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

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(New page: This litte application sends the coordinates of the points to the server. There, with the Statistics software R the data is analyzed. The return values are plotted and displayed. <html> <l...)
 
 
(95 intermediate revisions by 2 users not shown)
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−
This litte application sends the coordinates of the points to the server. There, with the Statistics software R the data is analyzed. The return values are plotted and displayed.
+
<h1>Normal Location and Scale</h1>
−
<html>
+
This litte application sends the y-coordinates of the points which are normal distributed (pseudo-)random numbers to the server.<br />
−
<link rel="stylesheet" type="text/css" href="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraph.css" />
+
There, location and scale of the sample are estimated using the [http://www.r-project.org Statistics software R].<br />
−
<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/prototype.js"></script>
+
The return values are plotted and displayed.<br /><br />
−
<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraphcore.js"></script>
+
<b>The computed estimates are:</b><br />
−
<div id="jxgbox" class="jxgbox" style="width:700px; height:400px;"></div>
+
* mean, standard deviation: red (non-robust!)<br />
−
<p id='output'>Statistics:<br></p>
+
* median and MAD: black (most-robust!)<br />
−
<script language="JavaScript">
+
* radius-minimax estimator: green (optimally robust; cf. Rieder et al. (2008))<br /><br />
−
         brd = JXG.JSXGraph.initBoard('jxgbox', {originX: 20, originY: 300, unitX: 60, unitY: 10});
+
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 />
−
        b1axisx = brd.createElement('axis', [[0,0], [1,0]], {ticksDelta:5, strokeColor:'#000000'});
+
===Online results:===
−
        b1axisy = brd.createElement('axis', [[0,0], [0,1]], {ticksDelta:5, strokeColor:'#000000'});
+
<html><script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/prototype.js"></script></html>
−
        b1axisx.ticksDelta = 5;
+
<pre id='output'>Statistics:<br></pre>
−
        b1axisy.ticksDelta = 5;
+
<jsxgraph width="700" height="400">
−
        brd.fullUpdate = true;
+
         brd = JXG.JSXGraph.initBoard('jxgbox', {boundingbox: [-0.15, 60, 11.15, -20],axis:true});
−
         brd.update();
+
         brd.suspendUpdate();
−
        brd.fullUpdate = false;
+
         var graph1,graph2,graph3,graph4,graph5,graph6,graph7,graph8,graph9;
−
       
 
−
         var graph1,graph2,graph3,graph4,graph5;
 
  
 
         var x = [];
 
         var x = [];
 
         var y = [];
 
         var y = [];
 
         var p = [];
 
         var p = [];
−
         for (var i=0;i<11;i++) {
+
        var r1,r2,rad,phi,z1,z2;
 +
         for (var i=0;i<6;i++) {
 
             x[i] = i;
 
             x[i] = i;
−
             y[i] = 10+(Math.random()-0.5)*10;
+
             // Box-Muller-Method for standard normal random numbers
−
             p[i] = brd.createElement('point', [x[i],y[i]],{name:' ',fixed:true,style:7});  
+
            r1 = Math.random();
 +
            r2 = Math.random();
 +
            rad = Math.sqrt(-2*Math.log(1-r1));
 +
            phi = 2*Math.PI*r2;
 +
            z1 = rad*Math.cos(phi);
 +
            z2 = rad*Math.sin(phi);
 +
            if(i < 5){
 +
                y[i] = 10+z1*3;
 +
                y[6+i] = 10+z2*3;
 +
                x[6+i] = 6+i;
 +
                p[i] = brd.createElement('point', [x[i],y[i]],{name:' ',fixed:true,size:2,face:'[]'});
 +
                p[6+i] = brd.createElement('point', [x[6+i],y[6+i]],{name:' ',fixed:true,size:2,face:'[]'});
 +
             }else{
 +
                y[i] = 10+z1*3;
 +
                p[i] = brd.createElement('point', [x[i],y[i]],{name:' ',fixed:true,size:2,face:'[]'});  
 +
            }
 
