STATISTICS 402 – Assignment 9
Due April 25, 2007
1. A fisherman conducted an experiment using 5 factors each at 2 levels. The factors and levels
are given below. The response is the number of fish (bluegills) caught in a four-hour period.
All experimental trails were performed at a lake stocked with bluegills in northern Wisconsin.
Factor
A: Fishing location
B: Bait type
C: Time of day
D: Cast location
E: Hook size
XA
–1
+1
–1
+1
–1
+1
–1
+1
–1
+1
–1
+1
–1
+1
–1
+1
XB
–1
–1
+1
+1
–1
–1
+1
+1
–1
–1
+1
+1
–1
–1
+1
+1
XC
–1
–1
–1
–1
+1
+1
+1
+1
–1
–1
–1
–1
+1
+1
+1
+1
XD
–1
–1
–1
–1
–1
–1
–1
–1
+1
+1
+1
+1
+1
+1
+1
+1
Low Level (–1)
Dock
Worm
Morning
Open Water
Small
XE
–1
–1
–1
–1
–1
–1
–1
–1
–1
–1
–1
–1
–1
–1
–1
–1
Fish
25
26
31
34
24
26
32
36
30
36
40
43
30
34
40
42
XA
–1
+1
–1
+1
–1
+1
–1
+1
–1
+1
–1
+1
–1
+1
–1
+1
High Level (+1)
Boat
Jig
Evening
Near brush and rocks
Large
XB
–1
–1
+1
+1
–1
–1
+1
+1
–1
–1
+1
+1
–1
–1
+1
+1
XC
–1
–1
–1
–1
+1
+1
+1
+1
–1
–1
–1
–1
+1
+1
+1
+1
XD
–1
–1
–1
–1
–1
–1
–1
–1
+1
+1
+1
+1
+1
+1
+1
+1
XE
+1
+1
+1
+1
+1
+1
+1
+1
+1
+1
+1
+1
+1
+1
+1
+1
Fish
2
21
26
43
4
20
25
44
10
27
33
51
9
27
32
53
a) Compute sample means for the low and high levels of each of the 5 factors and an overall
grand sample mean.
b) Display the means in main effects plots. Comment on the apparent effect of each of the
factors.
c) Display the 10 two-factor interaction plots. Comment on the apparent interaction effects
specifically indicate which pairs of factors appear to interact.
d) Give the 31 estimated full effects and construct a normal quantile plot of these effects.
Identify on your plot the effects that appear to be large.
e) Have JMP construct a normal plot and a Pareto plot of estimated half effects. Based on
these plots, what factors and interactions appear to be large?
f) You should be able to pick up pseudo-replication by dropping a factor. Which factor
should you drop and why?
g) Fit a full factorial model to the four remaining factors. Indicate what factors and what
interactions are statistically significant.
h) Give a reduced model prediction equation that includes only those factors and
interactions that are statistically significant.
i) Based on the reduced model prediction equation, indicate the values for the five factors
(use the names rather than the coded values) that will maximize the number of fish
caught.
j) Give the predicted number of fish for the values you chose in i).