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 sensory 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).
Analyze these data to determine if protein and/or gum have any effect on the sensory rating. Determine which, if any, proteins and/or gums differ in their sensory ratings.