• Boy you are doing well. Good question. Firstly, you have define a threshold such as 1%, 5% or 10% with your null hypothesis (there is no trend), you are judging the trend based on these threshold. However, there may have a  trend in the data behind your selected threshold. For example, you are analyzing a time series and you want see the trend at 5% significance level. You get the MK test statistic(Z) +1.645. Then based on your null hypothesis, there is no trend at 5% significance level. However, test statistic (Z value i.e., I say 1.645) reveals that there is a positive trend which is significant at 10% significant level.
• Moreover, if you calculate p value instead of z value. For example, your calculated p value is 0.11 what does it mean. As you are evaluating the null hypothesis at 5% significant level (or 95% CL), there is no trend based on your null hypothesis. However there is a trend that is significant at 11% significant level.
• I hope that you may get some idea from here. Boy, therefore, you need to calculate the changing rate/Slope. What types of data are you analyzing, please let me know? I do not prefer MK test for these days. You should apply some advance statistic, though MK test is a robust test. I know you have desire to publish your work in high quality journal. Boy, you also know analysis using MK test is saturated so I think prestigious journals may not agree to publish now a days.
• Best of luck with your work.

Thank you so much my big well wisher, I have caught my inexistent as my dependency was  only on p value and 5% level of significance. I will follow your instruction. For your kind information i am working on climatic data and rice production data about 30 years.

Please suggest me what will be the advance option instead of Mann- Kendall test. 

You may use some recent methodological advance in trend analysis . There is noise in meteorological data, therefore, it is necessary to denoise the  data before analyzing trend. Wavelet aided  denoising will  be good for your case. Or You may use wavelet transform data to detect trend and discrete wavelet transform will be good for you. If you face any difficulties, let me know or we have a discussion during Eid.

Thank you for your suggestion. Off course we have a discussion during Eid. I will inform you if there is any difficulties. 

Wish to meet you soon.................

Aoa

Dear Sakiur Rahman will you please help me regarding data homogenization and trend detection methods?

clear;

%PROGRAM TO TEST THE TREND IN DATA SERIES USING MAAN KENDAL TEST AND

%ESTIMATION OF TRENDLINE USING NON PARAMETRIC TEST

% 1ST COLUMN TREND IS INCREASING OR DECREASING

% 2ND COLUMN SIGNIFICANCE OR NOT AT 95 % LEVEL OF SIGNIFICANCE

% SLOPE OF TRENDLINE

% INTERCEPT OF TRENDLINE

% "0" MEANS THERE IS NO TREND AT 95 PERCENT LEVEL OF SIGNIFICANCE AND IF IT IS "1" INDICATES THE

%EXISTANCE OF TREND AT 95 PERCENT LEVEL OF SIGNIFICANCE.

% IF THE VALUE OF Z i.e. SECOND COLUMN OF RESULT MATRIX IS POSITIVE THEN

% THE TREND IS INCREASING WHEREAS IT IS SAID TO BE DECREASING IF IT IS

% NEGATIVE.

input_m=load('input.txt','r');

input_y=load('input_x.txt','r');

temp=size(input_m);

n_data=temp(1,1);

n_series=temp(1,2);

result=[];

for k=1:n_series

input=input_m(:,k);

input_x=input_y(:,k);

s=0;

a=[];

for j=1:n_data,

for i=j+1:n_data,

if(input(i,1)> input(j,1))

s=s+1;

elseif(input(i,1)== input(j,1))

s=s;

else

s=s-1;

end

end

a=[a;s];

end

score=s;

var=n_data*(n_data-1)*(2*n_data+5)/18;

if(s>0)

z=(s-1)/sqrt(var);

else if s==0

z=0;

else

z=(s+1)/sqrt(var);

end

end

if z>0

trend=1;

else if z==0

trend=0;

else

trend=-1;

end

end

prob=normcdf(z);

alpha=0.05;

if (z

Dear Khalid,

If you are doing trend analysis for a time series data better to perform break point test first like pettitt test or standard normal homogeneity test (SNHT) or buishand range test. Then you can identify better whether their any possibility of trend exists or not. Also the estimation of magnitude using sen slope can provide a better picture about acceptance or rejection of NULL hypothesis.

