Problem 8. A common statistical test used in sensory discrimination experiments in food science (as well as consumer products like household cleaning products, cosmetics, etc) is the so-called triangle test.It is often described as follows. To determine whether there is a perceivable difference 3 between products say, an established soft drink and a newly developed soft drink with a cheaper recipeyou assemble a tasting panel and present each member with three samples (cups of soft drink), two of which are the same (say, the established recipe) and the other different (the cheaper recipe). The samples should look identical and be presented in random order to each taster. The taster is asked to select the one sample that's different from the other two. The total number k of correct selections (for the n tasters) would be the result of random guessing if there were no perceivable difference, so a 1/3 chance of being correct, so look up k in the table of the cumulative binomial distribution with p = 1/3 and n = the number of tasters in the panel. If the p-value for k is less than 0.05 you declare that there's a significant perceivable difference. Suppose there are 23 tasters and 12 of them correctly select the different sample. What is the p-value here? How many tasters would need to be correct (out of 23) to declare a significant perceivable difference? 2. How does this procedure square with our hypothesis testing setup? Examine critically from the perspective of our setup: what are the hypotheses? What is the sample space? What are the probabilities?
Problem 8. A common statistical test used in sensory discrimination experiments in food science (as well as consumer products like household cleaning products, cosmetics, etc) is the so-called triangle test.It is often described as follows. To determine whether there is a perceivable difference 3 between products say, an established soft drink and a newly developed soft drink with a cheaper recipeyou assemble a tasting panel and present each member with three samples (cups of soft drink), two of which are the same (say, the established recipe) and the other different (the cheaper recipe). The samples should look identical and be presented in random order to each taster. The taster is asked to select the one sample that's different from the other two. The total number k of correct selections (for the n tasters) would be the result of random guessing if there were no perceivable difference, so a 1/3 chance of being correct, so look up k in the table of the cumulative binomial distribution with p = 1/3 and n = the number of tasters in the panel. If the p-value for k is less than 0.05 you declare that there's a significant perceivable difference.
- Suppose there are 23 tasters and 12 of them correctly select the different sample. What is the p-value here?
- How many tasters would need to be correct (out of 23) to declare a significant perceivable difference? 2. How does this procedure square with our hypothesis testing setup? Examine critically from the perspective of our setup: what are the hypotheses? What is the
sample space ? What are the probabilities? - Does a significant perceivable difference mean that there's a high probability of there being a difference? 95% or better? If not, what does it mean? Explain.
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