Correct significance test

#1
Can someone please let me know, in product testing, when a respondent evaluates say 2 products, what the correct significance test is for testing both the means and percentages? The independent t test is for different respondents, and it’s not strictly speaking a paired test with before and after. A respondent gives ratings on first product and same respondent then gives ratings on second product. Any help would be much appreciated, thank you.
 

Karabiner

TS Contributor
#2
For ordinal rating scales: sign test. For interval scaled ratings and small sample size: Wilcoxon signed rank test.
For interval scaled ratings and sample sizes > 30: dependent samples t-test.

With kind regards

Karabiner
 
#3
If the rating variable is normally distributed then the two sample t-test is fine for samples that are smaller than 30. Student himself (i.e. W.S Gosset) had a sample size of n=4. The t-test is a small sample test.

So if one person evaluated two products of origin A and two products of origin B ( preferably in random order) then it is fine to use a t-test (provided that it can be assumed that the data are normally distributed). The t-test is relatively robust to violations of assumptions.