly different.