BIOL933 Fall 2015
Due Thursday, October 29, at the beginning of lecture . Include your R codes, answer all parts of the questions completely, and interpret all results. To ensure maximum points for yourself, invest some time in presenting your answers in a concise, organized, and clear manner.
A study was carried out to determine the effect of kneading on the density of bread. Various treatments were applied, characterized by the following parameters:
Number : How many times the dough was kneaded before baking, ranging from 1 to 3 (N1-N3)
Strength: How strongly the dough was kneaded, ranging from 1 to 4 (S1-S4)
Time: How long the dough was kneaded each time, ranging from 1 to 4 (T1-T4)
All possible combinations of the levels of the three treatments were randomized in a RCBD with 2 blocks
(B1 and B2). The variable measured was density of the baked loaves (mg/cm 3 ). [Note: This is an RCBD with a 3x3x4 factorial treatment structure.]
T1 T2 T3 T4
S1
N1 N2 N3 N1 N2 N3 N1 N2 N3 N1 N2 N3
112 110 112 111 106 107 109 107 106 109 109 107
B1
S2
S3
S4
S1
114 110 111 111 108 110 111 109 109 109 109 111
113 110 114 110 108 108 109 105 111 111 107 110
109 112 113 109 109 111 106 112 110 109 112 114
113 113 113 110 111 110 111 107 112 114 109 112
B2
S2
S3
112 113 114 111 112 111 108 111 110 109 110 112
112 113 116 111 110 114 110 106 111 111 111 112
S4 115 115 119 111 114 115 113 112 112 114 110 114
(A SMALL GIFT: DON'T WORRY ABOUT TESTING ASSUMPTIONS)
1.1
Use an exploratory model to show that all the two- and three-way block interactions are NS, and that the three-way factor interaction (N*S*T) is NS. Then present and analyze the ANOVA table for the reduced model (i.e. the model that includes none of these NS interactions). Why is it necessary to assume the four-way interaction to be NS?
1.2
In light of the results from 1.1, present and discuss a plot of the main effect of Time. Present and discuss plots of the Strength*Number and Strength*Time interactions.
1.3
Analyze the main effect of Time using the Tukey fixed-range test. Assuming you wished to identify the amount of kneading time that produced the lightest (i.e. least dense) bread, is this an appropriate analysis? Is there a better analysis?
BIOL933 1 HW 6 (Topic 9)

A dairy farmer is interested in the effect of protein supplements on the milk production of her cows, so she enlists two recent BIOL933 graduates to help her out. They recommend testing three different sources of protein (fish meal, soy protein extract, and meat & bone meal) at two different levels in the diet
(Low and High). Each source-level combination of protein was randomly assigned to 10 cows. The measured gain in milk production in liters is presented:
MBM 143 170 161 189 164 148 123 151 154 161
High Soy
Fish
138 129 121 136 144 154 117
169 157 137
MBM 152 166 110
183
96
174
129
114
77
161
129
88
186
114
174 149
163
136
128
128
Soy 117 117 104 140 91 169 149 152 126 154 Low
Fish 80 113 142 149 122 142 120 142 101 136
(THE GIFT CONTINUES: DO NOT WORRY ABOUT TESTING ASSUMPTIONS)
2.1
Analyzing this experiment as a 2x3 factorial, determine if there is a significant interaction between the level of protein and the source of protein.
2.2
Now you are going to partition the SS found in the above ANOVA. Use contrasts to answer questions a-e: a.
Are there differences between animal and vegetable sources of protein? b.
Are there differences between animal sources? c.
Compare the two previous SS with the Source SS in the first analysis. d.
Are the differences between animal and vegetable sources different at the two protein levels? e.
Are the differences between animal sources different at the two protein levels? f.
Compare the two previous SS with the Interaction SS in the first analysis. g.
Discuss how it is possible that one of the components of the interaction is significant (2.2d) when the total interaction (2.1) is not.
BIOL933 2 HW 6 (Topic 9)