Power of Seasonal Kendall Trend test

Question

I was asked about doing a power analysis of a seasonal kendall trend test. I feel like that would be really difficult to do and I haven't found any documentation or software on how to do it. Is there some way to estimate the required sample size using regression? Hopefully someone can point me in the right direction. Thanks!

Answer 1

The first thing with power is to make sure you have clear specification on exactly the alternative (and assumptions) you're checking power at. This determines the sampling situation under which you evaluate the rejection rate

As I suggest in this answer, simulation is a simple way to approach questions on power.

In your case, you want to specify the rejection rate and compute an $n$. If you have the time (it's usually a matter of minutes) you can compute power across a range of sample sizes right at the start.

At a given $n$, the basic approach to power calculation is (as a kind of pseudocode):

0: choose the circumstances under which you evaluate power (alternative + assumptions)

1: repeat nsim times:
     generate a sample of size n under the alternative
     compute the test statistic, T
     if (T <= Tcrit) increment the count of rejections
   rejectrate = rejections/nsim

When you evaluate for many different $n$, step 0 doesn't change, but step 1 is repeated for each $n$ you want to look at. You can use search methods (i.e., root-finding - for example, binary search might be suitable for a Kendall's tau-type statistic) to converge on the required sample size for a given power.

The answer I pointed to before has discussion on computing standard errors of the power estimates, and if you consider smoothing across multiple sample sizes it has some suggestions about ways to approach smoothing rejection rates.

(It may be worth considering working on the scale of $\sqrt n$ for some of these tasks, e.g. it might be a more suitable scale for things like binary search or smoothing across multiple $n$.)