William Gosset published \"The Probable Error of the Mean, \" in a 1908 issue of

Question

William Gosset published "The Probable Error of the Mean, " in a 1908 issue of Biometrika, under the pseudonym "Student." In this article, data regarding the yields from two different types of seeds were included. He was interested in ways to improve the yield of grain that was being grown for use in Guinness beer. Regular: 19.25, 22.75, 23, 23, 22.5, 19.75, 245, 15.5, 18, 14.25, 17 Kiln dried: 25, 24, 24, 28, 22.5, 19.5, 22.25, 16, 17.25, 15.75, 17.25 a) Your uncle has never taken a statistics course. Explain to him, in a way that he could clearly understand, the process of comparing the two groups using nonparametric analysis (3 sentences max). b) Explain to your uncle why you might use this "nonparametric" analysis instead of this other analysis that he is vaguely aware of, the 't-test".

Explanation / Answer

a) We used wilcoxon test for non-parametric analysis in R:

data <- read_csv("D:/Backup/desktop/data.csv")
attach(data)
wilcox.test(Regular,`Kilk dried`)

Result:
Wilcoxon rank sum test with continuity correction

data: Regular and Kilk dried
W = 17.5, p-value = 0.4047
alternative hypothesis: true location shift is not equal to 0

since p-value>0.05 so cant reject H0 that hypothesises that there is no significant difference between 2 samples.

b) Since data is not Normally distributed here so we cant use parametric tests (t-test etc) as it has assumption of Normality

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