# Which statistical test should I use which variables I should compare with which ones?

I collaborated in a study in which people with Alzheimer underwent a cognitive training. They were tested on the same executive control tasks 3 times throughout the process. Half of the participants did it just before the cognitive training, just after and 2 months after it had finished. The other half of participants did it 2 months before the cognitive training, just before and just after. This was done to be able to control for repetition of the task effects (in which participants get better because they have done the task more than once and not because the cognitive training). I am now confused about which variables to compare with each other exactly.

Thank you very much!

• Hi Ellen, welcome to CV! On this site there's no need to say "thank you" at the end of your post - it might seem rude at first, but it's part of the philosophy of this site (tour) to "Ask questions, get answers, no distractions" and it means future readers of your question don't need to read through the pleasantries. May 17, 2018 at 12:05

Q. I am now confused about which variables to compare with each other exactly.

It depends solely on the question you are trying to answer through your study.

For example:

1) You can compare the mean of the groups using t-test (https://www.itl.nist.gov/div898/handbook/eda/section3/eda353.htm) provided you have sufficient number of data points, so that the mean follows normal distribution.

2) If you want to check for differences in the effects of cognitive training on the groups you should be comparing the change in the respective performance of the individuals in the group after the cognitive training, i.e. the change in the performance of individuals of group 1 compared to change in the performance of individuals of group 2. A better measure will be percent change. You can compare the mean change of the two groups and test the null hypothesis that the means are not different using t-test(https://en.wikipedia.org/wiki/Student%27s_t-test).

3) You can also compare the variance of the percent change in the performance scores of the two groups using F-test(https://www.itl.nist.gov/div898/handbook/eda/section3/eda359.htm).

4) You can also analyse how effective is the cognitive training by only comparing the performance of a group before and after the cognitive training.

Lot more could be compared. These are just small examples!