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## Mann-Kendall Test

version 1.0 (1.93 KB) by

Mann-Kendall non-parametric trend test.

Updated

The code performs original two tailed Mann-Kendall test. It tests the null hypothesis of trend absence in the vector V, against the alternative of trend.
The result of the test is returned in H = 1 indicates a rejection of the null hypothesis at the alpha significance level. H = 0 indicates a failure to reject the null hypothesis at the alpha significance level.

Nirav Rajani

### Nirav Rajani (view profile)

What is the procedure to run the mann-kendall trend test

### MOHAMMAD YASIR ALI (view profile)

for every value of alpha I am getting p_value=0 but pz is changing. what does this signify for my result. z is 8.3496 and s is 3366.

It would be good if the function didn't rely on other specialized functions that are only available in toolboxes.

Andre Almagro

### Andre Almagro (view profile)

Hi everyone! I'm working with a 34 years of annual rainfall data. I have 11299 points (latitude and longitude) that cover all Brazil's territory. How can I apply this function for each point? First column represent the year of observation and the others represent each point. So I have a variable with 34x11300 values. How can I solve this? Thank you!!!

Lei He

### Isabel Espadas Sánchez (view profile)

I'm working with a time series that have NaNs and I need to test it with the MK test, but at this moment I have any idea how use this code with my data since always gives me H = 0 and p_value=NaN. You have any idea how I can solve my problem?

arain zz

Ali A

### Ali A (view profile)

@blanca ortiz
You can use the following code

function[H,p_value]=Mann_Kendall(V,alpha)
V=reshape(V,length(V),1);
alpha = alpha/2; %
n=length(V);
S=0;
for i=1:n-1
S = S + sum(sign(V(i+1:n) - V(i)));
end
h=1;
while ~isempty(V)
g=find(V==V(1));
tp=length(g);
Sum(h)=tp*(tp-1)*(2*tp+5); %#ok<AGROW>
V(g)= [];
h=h+1;
end
VarS=((n*(n-1)*(2*n+5))-sum(Sum))/18;
%Standard deviation
De=sqrt(VarS);
if S>=0;
z= ((S-1)/De)*(S~=0);
else
z= ((S+1)/De);
end
p_value=2*(1-normcdf(abs(z),0,1)); % tail on both sides
pz=norminv(1-alpha,0,1);
H=abs(z)>pz;
return

Ali A

Ali A

blanca ortiz

### blanca ortiz (view profile)

Can anyone help me please? I have tried different types of vectors and it doesn't work. I am getting two errors, first:

??? Undefined function or method 'Sqrt' for input arguments of type 'double'
and then too many outputs.
I would really appreciate if anyone could tell me an example of the vectors and if there is any other mistake. Thanks

V=reshape(V,length(V),1);
alpha = alpha/2; %
n=length(V);
i=0;S=0;
for i=1:n-1
S = S + sum(sign(V(i+1:n) - V(i)));
end
h=1;
while ~isempty(V)
g=find(V==V(1));
tp=length(g);
Sum(h)=tp*(tp-1)*(2*tp+5);
V(g)= [];
h=h+1;
end
VarS=((n*(n-1)*(2*n-5))-sum(Sum))/18;
%Standard deviation
De=Sqrt(VarS);
If S>=0;
Z= ((S-1)/De)*(S~=0);
else
z= ((S+1)/De);
end
p_value=2*(1-normcdf(abs(z),0,1)); % tail on both sides
pz=norminv(1-alpha,0,1);
H=abs(z)>pz;
return

Jie

### Jie (view profile)

What is the vector type for this test? I tried different types but they didn't work.

Hydro

### Hydro (view profile)

I found exactly what i was doing..however, i am getting an error message of too many output argument.Any help would be appreciated.

function [H,P] = mann_kendall(x,alpha)
if nargin<2;
alpha=0.05;
end
n=length(x);
i=0; j=0; S=0;
alpha=alpha/2;

for i = 1:n-1
for j=i+1:n
S = S + sign(x(j) - x(i));
end
end

VS=(n*(n-1))*(2*n+5)/18; % Variance
De=sqrt(VS); % Standard Deviation

if S >= 0;
Z=((S-1)/De)*(S~=0);
else
Z=((S+1)/De);
end

P=2*(1-normcdf(abs(Z),0,1)); % tail on both side
pz = norminv(1-alpha,0,1);
H=abs(Z)> pz;

end

Roque Santos

### Roque Santos (view profile)

Hello,

Is showing an error that says: "Undefined function 'Mann_Kendall_Modified' for input arguments of type 'double'."

How do I correct?

Ehsan Jalilvand

### Ehsan Jalilvand (view profile)

Hi Simone,
First of all thank you. I've made some minor change to your code as follow,to include tied groups in Calculating the variance:
after line 48:
% Determining the variance (tied group included)
h=1;
while ~isempty(V)
g=find(V==V(1));
tp=length(g);
Sum(h)=tp*(tp-1)*(2*tp+5);
V(g)=[];
h=h+1;
end
VarS=((n*(n-1)*(2*n+5))-sum(Sum))/18;

Ehsan

Brian Novak

### Brian Novak (view profile)

Vectorizing the inner loop in the double sum for calculating S speeds it up significantly:

for i = 1:n-1
S = S + sum(sign(V(i+1:n) - V(i)));
end

Janak

### Janak (view profile)

Hi Fatichi,

I want to run your code for trend analysis. I have matlab 11 and statistical tool box in my computer. Can you provide example data file for this code.

Ram

Hari

### Hari (view profile)

Hi, Simone Fatichi,

I am new to Mat lab.Please tell me how to give input data and run your Mann_Kendall.m code using Mat lab.

Hanna Modin

### Hanna Modin (view profile)

Thank you!

It is working very well and is very convenient to use since it returns the result of the hypothesis test, not just the test statistic. But: the alternative of S = 0 --> Z = 0 is not accounted for if I'm right.

For future updates I would also wish for a default significance level (for convenience). And perhaps a mention in the help text that there should be no autocorrelation in residuals.

##### MATLAB Release
MATLAB 7.5 (R2007b)