What is the difference between doing a linear regression and exhaustive descriptive statistics?

Question

I'm doing a report of the differences between women and men in their performance on a test with variables like: age, education, race and of course genre. I have two options:

1. doing a linear regression of the performance over age, education and all my variables to check if being a women makes an statistically significant difference.

2. Presenting exhausting descriptive statistics to see the differences between men and women. This descriptive statistics are like some kind of three in which I start by setting groups of age, for each group I separate different levels of education, then for each of those smaller groups I separate race and finally genre. At the end I can do a t test to check if the performance on the test is different for women (compared to men) in each small group.

I'm struggling on deciding how to approach to this problem because:

• I feel that doing the second approach is the same as doing the first one because I feel like "controling" for all variables and then checking if there is a different effect of my variable of interest in each group.
• Nonetheless, my variable of interest can have a different effect in each of the groups as compared with just one possible observable effect with the regression method.
• Besides that, following the second method is easier to explain to the directives. Is easier to say that "white, educated, old women perform better on the test" than "ceteris paribus, women perform better on the test".

What thoughts do you have on my situation?. What would you do and why?. What differences do you find between these approaches?

Thank you!

Answer 1

Go with the regression. Don't go with cross-tabulate-everything-by-everything, because this opens you up to excessive Type I error. If your interest is narrowly about a "gender effect," interact gender with your other predictors for a start, like this, assuming R syntax will be helpful:

mod<-lm(outcome~(covariate1+covariate2+covariate3)*gender), data=data))

Of course, base R will appropriately include the necessary additive terms, with a specification like the above. If you're not using R, the approach is the same; just the syntax is different.

But as with all linear models with interaction terms, remember that you have to look at the marginal effect. That's the partial derivative of your outcome with respect to your predictor. The 'effects' package is helpful. So to get you moving in R, try:

library(effects)
allEffects(mod)
plot(allEffects(mod)) 

See Understanding Interaction Models, which has 3,000+ cites for a more complete discussion. And no, I am not Brambor, Clark or Golder$\dots$

Answer 2

The second method will lead to a slew of confusing pairwise comparisons. The main concern you express about multiple regression is "my variable of interest can have a different effect in each of the groups", but you can model that (and test that assumption) by specifying interactions between variables.