
1.

Finish the example for the twin data. Recall the paired differences were:
pair N H D
1 74 63 11
2 43 33 10
3 61 41 20
4 79 67 12
5 80 65 15
6 73 80 7
7 56 43 13
8 98 84 14
9 84 74 10
10 52 48 4

(a)

Obtain the value of the Wilcoxon test statistic. (Actually determine the
number of negative averages (2) and subtract it for 10(11)/2.

(b)

Obtain the pvalue for a two sidedtest. Use class code of course, Wilcoxon
for paired designs. Conclude in terms of the problem.

(c)

Obtain (from class code) the estimated effect and the associated confidence
interval. Conclude in terms of the problem.

2.

From Cushney and Peebles (1905)a, J. of Phisiology: Ten patients
were selected for a study. The average number of hours that they slept
was deterimed. There were two parts to the study. In Part 1, they were
given by a flip of the coin one of two drugs, Laevo and Dextro, and the
average (over a week) number of excess hours (over their usual average)
was recorded. In Part 2 (after a wash out period), they were given the
other drug, and the average (over a week) number of excess hours (over
their usual average) was recorded. The data are:
Patient Dextro Laevo
1 0.7 1.9
2 1.6 0.8
3 0.2 1.1
4 1.2 0.1
5 0.1 0.1
6 3.4 4.4
7 3.7 5.5
8 0.8 1.6
9 0.0 4.6
10 2.0 3.4

(a)

Obtain the value of the Wilcoxon test statistic, (diff = D  L).

(b)

Compare it what you would expect under H_{0}.

(c)

Obtain the pvalue for a two sidedtest. Use class code of course, Wilcoxon
for paired designs. Conclude in terms of the problem.

(d)

Obtain (from class code) the estimated effect and the associated confidence
interval. Conclude in terms of the problem.

3.

The data below are some measurements recorded by Charles Darwin in 1878.
They consist of 15 pairs of heights in inches of crossfertilized plants
and selffertilized plants, Zea mays, each pair grown in the same pot.
POT CROSS SELF
1 23.500 17.375
2 12.000 20.375
3 21.000 20.000
4 22.000 20.000
5 19.125 18.375
6 21.550 18.625
7 22.125 18.625
8 20.375 15.250
9 18.250 16.500
10 21.625 18.000
11 23.250 16.250
12 21.000 18.000
13 22.125 12.750
14 23.000 15.500
15 12.000 18.000

(a)

Obtain the value of the Wilcoxon test statistic, (diff = C  S).

(b)

Compare it what you would expect under H_{0}.

(c)

Obtain the pvalue for a two sidedtest. Use class code of course, Wilcoxon
for paired designs. Conclude in terms of the problem.

(d)

Obtain (from class code) the estimated effect and the associated confidence
interval. Conclude in terms of the problem.