Help needed: multiple test in a small size group

#1
The situation is: I have a group of data from 4 individuals. Each individual has tested under two different conditions, and the tests were repeated multiple times. Some are repeated four times and some are six times. Now I am going to use t-test to evaluate the difference of the measurements between the two conditions. To make an average for each individual would yield only 4 pair of data (n=4), which is of course lack of statistic power. Can I use pooled data (all tests from all the 4 individuals), which in total about 22? I guess this may create a bias that weighted towards the one with the most repeated test if the tests are unequal; If this is the case, can I randomly eliminate some of the tests to have the tests in each individual equal? Or if there is any way to make a correction when either an equal or unequal number of tests is used? Or after all, to use multiple tests from a small group is not a good idea at all!

Thanks for any suggestions, greatly appreciated!

Sand
 
#2
Sand,

The t-test is valid when all observations are made independently. However, we know in this case that the 22 observations are certainly not all independent. If you want to test for a difference in test score under the different conditions, then you must accept that the number of experimental units is 4, otherwise your inferences using the t-test will be misleading. This is because multiple tests for a single individual will only tell you about the WITHIN-individual variability. In order to make inferences about the different conditions, you must estimate the BETWEEN-individual variation.

If you cannot collect data using additional subjects, I would suggest looking into a non-parametric or exact test. Also, consider formulating your test with the differences in test scores for a particular individual rather than the test scores themselves.

BioStatMatt