Do MCAT scores really predict med school performance?

Question

I am looking for correlations between MCAT data and performance in medical school. I am given MCAT scores from several hundred anonymized students and their final grades in five classes in medical school. I have tried Spearman and Pearson's correlations and have found little correlation, but that could be due to the non-Normal distributions that both the MCAT scores and each class' data exhibit. The MCAT scores are almost normally distributed, but by Shapiro-Wilk and Anderson normality tests they are not technically normally distributed with a p=0.10

While these data might just show that there is not a strong positive correlation between MCAT scores and medical school performance, I am asking for help on other tests that I could try to assess their relationship.

Answer 1

I'll assume that grades are measured on a 0-100 scales, and that there are no edge effects to be worried about (that is, the majority of students do not score near 0 or 100 in their classes).

To investigate the effect (here, I should say effect or association since this is not a causal model, but I digress) of MCAT score on med school performance, you can do an ANCOVA. In essence, you will estimate a linear regression which uses MCAT score to predict the student's grade. The coefficient for the MCAT grade will tell you how the expected med school grade changes for every additional point scored on the MCAT.

This approach makes several assumptions about the outcome. Most notably:

• Linearity

• That groups of students who scored differently on the MCAT have the same variance in their med school grades.

• That the distribution of med school grades given MCAT scores is normal

We can assess to what extent these assumptions are violated by looking at residual plots.