[Students T Test] - paired or unpaired unequal variance?

#1
Hi,
i have a question as to whether a paired test in this instance is appropriate.
Scenario: an experimenter is testing a new treatment to see if it increases a certain property of a substance. The experimenter chooses 4 groups of the substance and takes 3 sample from each group and tests for the specific property. The experimenter then adds a known amount of the treatment to the 4 groups and then takes 3 new samples and tests for the specific property.

I'm just wondering, as the pre and post treatment samples came from the same 4 groups, does that qualify them for a paired T test? Or is an unpaired unequal variance test more appropriate?

Thanks in advance.
 

bryangoodrich

Probably A Mammal
#2
If the selection of treatments in the post tests are known and match those in the pretest, then the samples are paired. If you merely took 3 samples from the population and tested them, then took 3 samples from the population again and sampled them, we should expect the choice of samples to be independent (and we have no pairing between pre and post). The only difference I see in the design you explain is that instead of one overall population, say N, you have 4 group populations n1, ..., n4 (such that n1 + ... + n4 = N). Maybe some sort of block designed ANOVA would be better, but that is out of my reach at the moment. In any case, it does appear like a multitude of independent samples from the 4 groups. Pairing only occurs, from what I see, is if you can actually match the post treatments to the pre treatments, not just their group.