Change in proportion - two timepoints

Question

In the first time point - 75% (485 out of 646) of boys and 63% (350/555) of girls are in group A.

In the second time point - 80% (480/600) of boys and 45% (225/500) of girls are in group A.

So that is a difference of 5% for boys and 18% for girls between the two time points:

I was hoping someone could point me in the right direction as to what test I should use to compare this change (5% versus 18%) between two timepoints. Note that the boys and girls in the first timepoint are not the same ones in the second timepoint.

Is this percent change assumed to be normally distributed?

Answer 1

The following does not formally test the difference in change between boys and girl, but it tests whether the change over time in each of these groups is significant.

You could run a chi-square test on boys t1 vs. t2: p = 0.49

And on girls t1 vs. t2: p < 0.01

So boys do not change significantly over time, but the proportion of girls does significantly decrease.

For reference, this is the R code I used:

chisq.test(cbind(c(485,646),c(480,600)))
chisq.test(cbind(c(350,555),c(225,500)))