For
the following situations you should be able to RECOGNIZE which test should be
used, FIND THE FORMULA for the test statistic in Zar
or in your notes, and WRITE DOWN the appropriate tabled value for comparison at
the 5% level of significance.
a. 10 pairs of twin warthogs are randomly
selected and one warthog of each pair is randomly assigned to be treated with
wart remover; the other is treated with a placebo (an inert substance). We wish to test that the two treatments will
remove a different mean number of warts per warthog. Assume initially that our response has a
normal distribution.
This is a paired design, so we should
use a paired t-test:
b. Same as [a] above, except now we have two completely
independent random samples of warthogs, with 10 in each group.
In this case a two-sample t-test is
appropriate:
c. Same as [a] in the beginning, except no
longer assume the data are normally distributed.
We need a non-parametric test, in this
case a paired non-parametric test: Wilcoxon signed
rank test.
T-=sum(ranks
with minus sign); T+=sum(ranks with plus sign)
Tmin=
min(T-,T+)
Reject if Tmin
<= T0.05(2),10 = 8
d. Same as [b] above, but data are no longer
normally distributed.
We need a non-parametric test, in this case a two-sample
non-parametric test: Mann-Whitney/ Wilcoxon Rank Sum
test.
R1 = sum(ranks
for X1); R2 = sum(ranks for X2)
U1 = n1n2
+n1(n1+1)/2-R1; U2
= n1n2 +n2(n2+1)/2-R2
Umax
= max(U1,U2); Reject if Umax
>= U0.05(2),10,10 = 77
e. Same as [b] above, but now we want to test
whether the *variability* of response is the same in each of the two groups.
We want to compare the variance of two independent samples
from normally distributed populations, so we use the F-test:
Reject if F>F0.05(2),9,9 =
4.03