On 16-Feb-2012 Bert Gunter wrote: > On Thu, Feb 16, 2012 at 10:15 AM, Jun Shen <jun.shen...@gmail.com> wrote: >> Dear list, >> >> Let's say I have data >> >> _a=c(37.961,38.214,57.68) >> _b=c(77.56,61.875,67.683) >> >> >> >> the wilcoxon test only gives me a p value with one decimal place. Is this >> normal? > > No, it's discrete :-) > > (Actually, that's the answer. Read up on the Mann-Whitney test to see why). > > -- Bert > > Thanks. >> Jun
To expand on Bert's reply: Given two sets of 3 numbers (x,y,z), (X,Y,Z) with x < y < z and X < Y < Z, there are exactly 20 ways to merge them together (according to possible relationships between the values in the first and the second): x < y < z < X < Y < Z x < y < X < z < Y < Z x < y < X < Y < z < Z x < y < X < Y < Z < z [and so on until] X < Y < x < Z < y < z X < Y < Z < x < y < z Your example is the first of these so has probability 1/20. Since the default for wilcox.test is "two.sided", the result takes into account also arrangements which are at least as extreme as the one given, of which the only case is the last one in the above list, which also has probability 1/20. Hence the 2-sided P-value is 1/20 + 1/20 = 1/10, which is exactly 0.1, as returned by wilcox.test(). It would be possible to display the result as 0.10000, say, but there is no point! If you do wilcox.test(a,b, alternative="less") then you will get 0.05 as P-value -- again exactly right. Ted. ------------------------------------------------- E-Mail: (Ted Harding) <ted.hard...@wlandres.net> Date: 16-Feb-2012 Time: 18:57:08 This message was sent by XFMail ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.