         }
 
         }
−
        var q = [];
 
 
         var hlow = [];
 
         var hlow = [];
 
         var hup = [];
 
         var hup = [];
Line 48: Line 61:
 
         brd.removeObject(p[9]);
 
         brd.removeObject(p[9]);
 
          
 
          
−
         p[0] = brd.createElement('glider', [x[0],y[0],l[0]],{name:' ',style:6});  
+
         p[0] = brd.createElement('glider', [x[0],y[0],l[0]],{name:' ',size:4,face:'o'});  
−
         p[10] = brd.createElement('glider', [x[10],y[10],l[1]],{name:' ',style:6});  
+
         p[10] = brd.createElement('glider', [x[10],y[10],l[1]],{name:' ',size:4,face:'o'});  
−
         p[8] = brd.createElement('glider', [x[8],y[8],l[2]],{name:' ',style:6});  
+
         p[8] = brd.createElement('glider', [x[8],y[8],l[2]],{name:' ',size:4,face:'o'});  
−
         p[9] = brd.createElement('glider', [x[9],y[9],l[3]],{name:' ',style:6});  
+
         p[9] = brd.createElement('glider', [x[9],y[9],l[3]],{name:' ',size:4,face:'o'});  
−
 
+
         brd.unsuspendUpdate();
−
         var graph1,graph2,graph3,graph4,graph5;
 
  
 
         doIt();
 
         doIt();
Line 64: Line 76:
 
                 t += p[i].Y() + ';';
 
                 t += p[i].Y() + ';';
 
             }
 
             }
−
             new Ajax.Request('rserv.php', {
+
             new Ajax.Request('/~alfred/jsxgraph/examples/rserv.php', {
 
                 method:'post',
 
                 method:'post',
 
                 parameters:'input='+escape(t),
 
                 parameters:'input='+escape(t),
Line 77: Line 89:
 
                         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 estimator1 = a[4]*1.0;
+
                         var est2 = a[5]*1.0;
−
                         var estimator2 = a[5]*1.0;
 
−
                        if (!graph2) {
 
−
                            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});
 
−
                            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'});
 
−
                            graph1 = brd.createElement('curve', [[x[0],x[x.length-1]],[med-mad,med-mad]], {strokecolor:'gray',dash:3});
 
−
                            graph6 = brd.createElement('curve', [[x[0],x[x.length-1]],[med+mad,med+mad]], {strokecolor:'gray',dash:3});
 
−
                        } else {
 
−
                            graph2.dataY = [m,m];
 
−
                            graph3.dataY = [m+sd,m+sd];
 
−
                            graph4.dataY = [m-sd,m-sd];
 
−
                            graph5.dataY = [med,med];
 
−
                            graph1.dataY = [med-mad,med-mad];
 
−
                            graph6.dataY = [med+mad,med+mad];
 
−
                        }
 
−
 
 
−
                        $('output').innerHTML = 'Statistics:<br>'+
 
−
                                'Mean value=' + brd.round(m,2) + '<br />' +
 
−
                                'sd=' + brd.round(sd,2) + '<br />' +
 
−
                                'median=' + brd.round(med,2) + '<br />' +
 
−
                                'MAD=' + brd.round(mad,2) + '<br />' +
 
−
                                'optimal-robust radius-minimax estimator for location=' + brd.round(estimator1,2) + '<br />' +
 
−
                                'optimal-robust radius-minimax estimator for scala=' + brd.round(estimator2,2) + '<br />';
 
−
                        brd.update();
 
−
                    };
 
−
                }});
 
−
        }
 
−
</script>
 
−
</html>
 
−
 
 
−
=== The JavaScript code of the client ===
 
−
<source lang="javascript">
 
−
        brd = JXG.JSXGraph.initBoard('jxgbox', {originX: 20, originY: 300, unitX: 60, unitY: 10});
 
−
        b1axisx = brd.createElement('axis', [[0,0], [1,0]], {ticksDelta:5, strokeColor:'#000000'});
 
−
        b1axisy = brd.createElement('axis', [[0,0], [0,1]], {ticksDelta:5, strokeColor:'#000000'});
 
−
        b1axisx.ticksDelta = 5;
 
−
        b1axisy.ticksDelta = 5;
 
