I have confusion about a simple statistical analysis: one dependent variable measured before and after intervention in two groups. and the classical question is comparing effects between tow groups.

consider this case: (the value of independent vaiable presneted as 1 D vector)

group 1: Pre=[200 150 100 180] -> Post =[100 75 50 90]
group 2: Pre=[20 15 10 18] -> Post =[10 7.5 5 9]

the ratio(Post/pre) of change for both groups is 50%, which means no significant effect. while difference (Post-Pre) is significantly larger in the first group.

or maybe I should use Anova. what's your solution? Could you please help me to understand this issue!


It might clarify what is happening if we formalize it.

Suppose $Y_{it}$ is your outcome variable with $t\in\{0,1\}$ for pre and post, and $T_{it}\in\{0,1\}$ is the treatment indicator. (In your example we have that $T_{it}=t$.)

The question is, what is the conditional distribution of $Y_{it}$? If the conditional mean is $E(Y_{it}\mid T_{it})=\alpha+\beta T_{it}$, then you get $\beta$ by subtracting the pre mean from the post mean. If on the other hand $E(Y_{it}\mid T_{it})=e^{\alpha+\beta T_{it}}$, you get $e^\beta$ as $E(Y_{it}\mid T_{it}=1)/E(Y_{it}\mid T_{it}=0)$ which is the ratio, and $\beta$ by taking the log.

In other words, if you think the effect of the treatment is multiplicative, use the ratio. If you think it is additive, use the difference in means.

  • $\begingroup$ Thank for your insight. I am not familiar with the conditional distribution. Could you please tell me how i can check which one fits better to my data: additive or multiplicative? $\endgroup$ Nov 6 '19 at 3:28

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