Question

Comparing taste-test rating protocols. Taste-testers of new food products are presented with several competing food samples and asked to rate the taste of each on a 9-point scale (where$\mathbf{1}\mathbf{=}$"dislike extremely" and$\mathbf{9}\mathbf{=}$"like extremely"). In the Journal of Sensory Studies (June 2014), food scientists compared two different taste-testing protocols. The sequential monadic (SM) method presented the samples one-at-a-time to the taster in a random order, while the rank rating (RR) method presented the samples to the taster all at once, side-by-side. Consider the following experiment (similar to the one conducted in the journal): 50 consumers of apricot jelly were asked to taste test five different varieties. Half the testers used the SM protocol and half used the RR protocol during testing. In a second experiment, 50 consumers of cheese were asked to taste-test four different varieties. Again, half the testers used the SM protocol and half used the RR protocol during testing. For each product (apricot jelly and cheese), the mean taste scores of the two protocols (SM and RR) were compared. The results are shown in the accompanying tables.

a. Consider the five varieties of apricot jelly. Identify the varieties for which you can conclude that "the mean taste scores of the two protocols (SM and RR) differ significantly at$\mathit{\alpha }\mathbf{=}\mathbf{.}\mathbf{05}\mathbf{.}\mathbf{"}$

b. Consider the four varieties of cheese. Identify the varieties for which you can conclude that "the mean taste scores of the two protocols (SM and RR) differ significantly at$\mathit{\alpha }\mathbf{=}\mathbf{.}\mathbf{05}\mathbf{.}\mathbf{"}$

c. Explain why the taste-test scores do not need to be normally distributed for the inferences, parts a and b, to be valid.

Short answer

(a)In the first experiment, all$p$-values are greater than$\alpha =0.05$.

It is known that if $p$-value is less than the level of significance value, then it can be said that the varieties are significantly different.

(b) For $A$, $C$and $D$, the mean taste scores of the two protocols differ significantly.

(c) This is because the sample size is already large enough to be normally distributed as per the Central Limit Theorem, by which is stated that as the sample size becomes large, the sampling distribution becomes approximately normal.

Step-by-step solution

Step-by-Step SolutionStep 1: Given information

One survey was done on taste-teasers of a new food. The foods are rated on a 9 point scale. 50 consumers are divided in two groups. Half of the testers used the SM protocol and half used RR protocol. In another experiment, 50 consumers are asked in the same way but with four varieties of foods.

(a) The varieties of apricot jelly differ significantly

In the first experiment, all$p$-values are greater than$\alpha =0.05$.

It is known that if$p$-value is less than the level of significance value, then it can be said that the varieties are significantly different.

Here, it cannot be concluded that the mean taste scores of the two protocols differ for any of the varieties.

(b) The varieties of cheese differ significantly

In the second experiment, the $p$-values for variety $A,C$and $D$are $0.013,0.002$, and $0.034$respectively, which are less than $\alpha =0.05$.

It is known that, if$p$-value is less than the level of significance value, then it can be said that the varieties are significantly different.

Therefore, the mean taste scores of the two protocols differ significantly for variety A, C, and D.

(c) The taste-test scores do not need to be normally distributed for the inferences to be valid

Here, in two experiments the sample size is greater than 30.

If the samples are larger, then all samples follow approximately normal based on the central limit theorem. Therefore, the population of taste test scores that are normal is not needed.