−
        brd.fullUpdate = true;
 
−
        brd.update();
 
−
        brd.fullUpdate = false;
 
−
       
 
−
        var graph1,graph2,graph3,graph4,graph5;
 
−
 
 
−
        var x = [];
 
−
        var y = [];
 
−
        var p = [];
 
−
        for (var i=0;i<11;i++) {
 
−
            x[i] = i;
 
−
            y[i] = 10+(Math.random()-0.5)*10;
 
−
            p[i] = brd.createElement('point', [x[i],y[i]],{name:' ',fixed:true,style:7});
 
−
        }
 
−
        var q = [];
 
−
        var hlow = [];
 
−
        var hup = [];
 
−
        var l = [];
 
−
        hlow[0] = brd.createElement('point', [x[0],0],{name:' ',visible:false});
 
−
        hlow[1] = brd.createElement('point', [x[10],0],{name:' ',visible:false});
 
−
        hlow[2] = brd.createElement('point', [x[8],0],{name:' ',visible:false});
 
−
        hlow[3] = brd.createElement('point', [x[9],0],{name:' ',visible:false});
 
−
        hup[0] = brd.createElement('point', [x[0],20],{name:' ',visible:false});
 
−
        hup[1] = brd.createElement('point', [x[10],20],{name:' ',visible:false});
 
−
        hup[2] = brd.createElement('point', [x[8],20],{name:' ',visible:false});
 
−
        hup[3] = brd.createElement('point', [x[9],20],{name:' ',visible:false});
 
−
        l[0] = brd.createElement('line', [hlow[0],hup[0]],{visible:false});
 
−
        l[1] = brd.createElement('line', [hlow[1],hup[1]],{visible:false});
 
−
        l[2] = brd.createElement('line', [hlow[2],hup[2]],{visible:false});
 
−
        l[3] = brd.createElement('line', [hlow[3],hup[3]],{visible:false});  
 
  
−
        brd.removeObject(p[0]);
 
−
        brd.removeObject(p[10]);
 
−
        brd.removeObject(p[8]);
 
−
        brd.removeObject(p[9]);
 
−
       
 
−
        p[0] = brd.createElement('glider', [x[0],y[0],l[0]],{name:' ',style:6});
 
−
        p[10] = brd.createElement('glider', [x[10],y[10],l[1]],{name:' ',style:6});
 
−
        p[8] = brd.createElement('glider', [x[8],y[8],l[2]],{name:' ',style:6});
 
−
        p[9] = brd.createElement('glider', [x[9],y[9],l[3]],{name:' ',style:6});
 
−
 
−
        var graph1,graph2,graph3,graph4,graph5;
 
−
 
−
        doIt();
 
−
       
 
−
        function doIt() {
 
−
            brd.update();
 
−
            // Generate a ";"-separated list
 
−
            var t = '';
 
−
            for (var i=0;i<p.length;i++) {
 
−
                t += p[i].Y() + ';';
 
−
            }
 
−
            new Ajax.Request(''/~alfred/jsxgraph/branches/0.70/examples/rserv.php', {
 
−
                method:'post',
 
−
                parameters:'input='+escape(t),
 
−
                onComplete: function(transport) {
 
−
                    if (200 == transport.status) {
 
−
                        var t = transport.responseText;
 
−
                        var res = t.match(/"(.*)"/gi);
 
−
                        res = RegExp.$1;
 
−
                        var a = res.split(";");
 
−
                        var m = a[0]*1.0;
 
−
                        var sd = a[1]*1.0;
 
−
                        var med = a[2]*1.0;
 
−
                        var mad = a[3]*1.0;
 
−
                        var mad = a[3]*1.0;
 
−
                        var estimator1 = a[4]*1.0;
 
−
                        var estimator2 = 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:'gray',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:'gray',dash:3});  
+
                             graph6 = brd.createElement('curve', [[x[0],x[x.length-1]],[med+mad,med+mad]], {strokecolor:'black',dash:3});
 +
                            graph8 = brd.createElement('curve', [[x[0],x[x.length-1]],[est1,est1]], {strokecolor:'green'});
 +
                            graph7 = brd.createElement('curve', [[x[0],x[x.length-1]],[est1-est2,est1-est2]], {strokecolor:'green',dash:4});
 +
                            graph9 = brd.createElement('curve', [[x[0],x[x.length-1]],[est1+est2,est1+est2]], {strokecolor:'green',dash:4});  
 
