# Statistics on tastings

Some people at my workplace have had some fun lunch discussion as of late, concerning some people's alleged ability to taste the difference between things one thought one shouldn't be able to taste a difference between. We have hence decided to do a small "competition" (or however you want to call it), where said abilities are to be tested and quantified. Being the one of us who took a course in statistics, I'm trying to find out the best experimental design and statistics to use. Not really being a statistician, I went here to get some help, for which I'd be very appreciative!

One of the tests we will do is the ability to taste the difference between the bottom and top half of an apple (i.e. flower vs. stem parts). My initial thinking was a simply blind-folding the taster and giving them parts of an apple one at a time, recording if they were RIGHT or WRONG (categorical values). I'd also have pieces coming from different apples, both of the same and of difference kinds of apples. A null hypothesis here would be 50 % (i.e. same proportion of right/wrong, p=0.5), and alternative hypothesis would be > 50% (p_hat). Standard error (SE) is sqrt(p(1-p)/n) and Z = (p_hat - p)/SE.

Would this be a correct way of doing it? If not, how far off am I and what should I do instead, perhaps a t-test? What if the test is the tasting a difference between three things, rather than two; would it be wrong to still use a simple right/wrong metric, or should something else be used?

Fisher himself had such a discussion, which is detailed in his book, The design of experiments. Basically a lady working with him claimed she had the ability of differentiating tea made with boiled water than one without boiling, if I remember correctly; Fisher designed an experiment to check it. For an overview, see this wikipedia article, or check the book itself, I think it started with this example. He used the Fisher exact test.

• I'm not really sure how I get my data into a 2x2 contingency table. I mean, my only values are right/wrong, for a person - how do I expand that into a table? – erikfas Jan 16 '15 at 14:03
• She actually claimed she could taste whether the tea was added to the milk or the milk was added to the tea ;) – Nick Thieme Jan 16 '15 at 16:50
• @Sajber the contingency table is not right/wrong answer, but it would be 'person answer flower/stem part', for example for the rows, and 'real: flower/stem part'. The 'right' answer is if you fall into the diagonal of the contingency table. Ideally the test is double blind, so even the guy who asks doesn't know the correct answer (although is registered somewhere else). – chuse Jan 26 '15 at 10:08