Hello,
I would like to perform a Wilcoxon-Mann-Whitney step trend test on a time serie of environmental data, taking into account the seasonality (as my serie cover 30 years with several measurement per month).
Taking into account seasonality would mean perform the wilcoxon test for every monthy time serie, and after, combining all the 12 results in a common statistic.
This procedure is commonly described in the litterature from the 80's and 90's but without the mathematical details for taking into account the seasonality.
This is probably very simple but I do not find any details on the web. Furthermore, if somebody as some piece of R code to do it, that would be great :)
I am not sure it will be valid. I suppose you refer to combining independent tests of significance. But are these tests really independent ? Indeed, you have a time series, so an observation at time t is not independent of the observation at time t + 1. An alternative would be to create a specific test and obtain the critical values by simulations.
" I suppose you refer to combining independent tests of significance. "
Guy Mélard exactly, as it is stated in an old textbook:
"The rank-sum test can be implemented in a seasonal manner just like the Mann-
Kendall test, called the seasonal rank-sum test. It computes the rank-sum statistic separately for each season, sums the test statistics, their expectations and variances, and then evaluates the overall summed test statistic."
I am puzzled by the "evaluates the overall summed test statistic" part
I don't know the textbook you mention. I referred to something more general by Allan Birnbaum (1954) Combining independent tests of significance, Journal of the American Statistical Association, Vol. 49, No. 267 (Sep., 1954), pp.559-574. My point is that, at least in your case in your case but probably also in the textbook you mention, the tests are not independent because they are based on non-independent data.
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