I am studying, and am fairly new to research methods and design, and hence hope to get some guidance on my analysis plan.
I have 3 questions here, and attaching a structural model as reference.
Context: My research question aims to prove that a novel incentive scheme (which I shall call a ‘strong’ intervention), is better than a traditional scheme (‘weak’ intervention). In other words, applying X1 drives more increase in Y than X2.
I have 3 sets of participants: 1 set = strong intervention, 1 set = weak intervention, 1 set = control (i.e. no incentive scheme).
Q1: To answer my RQ, do I simply prove that the difference in means between Y (for X1 and X2) is significant? Is there any value in comparing Y_X1 and Y_Control (i.e. H1a) and Y_X2 and Y_Control (i.e. H1b), and if so, must I apply Bonferroni corrections by dividing significance level (0.05) by 3?
Q2: I intend to use a linear regression model (all assumptions satisfied, of course) to model the relationship between X1 and Y, as well as X2 and Y (i.e. H1a and H1b). When I am evaluating the effects of control variables (Age, Gender, etc.), do I need to once again “Bonferroni correct?”
Q3: I intend to use a SEM software to ‘solve’ the correlations from H2 to H5, so that I can investigate the effect that travels through the mediators. Can SEM give me the correlations for H1a and H1b as well, or do I need to do pairwise correlations to get my H1 and H1b?
Appreciate your guidance to a stats noob. Thanks!