# Triangle Test

The triangle test is a discriminative method with many uses in sensory science including:
•  gauging if an overall difference is present between two products
•  selecting qualified panelists for a particular test
•  determining whether shifts in processing or ingredients have significantly changed a product.

## Test Principle

During a triangle test, a panelist is presented with one different and two alike samples. If possible, all three samples should be presented to the panelist at once, and the panelist should be instructed to taste the samples from left to right. The six possible order combinations should be randomized across panelists. For samples A and B, the six possible order combinations are: AAB, ABA, BAA, BBA, BAB, and ABB. The panelist is instructed to identify the odd sample and record his answer.

## Data Analysis

For evaluation with the chi-square distribution, use: X2=Σ (|O-E|)2/E, where O=observed and E=expected. To determine the number of expected correct answers, multiply the chance of choosing a correct answer by chance by the total number of panelists. In a triangle test, the probability of a correct answer by chance is 1/3. The probability of choosing an incorrect answer by chance is 2/3.

## Example

For example, a baking company recently reformulated their famous peanut butter cookie in order to reduce costs. The company wished to know if the reformulation was identical to the original. The researchers administered a triangle test to a panel of 60 tasters. The panel obtained 24 correct answers. For this problem:

H0: A=B Ha: A and B are not the same
A=reformulated product
B=original product
Oc=observed number of correct responses=24
Ec=n(1/3)=(60)(1/3)=20
OI=observed number of incorrect responses=60-24=36
EI=n(2/3)=(60)(2/3)=40
α=risk of a Type I error=0.05

From a chi-square distribution chart, X21, 0.05=3.84
Since X2=1.2<3.84, we fail to reject the null hypothesis and conclude that there is no significant difference between samples A and B. In other words, the reformulated cookie is not significantly different from the original cookie.