# Interpretation of non significant results of the Mann-Kendall Trend Test

I am currently conducting a study on several climate datatsets, and am using the Mann-Kendall Trend Test to check if my Time Series Data contains monotonic (rising or falling) Temperature Trends. To do this I have been using the function MannKendall() in the R-Packet Kenddall, which uses Kendall Tau as a test statistic. So far all my results have been as expected but I am struggling with interpreting the values of Kendalls Tau (τ) for my non-significant results. τ can assume values between -1 to 1, which indicate the direction of the trend, with values near 1/-1 being a very strong trend. Values of τ near 0 however indicate that a weak or no trend is present in the data. I want to know where the cut off from weak trend to no trend is located.

As an example I tested 5 datasets for trends using the MK test. All results were non-signficant and produced the following τ values:

τ: 0.09443, 0.117838, 0.13556, 0.003025, 0.3090

I feel confident that the τ value of 0.003025 means that there really is no trend in the data. Where it gets tricky are the τ values of 0.09443 and 0.117838. Are they close enough to 0 that we could say there is no trend? Or do they instead indicate a weak (but non significant) positive trend?

I am guessing that this is up to interpretation and that something like a clear cut ranking of τ values (i.e. τ>.02= weak trend, τ>0.1= no trend) doesnt exist. I couldnt really find any literature on this problem specifically, so it would be great if any of you are able to point me in the right direction or know the answer to my question.

Thank you

Technically, you can't say there is no trend unless $$\tau = 0$$. But I suggest graphing the time series and deciding for yourself. You might want to add some sort of smooth line (such as moving average or loess) to guide you. Ideally, you would also put this graphs in your paper or presentation, to guide your readers.
• "Technically, you can't say there is no trend unless $\tau=0$" - this is correct, and I think that as statisticians we should insist that this is wrong to say, not only "technically", as there may well be situations in which such statements are associated with practically relevant misinterpretations. Better something like "there is no indication of any trend". Commented May 8 at 11:32