Kindly find the R code for SNHT test

sn

Hi Md. Khalid Hassan Real , I hope you were able to complete your analysis and paper. Please, were you able to apply the discrete wavelet transform to your data, as A T M Sakiur Rahman kindly suggested? I need it for my work and need some help.

Creio que a magnitude expressa uma variabilidade que independe de tendências. Não haver tendência não implica em não haver variabilidade.

What is the difference between mann-kendall and sen’s slope?

1. Determination of an upward or downward trend depends on Z value sign or Sens Slope Sign?

2. I know both of their sign should be the same for one case. But, I am facing a weird situation where z=0.012 and sen's slope= 0. What does it mean? upward trend? or no trend?

no trend

Binata Roy, it is absolutely normal to have this kind of result. Sen's slope is the median of the slopes of each pair of data. You can check the result checking Kendall's S and Tau value.

Md. Khalid Hassan Real , If Kendall's S is zero, you can ignore Sen slope calculation.

Sen's slope is basically use to identify the magnitude of trend in a data series which not serially auto-correlated and Mann-kendall test use for identifying the significance level (means is this magnitude statistically significant or not) at different confidence level (95 0r 99%).

As per your query, (I guess) : Sen's slope estimation is an important aspect to know about the magnitude of trend and it doesn't matter about it's significance level. Insignificant magnitude could be a result for sure.

Article An Analysis of Long-Term Rainfall Trends and Variability in ...

If there is no statistical trend using Mann-Kendall you can try the Sen's slop estimator to confirm the Mann-Kendall test result.

I am identifying the trend of average temperature and total rainfall over a 30 year period. At the 5% level, there is a trend for temperature but no trend for rainfall. The Sen's slope for Rainfall is 14.725. Can I know why it is so high? It is 0.012 for temperature. Should I calculate this at 10% level too?

Binata Roy positive value of Z variate indicates a positive trend and negative value of Z variate indicates a downward trend. You can refer my latest publication here DOI: 10.35940/ijitee.E2276.039520 for your refernce

I am working on an indicator based assessment. My aim is to be able to compare provinces in terms of their index results. One of the indicators is temperature and I use Mann-Kendall Test and Sen's slope estimator in order to detect trend and also the magnitude of that trend. Since I want to compare the temperature increase of corresponding provinces, should I use the Z value or Qmed value in order to use it for the assessment?

I am asking because I realized that the province with higher Z value has lower Qmed value than other province has. A T M Sakiur Rahman

@ Champika Kariyawasam If you are testing annual/ seasonal/ wet months rainfall trend, then the result seems alright. Because we generally use total rainfall for analysis. For temperature, trend is based on the average value mostly. Therefore, 0.012 seems alright also.

@ Mekonnen H Daba Mann-Kendall identifies if there is any trend. Whereas, sen's slope determine the magnitude of a trend.

Yes, you are adviced to do so. because the former test is for significance but later also tells about the trend either decreasing or increasing even if it is not significant or insignificant on the basis of Sen's value get positive or negetive.

When in doubt, report the information. So, yes, report both. Magnitude and sign of slope are still useful information...they describe the change over time...whether or not the trend is statistically significant.

Mann Kendall's Test shows the monotonic nature of the trend. Whether, there is monotonic trend in the data series or not.

Here I am assuming that you are familiar with "What is Monotonic Trend?"

On the other hand Sen's slope shows the magnitude of the increase or decrease in the trend. Existence of the monotonic trend is not the per-requisite to execute the Sen's slope method.

Therefore, I would say that there is no strict rule that one should run the Sen's slope test only if there is monotonic trend.

I hope this brings out some clarity.

A T M Sakiur Rahman What are other better methods of trend calculation for climatic data?

Sheikh Hefzul Bari I have total monthly streamflow data of 30 years for which I am getting Kendall's S = 0. I am confused because of it as I have not read a paper with the same result. Is it a valid result?

Harsh Upadhyay The result indicates there are no trend. This should be fine. However, there might be fluctuation in trends which can be an important finding.

Sheikh Hefzul Bari Thank you for replying. Just to be clear, by fluctuating trends, do you mean there are trends in different directions within the data for a shorter time period (say, 15 years) but are not reflected in the overall trend for the entire period of 30 years as they cancel each other out?