Trend statistic denoted as Z can be positive or negative. One one hand, the values of Z can be large; for instance, for the Cumulative Sum of rank Difference (CSD) approach which is also so highly comparable to the Mann-Kendall test, the Z values can be as large as in the range from -(n-1) to +(n-1) where n is the sample size. On the other hand, the p-values (probability values) vary in the range 0 to 1.

In testing the null hypothesis H0 (no trend), one can use the Z values or the p-values.

If you have to use the Z values, you must compare the computed Z with that value existing at the critical significance level. It means, first, you select your alpha. Let's assume our alpha is 0.05 in our case in which you are talking about two-tailed test, the inverse of the standard normal cumulative distribution with a probability of alpha = 0.05 would be 1.959964. So, if your computed Z is less than the critical value, H0 (no trend) is NOT rejected; otherwise, the H0 (no trend) is rejected. In testing the H0 (no trend) you consider the absolute values of the computed and critical Z values. However, because trends can be positive or negative, the signs before the computed Z determine the directions of the trend whether positive (increasing) or negative (decreasing). This means that the range of your Z you provided ([-1.65 1.65], [-1.96 1.96], and [-2.58 2.58]) are valid and correspond to our alpha values 0.1, 0.05, and 0.01, respectively. Considering one-tailed test, the values would be different, and for our case the absolute thresholds would correspondingly be 1.28, 1.64, and 2.33.

In the case of using the probability value for testing the H0 (no trend), you compute the p-value (probability value, p) for the computed Z value as the cumulative density function of the normal distribution based on the standard case with the mean of zero and standard deviation equal to one. If the computed p-value is less than nominal level (here, consider our selected alpha), the H0 (no trend) is rejected; otherwise, the H0 (no trend) is not rejected.

Based on the above information, you realize some of the values you provided are greater than 1. If you agree with me, then, indeed, why would, for instance, -0.86 (of April, Area1) be significant to the level of 99%? Could it be due to lack of consistence of the researcher in the use of both p-values (at one point) and z values (in another point)? Is the hypothesis being tested consistent with the question you are asking? Attempts to answer such questions (and many others) would take you through valuable paths of exploration in trend analyses especially for you as a researcher. However (for the case of -0.86 as an example), if you have the data, you would re-compute to check if the data can yield the Z value above 2.575. Alternatively, you can test the trend for the same data using the significance of the Sen's slope. Here, you can use the procedure which you can get in the first paper at the bottom of the text answering your question.

REGARDING YOUR INTEREST IN TREND ANALYSES,

• For consistence in inference in trend results, I emphasize the importance of testing both the directions and magnitudes of monotonic trends (see the second paper for the reasons).
• On the need to consider many trend detection methods to take into account the uncertainty due to the selection of the method, see the first paper below.
• On the CSD method and how it compares to the Mann-Kendall test (see the third and the fourth papers, and the supplementary material via the last link).
• Methods like the Mann-Kendall and Spearman's rho test are purely statistical and yield results which are meaningless sometimes. Thus, as it is typical of the CSD method, both graphical and statistical techniques should be used to yield more considered trend results for a careful inference.
• The CSD method is incorporated in a freely downloadable tool call CSD-NAIM (see the fifth item below).
• For further reading on the development of the CSD method, read the second, third and the sixth papers).

https://www.researchgate.net/publication/309695087

https://www.researchgate.net/publication/320711172

https://www.researchgate.net/publication/275462047

https://www.researchgate.net/publication/326608816

https://www.researchgate.net/publication/303813632

https://www.researchgate.net/publication/305386142

https://link.springer.com/article/10.1007/s00477-018-1587-0