(b) One of the goals in this investigation was to determine which gum type resul
ID: 3253569 • Letter: #
Question
(b) One of the goals in this investigation was to determine which gum type resulted in the best mean rating. Can this question be addressed marginally? or is it more appropriate to address it separately for each protein source? Which is the best gum type?
Please (a) and (b)! (If possible, use SAS)
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 3.5 3.6 2.1 4.0 3.1 3.0 2.9 4.5 7.2 6.8 6.7 7.5 6.8 4.8 6.9 9.3 4.1 5.8 4.5 5.3 4.1 5.6 4.8 4.6 7.3 5.3 4 5.3 4.8 5.0 6.7 5.2 3.2 7.2 6.7 4.2 4.5 5.1 5.0 4.9 4.5 2.7 3.7 4.5 4.7Explanation / Answer
a) The data is first imported to the R statistical software and then the aov function is used to analyze the main and interaction between gum type and protein source. The least squares method is used here for analyses purposes.
> tt <- read.csv("clipboard",sep=" ")
> tt$Gum <- as.factor(tt$Gum)
> tt$Protein <- as.factor(tt$Protein)
> Ratings_aov <- aov(Ratings~Gum+Protein+Gum*Protein,data=tt)
> summary(Ratings_aov)
Df Sum Sq Mean Sq F value Pr(>F)
Gum 4 58.67 14.667 10.610 0.000109 ***
Protein 4 7.88 1.969 1.425 0.264172
Gum:Protein 16 6.64 0.415 0.300 0.990685
Residuals 19 26.27 1.382
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Though the Gum is significant on the Ratings, the Protein main effect and the interaction effect are insignificant.
b)Since the interaction effect and main effect of Protein are both insignificant, the gum type can be addressed marginally. To find the best gum type, a boxplot is obtained:
The boxplot clearly shows that Gum type 2 is the having the maximum ratings.
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