In the context of the "Randomized Posttest-Only Control Group Design with Matched Subjects," a question arises regarding the appropriate statistical method for comparing the experimental and control groups. Should we utilize the paired samples t-test or the independent samples t-test, considering the matching process? The matching process aims to make the groups comparable, but does it imply treating them as if measurements were taken from the same individuals? Should we view them as distinct groups, despite the matching, and opt for the independent samples t-test, or is it more appropriate to employ the paired samples t-test, acknowledging the considerations of matched subjects?
A paired analysis is not restricted to data from the same subjects. The method is to eliminate common sources of (additive) variance from statistically non-independent measurements. It does not matter what the reason for the non-independence is.
let's say I have a group of 100 children aged 10-12. After calculating their ages in months, I paired the ones closest in age, randomly assigning one to the experimental group and the other to the control group. Subsequently, I had the experimental group play basketball for 6 months. Now, I want to compare the heights of the two groups. Should I use an independent samples t-test or a paired samples t-test?
There is no simple answer to that question. There are many subtleties to be considered that do play a role when the age difference plays a role. For instance, a paired analysis would assume that the effect under study is independent of age, something that is unlikely in your case. But the larger problem here may be that age is not a very direct measure of the relevant features. Properties like body size, weight, sportiness, sport experience (particularly in basketball), other talents and activities, social competence and so on may be much more relevant in determining or influencing the effect of your "treatment" than age. All you capture will be a very vague correlation between some of these variables and age (assuming, for instance, that body size is higher, on average, in older children). Therefor I think that pairing is not really helpful here, as it will introduce more problems (in clarifying the underlying assumptions being made and the interpretation) than it will solve.
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