How would you analyze this ?

Hello all

I have a relatively simple case, however tricky.

I am testing a new treatment vs a control.

This is a new treatment that you do on one's eye, and suppose to decrease an outcome Y. For each subject, I use the treatment on one eye and the control on the second.

Pre using the treatments, Y is not exactly the same in both eyes, so when I compare how good the treatments are, I can't use an absolute value.

I wanted to set a paired t-test, of the % of decrease.

For example, if in one eye Y was 40, and now it is 29, there was a decrease of 27.5%, while on the other eye it was 41 and now it is 13, a decrease of 68.29%. The difference is then D=68.29%-27.5%=40.79% for this subject. Let's say I have N of them. I want to check the hypothesis that the mean of D is 0 vs. not 0.

Is what I am doing makes sense ? Any other ideas ?

Thanks !


Ambassador to the humans
What exactly is your measurement unit? What do the 40 and 29 represent when you say " if in one eye Y was 40, and now it is 29"?


TS Contributor
% decrease means that the same absolute decrease
gives different percentages, depending on the baseline
value (e.g. 44 - 4 is -9% while 40 - 4 is -10%). Is
this appropriate here?

With kind regards

I can't be more specific about the units, let me just say that high values of Y are bad, thus the treatments aim to take it down.

If I use absolute values, then I have a problem with the different baseline.

If I use percentages, than Karabiner just said something true, the same absolute decrease gives different percentages depending on the baseline. This is less problematic in my opinion than the first problem, but it ain't ideal.

Can you think of another way of looking at it ?
how would you set a repeated measures anova, I mean, what will be the dependent variable, the absolute value of Y after treatment ? and the grouping variable will be the treatment ?

what about a mixed model, with Y being the response after, and X1 is the value before using the treatment, and X2 is the treatment, while the subject is a random effect ?

One more idea: if I tell you that a decrease of 30% is clinically significant, and that the control is not expected to do that, and I decide to solve the problem by comparing proportions of subjects that had a 30% decrease or more in the treatment eye but NOT on the control eye, will it be appropriate to use the McNemar's test instead and to solve the problem ?
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TS Contributor
You have one outcome variable which you measure before and after
("time of measrement" as within subjects factor). In addition, you have
a between subjects factor. The group x time interaction tells you whether
the change between measurements was different between groups.

With regard to categorization of the response, I don't know. This would
surely be a huge waste of statistical information, and it suffers from the
problem that the same absolute decrease yields different % decreases,
dependent on baseline. But maybe it is the crucial analysis in your field.

With kind regards