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I've been trying to find a definitive answer as to what is the proper application of t-tests in the two (fictitious) scenarios given below and the associated formulas (overlapping sample vs. non-overlapping samples):
(A) 400 respondents - 200 see product "X" only and give it an average rating of 4.75 on a 1-5 scale. 200 respondents see product "Y" only and give it an average rating of 4.25 on a 1-5 scale.
(B) 400 respondents see both product "X" and product "Y" - half see "X" first and half see "Y" first. Product "X" achieves an average rating of 4.75 while product "Y" gets an average rating of 4.25.
I've been trying to convince my colleagues that the t-test for significance (regardless of confidence levels) uses different formulas for the two scenarios - the first involves non-overlapping samples while the second uses overlapping samples. Would someone be able to provide me with 1.) refutation or validation of my argument that these two examples would require two different formulas and 2.) if my thinking is correct can i get the actual formulas that would be used in each case? I don't need the actual T-scores (since I didn't provide SD & SE anyway) - just need to know if two different T-Tests are called for and what the two formulas are (if, in fact, two are needed).
Thanks so much - this would resolve a lot of issues.
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