# One Sided Trend Tests?

I need to test that I have a decreasing rate for a variable I'm testing, but I'm not sure what one-sided trend tests are available? I originally started using the Mann Knedall test because my data are not normal, but I have not been able to find a one-sided version of this test. However, as I understand it, the test statistic is transformed to be normal, so can I simply divide the p-value by 2 to get a one-sided version?

I am using the MannKendall() function in the Kendall package in R, if that makes a difference.

## 1 Answer

You can certainly do a one-tailed Mann-Kendall trend test. Indeed, Mann's 1945 paper on it is essentially entirely concerned with the one sided test (he does the decreasing trend case but explains how that also covers a test against increasing trend).

You should be able to get a suitable one-tailed p-value for a pre-specified direction in the alternative by halving the two-tailed p-value, as you suggest, as long as the observed direction of trend (as measured by the Kendall correlation) is in the same direction as the alternative. If not, you'll need to halve and subtract from 1 (yielding p-values above $\frac12$ in that case).