Food Sensory scores on the hedonic scales of 5, 7 or 9 are logically categorical variables (ordinal variables). The scores scales stands for 1="extremely dislike to the largest 5 or 7 or9 = extremely like", with the scores indicating moderate, slight, neutral liking scales in between them. However the data is analyzed as though the scores are continuous variables. They are averages and the means are grouped (ANOVA and Multiple comparisons). Why are they treated like continuous data when they are not? Anyone with explanations? Thank you!
a) people know only ANOVA so they apply it to anything they have
b) people see that others do it (and successfully publish) so they parrot
c) there is no really continuous data, and all we have are more or less good approximations to that ideal; in some cases the approximation may be sufficient.
The main problem here is not that scores are treated as if it was a continuous random variable. The main problem is that most people do not evaluate thoroughly the assignment of quantities (the score values) to the original (ordinal) categories. Simply using ranks may not well reflect the practical implications. It is likely that a score of 2 does not mean "twice the amount" (of whatever) of a score of 1. So it remains unclear what the quantity is about anyway. But if we geneousely assume that the assignment of quantities is meaningful, the next step would be to find/identify/evaluate a sensible probability distribution that is associated with that (assumed continuous) variable. This is also usually completely neglected and it is frankly assumed that the probability distribution of the variable is the normal distribution (what often is not very sensible, because the domain is limited and interesting things happen when the mean is close to one of the limits).
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