FOOD9102 Chap.5 Binomial Analysis of Discrimination Data
Binomial Analysis of Discrimination Data
This chapter turns a count of correct answers into a verdict.
It builds the binomial probability from the guessing rate of each discrimination test, shows why the p-value is the whole tail of k or more correct answers and not the probability of exactly k, and teaches you to read the minimum-correct tables provided on Moodle at alpha 0.05 and 0.01. A 24-person triangle test is worked by tail sum and by table, and a drill page practises thresholds and the wording of conclusions.
The same reasoning applies to every discrimination test in the course.
Only the guessing rate changes, so once the method is secure for the triangle test it transfers directly to the 2-AFC, duo-trio and A-not-A tests used in the laboratory.
What this chapter covers
- 01
Two outcomes per ballot and the guessing rate p
- 02
The binomial probability of exactly x correct
- 03
The p-value as the tail of x or more correct
- 04
Reading the minimum-correct tables
- 05
Choosing alpha and the risk of a false positive
- 06
Writing the conclusion about the products
Worked example · free
Triangle test with 15 of 30 correct
- 1State the guessing rate: P = 1/3 for a triangle test, so chance alone expects 10 of 30 correct.
- 1Find the tail: P(X ≥ 15) for n = 30 and P = 1/3 is 0.0435.
- 1Compare: 0.0435 < 0.05 and the table needs 15 at 0.05, but 0.0435 > 0.01 and the table needs 17 at 0.01.
- 1Conclude: at alpha 0.05 the panel could tell the new blend from the old one; at alpha 0.01 the evidence is insufficient.
Key terms
- Guessing rate
- The guessing rate is the probability that a panellist answers a discrimination test correctly by chance, 1/3 or 1/2.
- Tail probability
- A tail probability is the chance of the observed count or any more extreme count, used as the p-value.
- Minimum-correct table
- A minimum-correct table lists, for each panel size and alpha, the fewest correct answers that reach significance.
- Type I error
- A type I error is a false positive: declaring a difference that is not really there, with probability alpha.
- Expected count
- The expected count is the number of correct answers chance alone predicts, the panel size times the guessing rate.
- Binomial calculator
- A binomial calculator is an online tool or spreadsheet function that returns exact or cumulative binomial probabilities.
Binomial Analysis of Discrimination Data FAQ
Why add up all the higher counts instead of using the probability of my exact count?
Because a p-value covers your result and every result more extreme than it. The probability of exactly your count is always smaller than the tail, so using it makes results look more significant than they are and can flip a verdict that sits close to alpha.
Which column of the binomial table do I use?
Use the P = 1/3 column for a triangle test and the P = 1/2 column for the 2-AFC, duo-trio and A-not-A tests. Then choose the alpha level, find your number of panellists and compare your count with the threshold printed there.
Should I use alpha 0.05 or 0.01?
The lecture leaves it to the company. Alpha is the accepted risk of a false positive, so 0.01 is safer but needs more correct answers. When a brief does not fix it, report both: a result can be significant at 0.05 and not at 0.01, and that difference is worth stating.
What should my panel size be for a triangle test?
A multiple of six, so that each of the six serving orders is used equally. Larger panels also lower the proportion of correct answers needed for significance, which is why the tables show the threshold count rising more slowly than the panel size.
Assessment move
Practise with the tables first, then confirm a few results with an online binomial calculator or the BINOM.DIST.RANGE function so that you trust both routes. For every problem, write the guessing rate, the expected count, the threshold or tail, the comparison and the conclusion, in that order. Most errors in this topic come from the wrong guessing rate, so check it first.
Then rehearse the borderline case where a result passes at 0.05 but fails at 0.01, and write both conclusions. Keep a printed copy of the tables with your lab notes, so you can check your group's result as soon as the class data appear on Moodle.
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