Regarding Modified Mann-Kendall test code from File Exchange

I am trying to understand the following code from File Exchange: Mann-Kendall Modified test

The author is no longer active it seems. Therefore, I am asking my doubt here.

On line 86: We have

if S >= 0

Z=((S-1)/StdS)*(S~=0);

else

Z=(S+1)/StdS;

end

Why is there a -1 and a +1 here when finding the Z-score here?

Thanks

Answer 1

[Shivansh]

Hi Atharva,

In the Mann-Kendall test, the step

if S >= 0

Z=((S-1)/StdS)*(S~=0);

checks if Kendall's rank correlation coefficient (S) is greater than zero. If S is positive, it indicates a positive trend in the data, meaning that there is a systematic increase in the values over time. In this case, we calculate the Z-score by subtracting 1 from S and dividing it by the square root of the variance of S. If S=0, Z is automatically assigned a value of 0.

Similarly, the step

else

Z=(S+1)/StdS;

checks if S is less than zero. If S is negative, it indicates a negative trend in the data, meaning that there is a systematic decrease in the values over time. In this case, we calculate the Z-score by adding 1 to S and dividing it by the square root of variance of S.

These adjustments ensure that the tie correction is properly applied to the test statistic S when calculating the Z-score. By subtracting -1 or adding +1, the code accounts for ties in the data and helps in obtaining accurate results.