Chapter 12
12.1 (a)
Source df SS MS F
Treatments 4 816.00 204.00 36.43
1,2 vs. 3,4,5 1 682.67 682.67 121.90
1 vs. 2 1 90.00 90.00 16.07*
3,4 vs. 5 1 3.33 3.33 , 1
3 vs. 4 1 40.00 40.00 7.14
Error 20 112.00 5.60
Total 24 928.00
p,.05 [F.05 (1,20) 5 4.35; F.05 (4,20) 5 2.87]
p,.01 [F.01 (1,20) 5 8.10; F.01 (4,20) 5 4.43]
(b) Orthogonality of contrasts:
Cross-products of coefficients:(c) 682.67 1 90.00 1 3.33 1 40.00 5 816.0012.3 for a5.05; PC 5a; FW 51 2 (1 2a)^25 .0975
12.5 q 5 7.101; t? 2 5 7.101
12.7 52 5.861 reject H 0. 52 6.77; reject H 0
12.9
Source Ftct (^9) .05(20, c) Signif
1,2 vs. 3,4,5 121.905 11.04 4 2.74
1 vs. 2 16.071 4.01 3 2.61
3 vs. 4 7.143 2.67 2 2.42 *
3,4 vs. 5 , 1 , 1 1 2.09
t¿ 1 t¿ 2
1 (.5)(-1) 1 (1)(0)= 0
acjdj=(0)(0)^1 (0)(0)^1 (.5)(1)
1 (0)(.5) 1 (0)(-1)= 0
abjcj=(1)(0)^1 (-1)(0)^1 (0)(.5)
1 (.333)(-1) 1 (.333)(0)= 0
aajdj=(.5)(0)^1 (.5)(0)^1 (.333)(1)
1 (.333)(.5) 1 (.333)(-1)= 0
aajcj=(.5)(0)^1 (.5)(0)^1 (.333)(.5)
1 (.333)(0) 1 (.333)(0)= 0
aajbj=(.5)(1)^1 (.5)(-1)^1 (.333)(0)
12.11 Tukey: W 55 W 45 W 35 W 25 3.973. For this analy-
sis, we have the same pattern of differences we had in
Exercise 12.10. In other words, Treatments 1 and 2 are
equal and Treatments 3, 4, and 5 are equal.
12.13 Group 1 is different from all other groups. Groups 2, 3,
and 4 are different from Group 5.
12.15 The variances are approximately equal, and so are the
sample sizes, so we will use the harmonic mean of the
n, which is 9.3264.
The 0.5 mg group is different from the control and the
2 mg group. No other differences are significant. The
maximum familywise error rate is .05 (see below).
12.17 Simply run the tests as standard ttests. Almost all soft-
ware will give you the actual pvalue. Reject H 0 for each
pvalue less than ac.
12.19 SSlinear 5 0.0088; F 5 0.145; no significant linear
trend. SSquad 5 1.149; F 5 18.99; significant quadratic
trend.
12.21 This is a computer exercise.
12.23 Trend analysis for Epineq.dat separately at each interval.
One Day: FLinear 5 9.44 (p 5 .0042);
FQuad 5 20.43 (p 5 .0001)
One Week: FLinear 5 4.33 (p 5 .0453);
FQuad 5 13.23 (p 5 .0009)
One Month: FLinear 5 6.91 (p 5 .0129);
FQuad 5 8.60 (p 5 .0061)
12.25 Using actual dose, FLinear 5 0.548; Using 1, 2, ...6,
FLinear 5 11.03.
(d) When we use the group number coding in our trend
analysis we find a significant linear trend. As the
dose of sucrose increases, memory increases
accordingly.
(e) The choice of coding system in not always obvi-
ous. Using 1, 2,... , 6 actually ranks the dose lev-
els and ignores the fact that dose increases in an
extreme way. (In other words, the difference
between the first 2 doses is 1 mg kg, while the dif-
ference between the last two doses is 250 mg kg.>
Wr=qr
B
MSerror
nh
=qr
B
240.35
9.3264
=qr(5.0765)
Answers 745
Results for Exercise 12.15
Control 2 mg1 mg 0.1 mg 0.5 mg
34.00 38.10 48.50 50.80 60.33 rqr Wr
34.00... 4.1 14.5 16.8 26.33 5 4.04 20.51
38.10... 10.4 12.7 22.23 4 4.04 20.51
48.50... 2.3 11.83 3 4.04 20.51
50.80... 9.53 2 4.04 20.51