statistical test to check difference between two groups

Question

I have dataset of 4000 students and for each student I recorded following variables:

1) Gender (Male or Female)

2) Dev score (a score on 1 to 10. The scores are in integers only). The dev score is basically the score of a child in the intelligence. Higher values represent more intelligence.

3) Diag score (a score on 1 to 10. the scores are in integers only). Represents whether a child's score of mental illness. Higher score means a child is more likely to develop some mental illness in the future.

I want to know whether there is a significant difference in Dev score between male and female students. I did a t-test for this. Similarly, I want to know whether there is a difference in Diag score between male and female. I also did a t-test for this.

If I want to know whether there is a significant difference in Dev score and Diag score between male and female students and whether the difference is higher in Dev comapred to Diag (or vice versa), which test (parametric and non-parametric test) should I do?

Answer 1

One way to compare the magnitude of the sex differences for dev and diag scores would be to create a linear contrast which would test for a difference of differences.

By creating a set of weights that sum to zero (a so called orthogonal contrast), and multiplying your means by those weights, you can test for specific combinations of means.

My understanding of the topic comes from Maxwell and Delaney's excellent book Designing Experiments and Analyzing Data and I highly recommend the treatment there. I note that my graduate stats instructor still has his detailed chapter notes on the topic online if you don't have access to the book itself: Maxwell and Delaney Notes Ch 4

In your case, the weights (1,1,-1,-1) should work just fine. Assuming a two-tailed test,

Null: (1)mu[male diag] + (-1)mu[female diag] + (1)mu[male dev] + (-1)mu[female dev] = 0

Which is really just different notation for:

mu[male diag] - mu[female diag] = mu[male dev] - mu[female dev]

which seems to be you question of interest.

The linked notes focus on implementation in R but should be general enough to get you going.

Bear in mind, that you will want want to consider if correction for multiple comparison is appropriate here, which it almost certainly is if you decided on the tests post-hoc.