Range, does it matters ?

#1
Hello

I am slightly confused about something. I will try to illustrate.

Let's say that if one takes a medication to treat a condition, the medication causes a side effect that reduces some attribute (blood test, etc...). A new medication was invented to be taken with it, to stop the reduction.

A small sample was taken, and the medication was given without the new medication to half of the sample, while for the other half, the two medications were taken together (treatment vs. control). The aim is to show that with the new medication, the reduction is significantly lower.

For each subject in the sample, the difference of the attribute was calculated: before-after, hoping for a difference as small as possible. In the treatment group the mean difference was 15, in the control it was 35 (s.d. 14 and 17 respectively).

other statistics: treatment: min=0 max=35 ; control: min=12 max=55

A t-test was statistically significant.

What confuses me, is that a second small sample was taken, and the attribute was measured at two time points, without getting any medication, and the variation is high. The attribute changed, the difference between the two time points was between -20 to 20 (looked "unbiased", but high variability).

I wanted to know, if the attribute is having a high variance, does that mean my t-test is not correct in a way ? What does it tell me about the means of the groups of subjects who did get 1 or 2 medications ?

thank you !
 
#3
Yes, you can say that. It is not another comparison group, because it didn't get the trigger that causes the reductions, and the whole point is to test the new drug after an event (the first drug ).

What bothers me is that the mean difference between the groups is just over 20, when the attribute itself vary sometimes in the same magnitude.

In other words, the first medication is NOT a treatment, it's a trigger that creates an event, which causes damage. The 2nd medication aim to treat this damage, and is being compared with those who just didn't get it (got the 1st, the event was created, but didn't get the 2nd to fix it).

The "3rd group", is just people who got nothing, and the attribute (my X) was measured twice in following weeks, and the variability was huge. It can mean the measure is not accurate or there is an unexplained variability. My question is if this influences the way I should look at the comparison test of groups 1 and 2.
 
Last edited:

Karabiner

TS Contributor
#4
wanted to know, if the attribute is having a high variance, does that mean my t-test is not correct in a way ?
The t-test takes into account the amount of variability,
as estimated from the sample data (have a look at the
t-test formula). One can nevertheless ask whether a
difference of > 1 SD between groups was actually to be
expected.

With kind regards

K.