Is a paired t-test correct for comparing two groups when there is a confounding variable? I have two groups of data, one is a group of people at age 5 and the other set of data is the same group of people when they are 8 years old. I want to test if group two (age 8) eat more food under a certain condition, compare to when they were 5 years old. 
However, I know that in general kids eat more when they are older, hence, simply a paired t-test would give me the statistical difference, but I wouldn't know if this difference is the result of the age or condition. 
I'm wondering what test I can use which would take into account this.
 A: In general, the approach that would be taken to this would be to have two groups of children. One group would be under the condition, and the other group would not. You would then compare the change in consumption between the children under the condition and the control children, using, for example, a two-way mixed ANOVA to determine whether there is a change in consumption after you've controlled for the natural change that occurs over time.
If you do not have a control condition, however, then there is no statistical test which can compensate for this by controlling for the natural change. All you will be able to do is to use the paired t-test, while accepting that any effect of your condition that you observe will be confounded by the natural change that may occur due to age.
A: Paired $t$-test is used when the exact items are treated before and after something special occurred on them. In your problem, you would like to examine the effect of age on eating patterns on the same kids. 
The paired $t$-test have more one assumption about Normality of the differenced data ($Dif_i = X^{before}_i - X^{after}_i$) that you should check it based on some standard tests like Kolmogorov-Smirnov Test. 
