It is known that the blood concentration of the hormone cortisol becomes elevate

Question

It is known that the blood concentration of the hormone cortisol becomes elevated in some animals prior to the start of spontaneous onset of birthing labor. It was desired to know if this is also the case in humans. Three groups of women were studied. The first group had elective caesarian sections (Elective). The second group gave birth either vaginally or via emergency caesarian section following artificial inducement of labor (Induced). The third group gave birth either vaginally or via emergency caesarian section following spontaneous onset of labor (Spontaneous). Cortisol concentrations were measured in these women at the time they gave birth. The data are below: Elective: 262, 307, 211, 323, 454, 339, 304, 154 Induced: 465, 501, 455, 355, 468, 362 Spontaneous: 343, 772, 207, 1048, 838, 687 It is desired to test: H_0: mu Elective = mu Induced = mu Spontaneous H_A: At least one mean differs from one other mean, using alpha = 0.05. Graph the data as you see fit. Why did you choose the graph(s) that you did and what does it (do they) tell you? Use R to perform a Kruskal-Wallis test. Give the code you used and the output. State the p-value. Make a conclusion in the context of the problem, i.e., is there evidence that any of the birthing methods show a change in cortisol levels? If you found significant differences in part (b), perform all pairwise comparisons using the Wilcoxon Rank Sum Test with Bonferroni correction. Make a conclusion in the context of the problem.

Explanation / Answer

(b) THe R-code

x=c(262,307,211,323,454,339,304,154)
> y=c(465,501,455,355,468,362)
> z=c(343,772,207,1048,838,687)
> kruskal.test(list(x, y, z))

        Kruskal-Wallis rank sum test

data: list(x, y, z)
Kruskal-Wallis chi-squared = 8.681, df = 2, p-value = 0.01303

The p-value is less than 0.05, we conclude that the mean of one group is differ from the other group.

Yes, there is a sufficient evidence that any of the birthing methods show a change in cortisol levels.

(c)

Using R

> x=c(262,307,211,323,454,339,304,154)
> y=c(465,501,455,355,468,362)
> z=c(343,772,207,1048,838,687)
> w1=wilcox.test(x, y, alternative = "greater")
> w1

        Wilcoxon rank sum test

data: x and y
W = 2, p-value = 0.9993
alternative hypothesis: true location shift is greater than 0

> w2=wilcox.test(y, z, alternative = "greater")
> w2

        Wilcoxon rank sum test

data: y and z
W = 12, p-value = 0.8452
alternative hypothesis: true location shift is greater than 0

> w3=wilcox.test(x, z, alternative = "greater")
> w3

        Wilcoxon rank sum test

data: x and z
W = 8, p-value = 0.9853
alternative hypothesis: true location shift is greater than 0

>

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