Homogeneity test of Global Trends using Chi-Square on Mann-Kendall

Test for homogeneity of trends in different seasons-stations,and global trends using Chi-Square.

Description

GlobalTrends- Homogeneity tests for multiple seasons and stations. This function will test for trends when seasonality is present and over multiple observation stations, all of which are Chi-square statistics. There are so many statistical tests being done, this function is more like a script or program than a function, but I prefer operating with functions.  
 
This function relies heavily on Matlab's Statistical Toolbox for obtaining Chi-square values and ktaub.m function.  
 
These tests will allow for ties, missing data, and multiple observations per time index, since it uses the enhanced ktaub.m function that was recently updated.  
 
There are numerous narratives as part of the output to the screen providing supporting interpretation of the results.  
 
This function is based on Chapter 17.5 in Gilbert.  
 
Syntax:  
      [ChiOutput K M sig] = GlobalTrends( datain, alpha )  
 
Inputs:  
To stay consistent with the previous trend statistics posted (ktaub, sktt, and SenT), data are expected to be in the following structure:  
       datain(:,1) = Year  
       datain(:,2) = season  
       datain(:,3) = value  
       datain(:,4) = station  
       alpha = scaler (e.g. 0.05)  
 
Outputs:  
   ChiOutput structure is like the following (labels are not included)  
        Total: Chi-square df p-value  
        Homogeneity: Chi-square df p-value  
        Season: Chi-square df p-value  
        Station: Chi-square df p-value  
        Station-Season: Chi-square df p-value  
        Trend: Chi-square df p-value  
      
And depending on significances of Stations, Seasons, and StationSeasons, one of three other outpus may occur:  
        K: significance of Seasons per station  
        M: significance of Stations for seasons  
 
 And when seasonal trend tests should not be done  
        sig: individual station-season p-values are given by row  
 
There is a lot of output to the screen as well, but using fprintf, one could easily redirect output to a file.  
    Requirements  
       - Matlab Statistical Toolbox  
       - ktaub.m  
 
Reference:  
      Richard O. Gilbert, Pacific Northwest National Laboratories,  
      "Statistical methods for Environmental Pollution Monitoring", 1987, Van Nostrand Reinhold, New York Publishing, ISBN 0-442-23050-8.  
 
One last note. I’ve posted enough functions that it makes sense to constitute forming a Matlab toolbox…so it’s in the works (slowly).  
 
    Written by:  
      Jeff Burkey  
      King County- Department of Natural Resources and Parks  
      email: [e-mail]  
      12/13/2008  

• Required Products: Statistics Toolbox
• MATLAB release: MATLAB 7.7 (R2008b)
• Other requirements: ktaub.m
• Other Files: ex1c.mat, ; GlobalTrends.m

[Jeff Burkey]

I've included a MAT file with example data to run the function. I hope this helps.