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I have annual average rainfall data in mm/day units. I want to see the trend of the rainfall, whether its increasing or decreasing. How to do this. My teacher told to put a linear regression line and see its slope. If the slope is negative, trend is decreasing and vice versa. Further, ttest can determine the significance level of the trend present. Is it a correct way to do? I know that the data is not normally distributed. What other way I can determine trend? Also, do I always have to check skewness and kurtosis to see data is normally distributed and then apply ttest or any other test?

Please help, I am new in statistics and very confused. Thanks.

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I'd say first that you probably want to do what your teacher says for the purposes of the assignment. As for the actual statistics, determining trends can be pretty hard, especially if you're new to statistics and don't have all the tools. For any answer provided, let us know whether it needs clarification, or an idea of how to implement it. What data do you have? Is there any way for you to post the dataset?

My suggestion for this would be something Bayesian. First, calculate the linear trend in the data. Then, randomly re-order the data and calculate the linear trend of that. Keep going until you have the actual linear trend and a few hundred or thousand "randomized" trends. Then you can see how often you get a random trend that's as big or bigger than the actual one for the data. Doing it this way doesn't assume much else about the data, since it's using the actual sample to create a distribution. It does, however, assume that whatever trend underlying it is a linear trend, not exponential or cubic.

I've seen some use of the Kendall-Mann test for trends. I like this one because 1) the trend doesn't have to be linear; 2) the fluctuations about the trend only have to be independent and identically distributed; and 3) there are some modifications for handling missing data, which is always a plus in environmental science. My primary issue with it is that rainfall data, even annually-averaged, can have a lot of correlations in it, which the test is bad at addressing. How much this matters depends on which location you're looking at.

A final possibility: Calculate the trends for the logarithm of the rainfall! Annual average rainfall has to be $\ge0$, so deviations can't be normally distributed. But its logarithm might be. It'll take some time for me to work through the math, but at least then you're starting with an assumption that might be true. Rainfall data in general tend to have long tails, so log-normally distributed variance makes sense to me.

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  • $\begingroup$ Thanks for the answer. The data is like series: 1950-7.6 1951-8.2 1952-5.3 and so on. I tried mann kendall, but I guess it just tells that there is some trend present but not exactly whether it is increasing or decreasing. I tried logarithm also, but with kolmogorov-smirnoff test it says that data is not normally distributed. I hope I am doing right. $\endgroup$
    – Windy Day
    Commented Jul 5, 2015 at 14:32
  • $\begingroup$ On that Kendall-Mann page, the statistic $Z_{MK}$ is what you test for significance, right? If $Z$ is positive, then the trend is increasing; if it's negative, decreasing. $\endgroup$
    – Jareth Holt
    Commented Jul 6, 2015 at 14:52

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