Question

Modern ice creams are not simple recipes. Many use some type of gum to enhance texture, and a non-cream protein source (for example, whey protein solids). A food scientist is trying to determine how types of gum and protein added change a sen- sory rating of the ice cream. She runs a five by five factorial with two replications using five gum types and five protein sources. Unfortunately, six of the units did not freeze properly, and these units were not rated. Ratings for the other units are given below (higher numbers are better) Protein Gum 1 2 3 4 5 2.1 4.0 3.1 1 3.5 3.6 3.0 2.9 4.5 2 7.2 6.8 6.7 7.5 6.8 4.8 6.9 9.3 4.1 3 5.8 4.5 5.3 4.1 5.6 4.8 4.6 7.3 5.3 4 5.3 4.8 6.7 5.0 5.2 3.2 7.2 6.7 4.2 4.5 5.1 4.9 4.5 5 5.0 2.7 3.7 4.5 4.7

According to whichever is more appropriate, a marginal comparison of gum types or a comparison of gum types within each protein source, compare the best gum type (the gum type with the highest mean rating) to each of the other gum types using pairwise comparisons. This question asks you to compare one specific level of a factor (in this case the best level, but in other contexts it might be the “control” level or even the worst level) to each of the other level through pairwise comparisons. There is a particular multiple comparison technique which is designed to do this: the Dunnett procedure. The Dunnett procedure

Answer 1

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