I have two groups (treatment/placebo).
for each group i have patients with paired data (before and after treatment).
Paired t test underlines a significant change for the after treatment (however this is for both study groups).
Which tests should i RUN to test whether there is a difference between the treatment and the placebo groups? (i.e the treatment group had a higher change than the placebo groups in the paired samples).
One more piece of information is required: what for of data is collected? can you share a sample data with a bit more insight to methodology?
continuous clinical scores.
scores before treatment, scores after treatment (paired). Two study groups: treatment and placebo.
One option would be to take the difference of the two data sets within each group (i.e., post minus pre) and then compare these difference scores between groups using an independent samples t-test (or if the data don't follow a t-distribution, then you can use a Wilcoxon rank-sum test, which is the non-parametric equivalent).
do these clinical scores represent Likert scale data? if yes, please go for the Wilcoxon rank sum test(as suggested by Seth M Levine), and pre the Shapiro Wilk test can be a good option to test the normal distribution of data.
You could just use a simple mixed analysis of variance (ANOVA) with treatment group as the between-subjects factor and pre/post as your within-subject factor.
what is the number in each group? for small groups you can use for each group: placebo before then after / the treatment group before and after Wilcoxon, for the comparison between the placebo group and treatment before then after, use the Man withney. both of these tests are non-parametric and are not demanding like the t test.
As Connor Sppiech suggested (assuming the data enables it), Mixed ANOVA, and hope for an interaction effect (GroupxTime). Then FU T-tests (corrected or not corrected is a topic for anothe discussion).
A more unorthodox answer might be to run a unit fixed effects model with a Differences-in-Difference predictor. This accounts for time-invariant unobserved heterogeneity.
Data should be in long-format. What you are doing is basically:
1. create a time dummy variable (0 - pre, 1 - post)
2. create a treatment variable (0 - control, 1 - treatment)
3. create a differences-in-difference predictor (time * treatment interaction)
3. run a unit fixed effects model (f.e. with plm for R, or fixef for R) with the did and the time-predictor as independent variables
The did-predictor estimates the within-subjects treatment effect. Traditional approaches with a repeated measures anova or simple t-tests often do a poor job in terms of controlling for time-invariant unobserved heterogeneity.
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