anova vs regression vs paired t-test

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    Thank you to anyone who has the expertise and the time to respond to my querry.  🙂


    My experiment involves complementary medicine, memory, and anxiety.  There are two groups, acupuncture and control.  Everyone takes an anxiety test that offers numerical scores for state and trait level anxiety, between 20 (lowest) and 80 (highest).  This gives us the initial state level value (SA1) and the trait level (TA, which is believed to be stable across situations).  Then 1/2 get the complementary treatment and 1/2 do not.  Then everyone takes the state-portion of the anxiety inventory again, giving us both the “after” score for state anxiety (SA2) and the “change from before to after”, or ∆SA.  Then everyone takes a computerized memory test that gives a numerical score between 0 (lowest) and 75 (highest). 

    Our variables are:

    • SA1
    • SA2
    • ∆SA
    • TA
    • Memory score
    • Treatment or control group

    My main hypotheses are that the treatment will improve performance on the memory test and that it will reduce anxiety.  In a paired t-test between the two groups, treatment group does 7% better on the memory test (p<0.03) and has lower SA2 anxiety (p,0.05).  I plotted the data for SA1 vs memory score, SA2 vs memory score, ∆SA vs memory score, and TA vs memory score; and the data points were all over the place, showing no clear trend.  Question is, do I need to run analysis to prove that there is no relationship between three or more variables?  Or can I say that no clear pattern emerged?  If I do need to prove it statistically, would it be more appropriate to run regression analysis or ANOVA?  Is it appropriate to use the paired t-tests to show the relationship between the two variables (treatment and memory; and treatment and anxiety)? 


    Thank you for your reply.  My hypotheses did include the three-way interaction.  Does this intervention improve memory, and is that improvement due to the drop in anxiety.  I know we can only show correlation and not causation.  So the intervention did reduce anxiety and did improve memory, but it is not the case that those with the lowest anxiety (nor with the greatest drop in anxiety) performed best on the memory test.  So I think I want to report that the improvement in memory did not appear to be related to the effect on anxiety.  What type of test would you recommend for that?  I was thinking ANOVA or regression, but I am not familiar with pearson r or point biserail.  Are those better?

    darrin coe, ph.d.

    I would suggest multiple regression.  you can use dummy variables to indicate membership in tx or control group.  then enter each variable in a theoretically appropriate way.  score on memory will be the outcome variable.  If this was my analysis I’d enter trait anxiety, state anxiety 1, state anxiety 2, change in state anxiety, control membership, and finally treatment membership.  This should tell you ultimately if tx reduces SA.  You could then designate interaction terms i.e. tx X change in state anxiety; Control X change; etc. 


    I think this type of modeling would get you want you want to know.


    darrin coe

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