One of the questions repeatedly asked is whether the age difference between an older man and his partner is different than it is for a younger man and his partner. I approached this question from two directions. First, I segmented the men into 5-year groups and calculated the mean age difference for each group and their respective partners. This is the resulting graph:
Notice that the mean age difference steadily increases as the man gets older, ranging from under 5 years for men under 30, to almost 20 years for men in their late 50s. Performing an ANOVA on this reveals that overall the mean age difference is different for different age groups of men, F(9,179)=12.6, p<.0005.
After seeing this relationship I decided to perform a statistical procedure known as linear regression analysis to determine if this relationship was significant or not. And it is. For the statistically minded, F(1,187)=121.9, p<.00005; and more importantly, the man's age accounted for 39 percent of the variance in his partner's age (adjusted R2 =.39). The result of regressing age difference on the man's age is shown graphically below.
In plain English what these two graphs show is that the man's age is a very good predictor of how old his partner will be. The man's age alone accounts for 39 percent of the variance (a measure of variation) in the age of his partner. So it is a meaningful relationship in addition to being statistically significant. (Note: Many factors affect a man's selection of partner. The only raw data I had was the man's and woman's age, and based on this information alone the woman's age appears to be very important. Of course if I had more complete data other things would be revealed as important, possibly more important than age.)