When sage crickets mate, the male allows the female to eat part of his hind wing

Question

When sage crickets mate, the male allows the female to eat part of his hind wings. The primary research question is: do starved females attempt mating more or less quickly than normally fed females? One group of 11 was starved for two days, and the other group of 13 was fed normally. Each female was presented with a male and the time to mating (in hours) was recorded. Starved: 1.9, 2.1, 3.8, 9.0, 9.6, 13.0, 14.7, 17.9, 21.7, 29.0, 72.3 Fed: 1.5, 1.7, 2.4, 3.6, 5.7, 22.6, 22.8, 39.0, 54.4, 72.1, 73.6, 79.5, 88.9. Conduct the Mann-Whitney Test and find the P-value.

Explanation / Answer

I am conducting Mann- Whitney test

This is the detailed data table sheet

Result Details
Sample 1
Sum of ranks: 121
Mean of ranks: 11
Expected sum of ranks: 137.5
Expected mean of ranks: 12.5
U-value: 88
Expected U-value: 71.5

Sample 2
Sum of ranks: 179
Mean of ranks: 13.77
Expected sum of ranks: 162.5
Expected mean of ranks: 12.5
U-value: 55
Expected U-value: 71.5

Sample 1 & 2 Combined
Sum of ranks: 300
Mean of ranks: 12.5
Standard Deviation: 17.2603

C value = n1n2 + n2(n2+1)/2 - Min R = 13 * 11 + 11 * 12/2 - 121 = 88

n1 n2 -C = 13 * 11 - 88 = 55

The U-value is 55. The critical value of U at p < .05 is 37.

Ucritical = 37 for n1= 13 and n2=11

Z-ratio

Z =(U - mU )/ U

mU = n1 n2 /2 = 13 * 11 /2 = 71.5

U = sqrt [ n1n2/12 [(n1+n2+1) - Factor k)] [ Here factor k is related to equal terms which is not here so can be neglected]

U = sqrt [ 13 * 11 * 25/12] = 17.26

Z =(U - mU )/ U = ( 55 - 71.5) / 17.26 = - 0.95

The Z-Score is -0.95. p-value is .3238. The result is not significant at p < .05. so we can reject the null hypothesis H0 which entails that there is significant difference between starved and fed cricket females.

Starved Rank Fed Rank Cumulative List Rank 1.9 3 1.5 1 1.5 1 2.1 4 1.7 2 1.7 2 3.8 7 2.4 5 1.9 3 9.0 9 3.6 6 2.1 4 9.6 10 5.7 8 2.4 5 13.0 11 22.6 15 3.6 6 14.7 12 22.8 16 3.8 7 17.9 13 39.0 18 5.7 8 21.7 14 54.4 19 9.0 9 29.0 17 72.1 20 9.6 10 72.3 21 73.6 22 13.0 11 Sum 121 79.5 23 14.7 12 88.9 24 17.9 13 Sum 179 21.7 14 22.6 15 22.8 16 29.0 17 39.0 18 54.4 19 72.1 20 72.3 21 73.6 22 79.5 23 88.9 24

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