Bio-engineers and material scientists are interested in the amazing strength of spider webs. However, they suspect that not all webs are created equal. They evaluate the strength of webs from 6 different spider species. They measure the breaking tension of each of three types of spider silk: anchor threads attaching webs to whatever its hanging on, spokes giving the web structure, and the sticky threads that catch the prey.
Average thread strength observed
Spider species Anchor thread Sticky
thread Spoke thread
1 54.7 24.0 43.7 40.8
2 76.0 51.0 25.7 50.9
3 30.7 12.7 25.0 22.8
4 104.7 49.3 84.7 79.6
5 82.3 21.0 34.3 45.9
6 46.0 33.7 47.3 42.3
65.7 31.9 43.4
The ANOVA table below has been partially filled in for you.
Silk type 3-1=2 10,620.7 5310.35 8.255 4.10 0.0076
Spider species 6-1=5 15,506.4 3101.28 40.847 2.49 <
0.001
Interaction 2*5=10 6,432.7 643.27 8.472 1.79 < 0.001
Total (corrected) 53 35,293.0
A plot of the means will be displayed on the overhead to assist in interpreting your results. (This will either be 3 or 6 jagged lines, depending if you decide to make each line represent a thread type or a spider species. Either is correct.)
a.) Fill in the reminder of the ANOVA table, including the F-tests, as if this were a mixed model (that is, where one factor is random and one is fixed). Please specify which factor you believe is fixed and which you believe is random and why. Conduct your test for the main effects at a = 0.05; interaction at .10.
Spider species is the random effect
because the question regards web strength of spiders, not web strength of these
six species in particular. These six
species are a sample of all spider species.
b.) Now re-run the tests as though both factors are fixed effects. (In what case would this be true?)
This would be true if we are only
interested in the difference in web strength of these three web types and only
for these 6 species (random when these six species are a sample of all spider
species).
Silk type 3-1=2 10,620.7 5310.35 69.94 3.27 <0.001
Spider species 6-1=5 15,506.4 3101.28 40.847 2.49 <0.001
Interaction 2*5=10 6,432.7 643.27 8.472 1.79 <0.001
Total (corrected) 53 35,293.0
c.) From the ANOVA table, given that this was a balanced design, how may webs of each spider did they test? (That is, what is n?)
N = 53+1 = 54; a = 3, b = 6, for a balanced design n = 54/(6*3) = 3