Exercise 2

Ten different chill or freezer storage treatments were tested on a type of cookies, and after storage the cookies were evaluated by a sensory panel composed of 13 assessors. Each assessor tasted the cookies in a randomized order, and tasted each type twice. In connection with each test, the assessor gave a score for each of the following properties: colour, consistency, taste, and quality (a combined score). The score was an integer between 0 and 10 with 10 being the best. The treatments are numbered 46, . . . , 55, and the assessors are numbered 1, . . . , 13. One assessor did not give any score for quality.

(a) Think about which kind of plots would be suitable to explore the information in the quality response, and try to make some of these.

Answer: The proportional density plot below is useful to see how levels of a factor share the density at different continuous values.

Exploring the quality of cookies between treatments. A proportional density plot tells us which treatments have the most density at different values of quality. Treatment 48 seems to have the highest share of quality responses over 5, while treatment 50 has many low scores.

Exploring the quality of cookies between treatments. A proportional density plot tells us which treatments have the most density at different values of quality. Treatment 48 seems to have the highest share of quality responses over 5, while treatment 50 has many low scores.

Assessor 12 seems to not like the cookies very much.

Assessor 12 seems to not like the cookies very much.

Patterns of assessor scores between treatment types. Big grey circles are the overall means for each treatment, points and lines are mean responses for each assessor. As in the density plot, assessor 12 is consistently below the mean.

Patterns of assessor scores between treatment types. Big grey circles are the overall means for each treatment, points and lines are mean responses for each assessor. As in the density plot, assessor 12 is consistently below the mean.

(b) Carry out a statistical analysis of the quality response with the aim of investigating assessor and treatment differences (use ordinary analysis of variance techniques) and try to answer the following questions:

Anova table for model with interactions. There are significant differences between treatments and assessors but non-significant interactions
Predictor Df Sum Sq Mean Sq F p
treatm 9 77.337 8.593 12.652 0.000
assessor 11 78.546 7.141 10.514 0.000
treatm:assessor 99 72.913 0.736 1.084 0.334
Residuals 120 81.500 0.679

1. Are there any assessor differences?

Answer: Yes, there are significant differences.

2. Are there any treatment differences?

Answer: Yes there are significant differences.

3. Are possible treatment differences the same for all assessors?

Answer: The difference of treatment effect between assessors is non-significant.

(c)

Answer: There are significant interaction effects for colour, non-significant for taste, and cons require further research.

Anova table for models on colour, cons and taste.
Dependent Predictor Df Sum Sq Mean Sq F p
colour treatm 9 54.785 6.087 13.883 0.000
assessor 12 32.415 2.701 6.161 0.000
treatm:assessor 108 88.815 0.822 1.876 0.000
Residuals 130 57.000 0.438
cons treatm 9 57.062 6.340 7.425 0.000
assessor 12 49.562 4.130 4.837 0.000
treatm:assessor 108 124.438 1.152 1.349 0.051
Residuals 130 111.000 0.854
taste treatm 9 87.677 9.742 8.919 0.000
assessor 12 118.900 9.908 9.071 0.000
treatm:assessor 108 109.023 1.009 0.924 0.663
Residuals 130 142.000 1.092