# Statistics: check independence of two continuous variables

1. May 20, 2010

### azay

1. The problem statement, all variables and given/known data

I have a table of paired measurements: IQ and brainsize of a person.

Question: is there a significant connection between brainsize and IQ?

2. Relevant equations
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3. The attempt at a solution

The only test in my course notes that checks indepedence of continuous variables is a correlation test (Pearson's I think). For this test it is assumed the variables stem from a normal distribution. Brain size data stems from a normal distribution. However, a histogram shows that the IQ's stem from a bimodal distribution. (we must not use any a priori knowledge about IQ tests). So I cannot use this test. The only other relevant test is the 'independence test between 2 discrete variables (with the contingency table and chi-square distribution)'. I could use this test as a second choice by putting the data in classes. However, the number of measurements is too small for this test to be of any use. (there are only 38 measurements and each class needs to contain at least 5 elements)

In the bimodal distribution, the IQ's below 110 can be considered to be normally distributed, and those above 110 too.

Is it then a 'correct' idea to do a Pearson correlation test on those 2 seperate sets? Ie. to do the test for people with IQ's below 110, and again for people with IQ's above 110?

Thanks