I am carrying out a DIF analysis comparing the scores of men and women on a questionnaire. A preliminary ANOVA revealed that when comparing total scores on the test, there is a significant effect of sex, but not of age or an interaction between sex:age.
I was going to have equal numbers of men and women (in total 530 men and 530 women), but I can't decide how to match them. I thought that matching approximately by age can't hurt, even if there is no significant effect of it. But would I be better off matching randomly?