In R, why do wilcox.test gives different answerin case of formula and not using formula?

#running wilcox.test using formula 
r = wilcox.test(mpg ~ am, data=mtcars)
[1] 0.001871391

#running wilcox.test by variables
s= wilcox.test(mtcars$mpg, mtcars$am)
[1] 2.74978e-12

s= wilcox.test(mtcars$am, mtcars$mpg)
[1] 2.74978e-12

Why is p-value is different in these two cases?


1 Answer 1


In the formula, case one, is comparing the 'mpg' variable subsetted with the 'am' variable. In this case a vector of 19 values versus a vector of 13 values.
In the non-formula example, one is comparing the 'mpg' vector vs 'am' vector. This is two 32 values vectors.

 wilcox.test(mtcars$mpg[mtcars$am==0], mtcars$mpg[mtcars$am==1])

This will provide the same result as the formula format.

  • $\begingroup$ code gives error : Error in wilcox.test.default(mtcars[mtcars$mpg == 0], mtcats[mtcars$mpg == : 'x' must be numeric $\endgroup$
    – cNinja
    Oct 4, 2018 at 20:13
  • $\begingroup$ @cNinja, sorry slight error in formula, corrected and now provides the same answer as the formula format. $\endgroup$
    – Dave2e
    Oct 5, 2018 at 2:43

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