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

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* mean, standard deviation: red (non-robust!)<br />
 
* mean, standard deviation: red (non-robust!)<br />
 
* median and MAD: black (most-robust!)<br />  
 
* median and MAD: black (most-robust!)<br />  
−
* optimally robust radius-minimax estimator: green (cf. Rieder et al. (2008))<br /><br />
+
* radius-minimax estimator: green (optimally robust; cf. Rieder et al. (2008))<br /><br />
 
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.<br /><br />
 
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.<br /><br />
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<html>
 
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<link rel="stylesheet" type="text/css" href="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraph.css" />
 
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<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/prototype.js"></script>
 
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<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraphcore.js"></script>
 
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<div id="jxgbox" class="jxgbox" style="width:700px; height:400px;" onmouseup="doIt();"></div>
 
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</html>
 
 
===Online results:===
 
===Online results:===
 +
<html><script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/prototype.js"></script></html>
 
<pre id='output'>Statistics:<br></pre>
 
<pre id='output'>Statistics:<br></pre>
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<html>
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<jsxgraph width="700" height="400">
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<script language="JavaScript">
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         brd = JXG.JSXGraph.initBoard('jxgbox', {boundingbox: [-0.15, 60, 11.15, -20],axis:true});
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         brd = JXG.JSXGraph.initBoard('jxgbox', {originX: 20, originY: 300, unitX: 60, unitY: 5});
 
 
         brd.suspendUpdate();
 
         brd.suspendUpdate();
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        brd.update();
 
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         var graph1,graph2,graph3,graph4,graph5,graph6,graph7,graph8,graph9;
 
         var graph1,graph2,graph3,graph4,graph5,graph6,graph7,graph8,graph9;
  
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                 y[6+i] = 10+z2*3;
 
                 y[6+i] = 10+z2*3;
 
                 x[6+i] = 6+i;
 
                 x[6+i] = 6+i;
−
                 p[i] = brd.createElement('point', [x[i],y[i]],{name:' ',fixed:true,style:7});  
+
                 p[i] = brd.createElement('point', [x[i],y[i]],{name:' ',fixed:true,size:2,face:'[]'});  
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                 p[6+i] = brd.createElement('point', [x[6+i],y[6+i]],{name:' ',fixed:true,style:7});
+
                 p[6+i] = brd.createElement('point', [x[6+i],y[6+i]],{name:' ',fixed:true,size:2,face:'[]'});
 
             }else{
 
             }else{
 
                 y[i] = 10+z1*3;
 
                 y[i] = 10+z1*3;
−
                 p[i] = brd.createElement('point', [x[i],y[i]],{name:' ',fixed:true,style:7});  
+
                 p[i] = brd.createElement('point', [x[i],y[i]],{name:' ',fixed:true,size:2,face:'[]'});  
 
             }
 
             }
 
         }
 
         }
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         brd.removeObject(p[9]);
 
         brd.removeObject(p[9]);
 
          
 
          
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+
         p[9] = brd.createElement('glider', [x[9],y[9],l[3]],{name:' ',size:4,face:'o'});  
 
         brd.unsuspendUpdate();
 
         brd.unsuspendUpdate();
  
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                 t += p[i].Y() + ';';
 
                 t += p[i].Y() + ';';
 
             }
 
             }
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             new Ajax.Request('/~alfred/jsxgraph/branches/0.70/examples/rserv.php', {
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             new Ajax.Request('/~alfred/jsxgraph/examples/rserv.php', {
 
                 method:'post',
 
                 method:'post',
 
                 parameters:'input='+escape(t),
 
                 parameters:'input='+escape(t),
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                         var sd = a[1]*1.0;
 
                         var sd = a[1]*1.0;
 
                         var med = a[2]*1.0;
 
                         var med = a[2]*1.0;
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                        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'});  
 
                             graph3 = brd.createElement('curve', [[x[0],x[x.length-1]],[m+sd,m+sd]], {strokecolor:'red',dash:2});  
 
                             graph3 = brd.createElement('curve', [[x[0],x[x.length-1]],[m+sd,m+sd]], {strokecolor:'red',dash:2});  
 
                             graph4 = brd.createElement('curve', [[x[0],x[x.length-1]],[m-sd,m-sd]], {strokecolor:'red',dash:2});  
 
                             graph4 = brd.createElement('curve', [[x[0],x[x.length-1]],[m-sd,m-sd]], {strokecolor:'red',dash:2});  
−
                             graph5 = brd.createElement('curve', [[x[0],x[x.length-1]],[med,med]], {strokecolor:'gray'});  
+
                             graph5 = brd.createElement('curve', [[x[0],x[x.length-1]],[med,med]], {strokecolor:'black'});  
 
                             graph1 = brd.createElement('curve', [[x[0],x[x.length-1]],[med-mad,med-mad]], {strokecolor:'black',dash:3});  
 
                             graph1 = brd.createElement('curve', [[x[0],x[x.length-1]],[med-mad,med-mad]], {strokecolor:'black',dash:3});  
 
                             graph6 = brd.createElement('curve', [[x[0],x[x.length-1]],[med+mad,med+mad]], {strokecolor:'black',dash:3});  
 
                             graph6 = brd.createElement('curve', [[x[0],x[x.length-1]],[med+mad,med+mad]], {strokecolor:'black',dash:3});  
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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 />' +
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                                 'Mean = ' + brd.round(m,2) + '<br />' +
+
                                 'Mean = ' + Math.round(m,2) + '<br />' +
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                                 'Median = ' + brd.round(med,2) + '<br />' +
+
                                 'Median = ' + Math.round(med,2) + '<br />' +
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                                 '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();
 
                     };
 
                     };
 
                 }});
 
                 }});
 
         }
 
         }
−
</script>
+
brd.addHook(doIt, 'mouseup');
−
</html>
+
</jsxgraph>
  
 
=== The underlying source code ===
 
=== The underlying source code ===
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[[Category:Examples]]
 
[[Category:Examples]]
 +
[[Category:Statistics]]

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

Retrieved from "http://jsxgraph.org/wiki/index.php?title=Analyze_data_with_the_Statistics_software_R&oldid=6042"