Question

Use the computer to perform a permutation test approach to implement Wilcoxon Rank Sum Test and report a two-tailed p-value. Please show steps in detail.

Also, provide R code if RStudio used.

1. Nonparametric methods Table 1 Pod weight (g) from inoculated (I) and uninoculated (U) plants 0.49 1.76 1.45 1.03 1.53 2.34 0.85 1.00 1.54 1.01 0.75 2.11 0.92 1.96 1.79 1.21 Mean sd 1.634 0.420 1.084 0.510 "The data for this problem were supplied by David Rosner.

Answer 1

Mann Whitney U test (Wilcoxon rank-sum);

H0: Group1 = Group2 Vs H1: Group1 ≠ Group2

Test statistic

U-utc 2 6

Two (H₁: Group1≠Group2)Left (H₁: Group1<Group2)Right (H₁: Group1>Group2)

Significance level (α):0.05

Sample average (X1):1.633750

Sample average (X2):1.083750

Sample SD (S1):0.419896

Sample SD (S2):0.509788

The test statistic Z equals 2.313991, is not in the 95% critical value accepted range: [-1.9600 : 1.9600].
U=53.00, is not in the 95% accepted range: [13.0000 : 51.0000].
The statistic S' equals 9.522

p-value equals 0.0281274, ( p(x≤Z) = 0.989666 ). This means that the chance of type1 error (rejecting a correct H0) is small: 0.02813 (2.81%).
The smaller the p-value the more it supports H1.

Since p-value < α, H0 is rejected.
The randomly selected value of Group1's population is considered to be not equal to the randomly selected value. of the Group2's population.

R Code:

x1<-c(1.03,1.21,1.45,1.53,1.76,1.79,1.96,2.34)
x2<-c(0.49,0.75,0.85,0.92,1.00,1.01,1.54,2.11)

wilcox.test(x1, x2, alternative = "two.sided", paired = FALSE, exact = TRUE, correct = TRUE).