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Mann Kendall

Hi all. I'm trying to run a Mann-Kendall to test if a temporal trend is significant. Can't find it in the JMP manual or anything online. Anyone have any ideas?

Thanks!

1 ACCEPTED SOLUTION

Accepted Solutions

Mann Kendall

Even if the definitions Mann-Kendall test statistic and the Kendall Tau b often is described in different terms (from time series and correlation perspectives, respectively), they are essentially the same as far as I can tell.

Below is a script I wrote quite long ago. It calculates and shows the Theil's slope and performs the Mann-Kendall test. A parametric linear regression line is shown in the plot just for comparision. I planned to generalize the script by include a "By" function as well as the posibilty to account for seasonal patterns. But I have not had the time to realize those plans yet. I hope this will give you some ideas.

dt = Current Data Table();

dlg = Column Dialog(

"Estimate Theil slope and Kendall Tau from Data Table " ||

Char( dt << get name ),

Ys = ColList( "Select Y",

maxcol( 1 ),

mincol( 1 ),

Datatype( numeric )

),

Xs = ColList( "Select X",

maxcol( 1 ),

mincol( 1 ),

Datatype( numeric )

),

Group = ColList( "By (not working)", maxcol( 1 ) )

);

colY = Column( dt, dlg["Ys"] );

colX = Column( dt, dlg["Xs"] );

colGroup = Column( dt, dlg["Group"] );

//Calculation of Theil slope

n = N Rows( dt );

slopes = J( n, n, . );

For( i = 1, i < n, i++,

For( j = i + 1, j <= n, j++,

slopes[i, j] = (colY[j] - colY[i]) / (colX[j] - colX[i])

)

);

theil = Quantile( 0.5, slopes );

//Kendall's Tau b to test if slope differs from zero

mv = Multivariate(

Y( colY, colX ),

Scatterplot Matrix(0),

Correlations multivariate(0),

Kendall's Tau( 1 )

);

//Plot data and add linear regression and Theil's slope

biv = Bivariate(

Y( colY ),

X( colX ),

Fit Line( {Line Color( "Red" )} ),

Fit Special( Slope( theil ), {Line Color( "Green" )} ),

invisible

);

rbiv = biv << report;

rbiv["Linear Fit"] << close all like this;

rbiv[Outline Box( 7 )] << set title( "Theil's Slope" );

db = Report( mv )["Multivariate"] << parent;

db << prepend( rbiv );

db[Text Box( 4 )] << set text( "Theil's Slope" );

rbiv << close window;

3 REPLIES 3  David_Burnham
Super User

Re: Mann Kendall

I'm not sure to what degree (if at all) the Mann-Kendall test is related to the Kendall Tau statistic for non-parametric correlation.  The later can be accessed under the multivariate platform: Analyze>Multivariate Methods then from the multivariate report select Nonparametric Correlations from the hotspot.

If the tests are completely different I'd be interested in any references that you have for this method.  I'm considering building an add-in that implements a number of methods (e.g. Hurst Index) that have been developed for the field of hydrology

Regards

Dave

-Dave

Mann Kendall

Even if the definitions Mann-Kendall test statistic and the Kendall Tau b often is described in different terms (from time series and correlation perspectives, respectively), they are essentially the same as far as I can tell.

Below is a script I wrote quite long ago. It calculates and shows the Theil's slope and performs the Mann-Kendall test. A parametric linear regression line is shown in the plot just for comparision. I planned to generalize the script by include a "By" function as well as the posibilty to account for seasonal patterns. But I have not had the time to realize those plans yet. I hope this will give you some ideas.

dt = Current Data Table();

dlg = Column Dialog(

"Estimate Theil slope and Kendall Tau from Data Table " ||

Char( dt << get name ),

Ys = ColList( "Select Y",

maxcol( 1 ),

mincol( 1 ),

Datatype( numeric )

),

Xs = ColList( "Select X",

maxcol( 1 ),

mincol( 1 ),

Datatype( numeric )

),

Group = ColList( "By (not working)", maxcol( 1 ) )

);

colY = Column( dt, dlg["Ys"] );

colX = Column( dt, dlg["Xs"] );

colGroup = Column( dt, dlg["Group"] );

//Calculation of Theil slope

n = N Rows( dt );

slopes = J( n, n, . );

For( i = 1, i < n, i++,

For( j = i + 1, j <= n, j++,

slopes[i, j] = (colY[j] - colY[i]) / (colX[j] - colX[i])

)

);

theil = Quantile( 0.5, slopes );

//Kendall's Tau b to test if slope differs from zero

mv = Multivariate(

Y( colY, colX ),

Scatterplot Matrix(0),

Correlations multivariate(0),

Kendall's Tau( 1 )

);

//Plot data and add linear regression and Theil's slope

biv = Bivariate(

Y( colY ),

X( colX ),

Fit Line( {Line Color( "Red" )} ),

Fit Special( Slope( theil ), {Line Color( "Green" )} ),

invisible

);

rbiv = biv << report;

rbiv["Linear Fit"] << close all like this;

rbiv[Outline Box( 7 )] << set title( "Theil's Slope" );

db = Report( mv )["Multivariate"] << parent;

db << prepend( rbiv );

db[Text Box( 4 )] << set text( "Theil's Slope" );

rbiv << close window;

Mann Kendall

thanks MS and Dave! I was not sure if Kendall's Tau and the Mann-Kendall test were the same (and/or related) either. Thanks for the info on the multivariate test and then for the script as well!