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.

Source of Variation       df                     SS                    MS(SS/df)       Fmix                  Fc         p         

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

Error                53-(2+5+10)=36         2,733.3            75.925

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).

Source of Variation       df                     SS                    MS(SS/df)       Ffixed                 Fc         p         

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

Error                53-(2+5+10)=36         2,733.3            75.925

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