We have a software package used by our sensory lab, and one basic test that is done is a 'Triangle Test', where tasters are presented 3 samples, A B and C, of two products, 1 and 2. For taster #1, A and B might be the same (Product 2), while C is different (Product 1); for taster #2 it might be A and C (Product 1), with B being different (Product 2). Etc. Etc. The tasters select which of A, B, or C they think is the odd man out. The goal is to determine if there is a significant difference between Product 1 and 2. The software package appears to use a Pairwise t-test to evaluate the results. Is this the correct way to do this in JMP? The data for each taster would seem to me to be simply a 0 or 1, as in 'they either did or did not detect a difference'. Please advise how I might analyze these results in jmp (I have 6.0.3) and how the data table should be built. Thank you, D. Lewis
The use of a paired t-test in this situation seems very strange to me, as a triangle test is essentially a one-tailed comparison calculated from a binomial distribution with P=1/3. If there's no difference between the products, you'd expect roughly one-third of your panel to pick the odd man out purely by chance, but if there's a genuine difference between the products then you'd expect that proportion to rise. The question therefore is how high it needs to rise above 1/3 before you're forced to conclude that they're not just guessing.
Most people would use a set of look-up tables in this situation (for example in the back of "Sensory Evaluation of Food: Statistical Methods and Procedures" by Michael O'Mahony) to decide how high the proportion of correct panelists needs to be to set a significant result, but the actual calculation is easy enough to perform. There is now a small JSL program for calculating the significance levels for an assortment of difference tests, including triangle tests, in the Biotechnology Industry section of the JMP File Exchange section of this site, which might be useful to you.