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I am doing a Wilcoxon test in R and one thing that has surprise me is that when I compute the confidence interval for the below mentioned dataset I get a 95% confidence interval of (-807,198), and non of the values for the treated and untreated groups are within that interval.

For example:

treated <- c(323,421,578,300,256,640,912,370)
untreated <- c(2388,210,380,345,1130,260,665,1157)

wilcox.test(treated,untreated,conf.int=TRUE)

This is the output of the test with the 95% confidence interval

    Wilcoxon rank sum test
data:  treated and untreated
W = 25, p-value = 0.5054
alternative hypothesis: true location shift is not equal to 0
95 percent confidence interval:
   -807  198
sample estimates:
difference in location 
             -83.5

Can anyone help me solving or understanding this issue?

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4
  • $\begingroup$ Notice the test is highly non-significant $\endgroup$ Dec 6, 2017 at 10:09
  • $\begingroup$ Thanks, I have notice that, but as the confidence interval is computed from the data shouldn't it cover my values? $\endgroup$
    – Praderas
    Dec 6, 2017 at 10:27
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    $\begingroup$ It's the confidence interval for the location shift, not for the distribution of your data. $\endgroup$
    – Firebug
    Dec 6, 2017 at 11:28
  • $\begingroup$ How did you compute C.I. values and difference in location ? $\endgroup$
    – user10619
    Dec 6, 2017 at 12:29

2 Answers 2

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According to the help page,

conf.int    = a confidence interval for the location parameter.
estimate    = an estimate of the location parameter.

Now, the value of estimate is -83.5, i.e. the difference in location.

Thus, I deduce that the confidence interval is actually a confidence interval for the difference in location.

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Adding to Ocram's answer (which is correct + 1), suppose you subtracted 500 from all the values:

t2 <- treated - 500
u2 <- untreated - 500

then did the same test:

wilcox.test(t2, u2, conf.int=TRUE)

you get the same result as with your original. What matters is the shift in location between treated and untreated, not the actual location.

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