I have 60 consumers who have all rated the same 2 food samples. Should I use a 2 sample t-test to check for a difference between the 2 foods?
The word ‘sample’ can have 2 different meanings. Market researchers and product developers will often refer to the products that they give to consumers as samples. In statistics, and in the context of our example, a sample refers to the group of consumers who are taking part in your study; as the consumers have been selected, or ‘sampled’, from the wider population of consumers. So the 60 consumers taking part in your study constitute a single ‘statistical sample’, and the answer to the original question is ‘no’. The appropriate analysis here is to use a paired sample t-test, since there is a pair of product scores from each consumer in the statistical sample. In a different experiment where one group of consumers test the 1st food product, and another, unrelated, group of consumers test the 2nd food product, then the 2 sample t-test would be the appropriate thing to do.