I have two datasets (both with experimental group and control group) which measure the same construct with two different forms due to age differences. All groups completed the measure at a pretest and post-test. The summation score of each individual at each time point was calculated.
Form A (10 items):
Exp group Pretest Post-test
Control group Pretest Post-test
Form B (6 items):
Exp group Pretest Post-test
Control group Pretest Post-test
I would like to transform the raw score into Z-score and aggregate the data from two groups, so that I can evaluate if there is any pre-post change in this construct. I wonder which mean and standard deviation to use for the calculation. Here are some of my considerations.
Option 1: Overall M and SD of both groups at pretest (T1)
The assumption is that the pretest M and SD represent the population without intervention. The post-test Z-score should reflect how much the score varies from the population mean at baseline (when Z = 0). My main concern is whether this ignored the differences between the time points where the data is collected (i.e. the M at the two time points may be different) and I can't attribute the pre-post difference to the intervention.
Option 2: Aggregating all the data and calculating a single overall M and SD
The assumption is all the data collected are from the same population/distribution, which is not true for the experimental group (as they received the intervention). However, the time-point difference seems to be considered and the M should be between T1 and T2.
Option 3: Use the overall M and SD for pretest score and use the control group M and SD for post-test score
This is a weird one, which I am not comfortable with. The overall M and SD represent the population at T1, while the post-test score of control group represent the population at T2.
May I have some advice on which option would be appropriate?