Question

Trout were sampled from two different lake populations and their lengths measured. The researchers are interested in knowing whether the average length distribution for the trout in lake 1 (group1) are greater than the average length distribution for the trout in lake 2 (group 2). Using R and the Wilcoxon Rank Sum-test answer the following questions for the data available:

Lake1	Lake2
21.85	42.6
31.4	32.65
78.5	28.3
11.7	19.7
41.15	29.45
27.55	16.05
25.4	24.15
35.8	14.3
8.05	39.65
38.35	24.65
27.7	34.95
26.3	27.45
31.25	28.15
57.35	32.25
33.15	69.75
27.85	32.2
39.25	30.35
36.65	45.4
44.4	34.3
35.85	28.1
31.6	31.65
14.4	11.35
19.85	41.2
31.75	51.65
28.05	30.6
32.1	21
33.6	31.95
43.3	57.75
24.05	35.85
29.7	20
14.4	20.25
26.35
32.1
40.5
30.05
24.95
32.5
28.3
27.7
53.65

Calculate the value of the test statistic W

Answer 1

The test has been coded been in R.
The Code of R is given below:

> lake1<-c(21.85,31.4,78.5,11.7,41.15,27.55,25.4,35.8,8.05,38.35,27.7,26.3,31.25,57.35,33.15,27.85,39.25,36.65,44.4,35.85,31.6,14.4,19.85,31.75,28.05,32.1,33.6,43.3,24.05,29.7,14.4,26.35,32.1,40.5,30.05,24.95,32.5,28.3,27.7,53.65)
> lake2<-c(42.6,32.65,28.3,19.7,29.45,16.05,24.15,14.3,39.65,24.65,34.95,27.45,28.15,32.25,69.75,32.2,30.35,45.4,34.3,28.1,31.65,11.35,41.2,51.65,30.6,21,31.95,57.75,35.85,20,20.25)
> wilcox.test(lake1,lake2,alternative = "greater")

   Wilcoxon rank sum test with continuity correction

data: lake1 and lake2
W = 624, p-value = 0.4838
alternative hypothesis: true location shift is greater than 0

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