A question about paired sample t test

Pele

New Member
#1
I have a question about paired sample t test, your advices are much appreciated. Thanks.

I know paired-sample t test is for the same group of people to test their pre and post tests and see if they have a significant gain between their pre and post tests. If the treatment is progressive, can I use the same people to collect data over time and run paired-sample t test together because the sample size is very small (only 6 persons)?

The research design looks like this:

Year 1: Treatment 1 with 3 persons' (ABC) pre and post tests
Year 2: Treatment 2 (improvement of treatment 1) with the same 3 person's (ABC) pre and post tests
Year 3: Treatment 2 (improvement of treatment 1) with the other 3 persons' (DEF) pre ad post tests

In this case, can I run paired-sample t test for 9 data points (3 data points [ABC] from Year 1, 3 data points [ABC] from Year 2, and 3 data points [DEF] from Year 3) and then report the effect of treatment 1 in general (since treatment 2 is based on the improvement of treatment 1)?

I know some people might argue that I use the same people twice (ABC) in year 1 and year 2. But can I argue that paired-sample t test is concerned with the "gain" between pre and post tests. Thus, although they (ABC) might have a higher score for the pre test in the second year, we expect them to have a higher score for the post test too. That is, we expect ABC to have a "gain" in both Year 1 and Year 2.

Your insights and advices are much appreciated. References are much appreciated too.
 

CB

Super Moderator
#2
A paired t-test is generally used with a single sample of people, and two time points. In your case you might do something like *three* separate t-tests (one for treatment 1, one for treatment 2 sample 1, and one for treatment 2 sample 2). There is no straightforward way that you could combine results from multiple groups and time points into a single paired t-test.

The bigger issue here is that you do not have a large enough sample to be doing any sensible inferential stats. Unless the treatment effect is huge, you are not going to find any significant effects. You might be better off doing something like a case study design, or alternatively looking at a different data collection method. E.g. larger sample with random assignment to conditions.