Change significance level MannKendall trend test -- R

Question

I want to perform Mann-Kendall test at 99% and 90% confidence interval (CI). When running the lines below the analysis will be based on a 95% CI. How to change the code to perform it on 99 and 90% CI?

vec = c(1,2,3,4,5,6,7,8,9,10)
    MannKendall(vec)

question from:https://stackoverflow.com/questions/66046689/change-significance-level-mannkendall-trend-test-r

Answer 1

I cannot comment yet, but I have a question, what do you mean when you say that you need to perform the analysis on a 99 and 95% CI. Do you want to know if your value is significant at the 99 and 90% significance level?

If you just need to know if your score is significant at 99 and 90% significance then r2evans was right, the alpha or significance level is just an arbitrary threshold that you use to define how small your probability should be for you to assume that there "is no effect" or in this case that there is independence between the observations. More importantly, the calculation of the p-value is independent of the confidence level you select, so if you want to know if your result is significant at different confidence levels just compare your p-value at those levels.

I checked how the function works and did not see any indication that the alpha level selected is going to affect the results. if you check the source code of MannKendall(x) (by typing MannKendall without parenthesis or anything) you can see that is just Kendall(1:length(x), x). The function Kendall calculates a statistic tau, that "measures the strength of monotonic association between the vectors x and y", then it returns a p-value by calculating how likely your observed tau is under the assumption that there is no relation between length(x) and x. In other words, how likely it is that you obtain that tau just by chance, as you can see this is not dependent on the confidence level at all, the confidence level only matters at the end when you are deciding how small the probability of your tau should be for you to assume that it cannot have been obtained just by chance.