Today I was asked about the following variant of a testing-question, and the proposal by the asker was a modification of a t-test, but I'm not sure about this.
The situation is as follows:
there is a certain method to cure some physical problem, measured metrically by cm (say growth of bones, angle of mobility of an arm or whatever (don't want to disclose the actual item here)). We have, per subject, two measures: status before intervention/cure and status after intervention.
There are 50 people treated/tested and the differences "cm_after_treat - cm_before_treat" are evaluated by a paired t-test, finding some average improvement of the test-item, and a significance indication with $p \lt 0.05$ .
But now, there are two concuring methods of intervention, taken in two subsets of clients. We want to test, whether the difference of the improvements by method_1 is better than by method_2. Because this subgroups are independent, one would think of a second t-test, this time not the paired one.
Would one possibly apply a "2-sample" t-test on the calculated individual differences/improvements "cm_after - cm_before"?
Or would one apply a procedure from the wider portfolio of variance-analysis here ("Oneway" "Anova" "..." - I'm likely talking in the jargon of SPSS here, thus
SPSS as tag might be appropriate for the question) on the two items "test_before", "test_after" with a 2-level-factor "method"?
Maybe this is a rather trivial question but I feel no more fluent with this after a couple of years of distance to concrete application of statistical testing.