Difference between revisions of "Analyze data with the Statistics software R"

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Line 76: Line 76:
 
                 t += p[i].Y() + ';';
 
                 t += p[i].Y() + ';';
 
             }
 
             }
             new Ajax.Request('/~alfred/jsxgraph/trunk/examples/rserv.php', {
+
             new Ajax.Request('/~alfred/jsxgraph/examples/rserv.php', {
 
                 method:'post',
 
                 method:'post',
 
                 parameters:'input='+escape(t),
 
                 parameters:'input='+escape(t),
Line 88: Line 88:
 
                         var sd = a[1]*1.0;
 
                         var sd = a[1]*1.0;
 
                         var med = a[2]*1.0;
 
                         var med = a[2]*1.0;
                        var mad = a[3]*1.0;
 
 
                         var mad = a[3]*1.0;
 
                         var mad = a[3]*1.0;
 
                         var est1 = a[4]*1.0;
 
                         var est1 = a[4]*1.0;
 
                         var est2 = a[5]*1.0;
 
                         var est2 = a[5]*1.0;
 +
 
                         if (!graph2) {  
 
                         if (!graph2) {  
 
                             graph2 = brd.createElement('curve', [[x[0],x[x.length-1]],[m,m]], {strokecolor:'red'});  
 
                             graph2 = brd.createElement('curve', [[x[0],x[x.length-1]],[m,m]], {strokecolor:'red'});  
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                         }
 
                         }
  
                         $('output').innerHTML = '<b><font size="+1">Normal location and scale:</font></b><br /><br />'+  
+
                         document.getElementById('output').innerHTML = '<b><font size="+1">Normal location and scale:</font></b><br /><br />'+  
 
                                 '<b>Estimates for location (true value = 10):</b><br />' +
 
                                 '<b>Estimates for location (true value = 10):</b><br />' +
                                 'Mean = ' + brd.round(m,2) + '<br />' +
+
                                 'Mean = ' + Math.round(m,2) + '<br />' +
                                 'Median = ' + brd.round(med,2) + '<br />' +
+
                                 'Median = ' + Math.round(med,2) + '<br />' +
                                 'Radius-minimax estimator = ' + brd.round(est1,2) + '<br /><br />' +
+
                                 'Radius-minimax estimator = ' + Math.round(est1,2) + '<br /><br />' +
 
                                 '<b>Estimates for scale (true value = 3):</b><br />' +
 
                                 '<b>Estimates for scale (true value = 3):</b><br />' +
                                 'Standard deviation = ' + brd.round(sd,2) + '<br />' +
+
                                 'Standard deviation = ' + Math.round(sd,2) + '<br />' +
                                 'MAD = ' + brd.round(mad,2) + '<br />' +  
+
                                 'MAD = ' + Math.round(mad,2) + '<br />' +  
                                 'Radius-minimax estimator = ' + brd.round(est2,2) + '<br />';
+
                                 'Radius-minimax estimator = ' + Math.round(est2,2) + '<br />';
 
                         brd.update();
 
                         brd.update();
 
                     };
 
                     };

Latest revision as of 12:35, 21 February 2013

Normal Location and Scale

This litte application sends the y-coordinates of the points which are normal distributed (pseudo-)random numbers to the server.
There, location and scale of the sample are estimated using the Statistics software R.
The return values are plotted and displayed.

The computed estimates are:

  • mean, standard deviation: red (non-robust!)
  • median and MAD: black (most-robust!)
  • radius-minimax estimator: green (optimally robust; cf. Rieder et al. (2008))

By changing the y-position of the four movable points you should recognize the instability (non-robustness) of mean and standard deviation in contrast to the robust estimates; e.g., move one of the four movable points to the top of the plot.

Online results:

Statistics:<br>

The underlying source code

The underlying JavaScript and PHP code

The R script can be downloaded here.

References

  • The Costs of not Knowing the Radius, Helmut Rieder, Matthias Kohl and Peter Ruckdeschel, Statistical Methods and Application 2008 Feb; 17(1): p.13-40; cf. also [1] for an extended version.
  • Robust Asymptotic Statistics, Helmut Rieder, Springer, 1994.
  • Numerical Contributions to the Asymptotic Theory of Robustness, Matthias Kohl, PhD-Thesis, University of Bayreuth, 2005; cf. also [2].

External links