                         } else {
 
                         } else {
 
                             graph2.dataY = [m,m];
 
                             graph2.dataY = [m,m];
Line 199: Line 109:
 
                             graph1.dataY = [med-mad,med-mad];
 
                             graph1.dataY = [med-mad,med-mad];
 
                             graph6.dataY = [med+mad,med+mad];
 
                             graph6.dataY = [med+mad,med+mad];
 +
                            graph8.dataY = [est1,est1];
 +
                            graph7.dataY = [est1-est2,est1-est2];
 +
                            graph9.dataY = [est1+est2,est1+est2];
 
                         }
 
                         }
  
−
                         $('output').innerHTML = 'Statistics:<br>'+  
+
                         document.getElementById('output').innerHTML = '<b><font size="+1">Normal location and scale:</font></b><br /><br />'+
−
                                 'Mean value=' + brd.round(m,2) + '<br />' +
+
                                '<b>Estimates for location (true value = 10):</b><br />' +
−
                                 'sd=' + brd.round(sd,2) + '<br />' +
+
                                 'Mean = ' + Math.round(m,2) + '<br />' +
−
                                 'median=' + brd.round(med,2) + '<br />' +
+
                                 'Median = ' + Math.round(med,2) + '<br />' +
−
                                 'MAD=' + brd.round(mad,2) + '<br />' +  
+
                                 'Radius-minimax estimator = ' + Math.round(est1,2) + '<br /><br />' +
−
                                 'optimal-robust radius-minimax estimator for location=' + brd.round(estimator1,2) + '<br />' +
+
                                '<b>Estimates for scale (true value = 3):</b><br />' +
−
                                 'optimal-robust radius-minimax estimator for scala=' + brd.round(estimator2,2) + '<br />';
+
                                 'Standard deviation = ' + Math.round(sd,2) + '<br />' +
 +
                                 'MAD = ' + Math.round(mad,2) + '<br />' +  
 +
                                 'Radius-minimax estimator = ' + Math.round(est2,2) + '<br />';
 
                         brd.update();
 
                         brd.update();
 
                     };
 
                     };
 
                 }});
 
                 }});
 
         }
 
         }
−
</source>
+
brd.addHook(doIt, 'mouseup');
−
 
+
</jsxgraph>
−
=== The R code of the server ===
 
−
<source lang="R">
 
−
x <- commandArgs(TRUE)
 
−
x <- as.numeric(unlist(strsplit(x, ";")))
 
  
−
MW <- mean(x)
+
=== The underlying source code ===
−
SD <- sd(x)
+
[[The underlying JavaScript and PHP code]]
−
Med <- median(x)
 
−
Mad <- mad(x)
 
  
−
## Radius = 0.6
+
The R script can be [http://jsxgraph.uni-bayreuth.de/~alfred/jsxgraph/branches/0.70/examples/LokSkala.R downloaded here].
−
A1 <- 1.7756*Mad^2
 
−
A2 <- 1.4322*Mad^2
 
−
a2 <- -0.5034*Mad
 
−
b <- 1.8390*Mad
 
−
u <- A1*(x-Med)/Mad^2
 
−
v <- A2*(((x-Med)/Mad)^2-1)/Mad - a2
 
−
w <- pmin(1, b/sqrt(u^2 + v^2))
 
−
res <- c(Med, Mad) + c(mean(u*w), mean(v*w))
 
  
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paste(round(c(MW, SD, Med, Mad, res), 3), collapse = ";")
+
=== References ===
−
</source>
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* ''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 [http://www.stamats.de/RRlong.pdf] 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 [http://www.stamats.de/ThesisMKohl.pdf].
  
−
=== The PHP code of the server (rserv.php) ===
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=== External links ===
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<source lang="php">
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* [http://www.r-project.org The R Project for statistical computing.]
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<?php
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* [https://r-forge.r-project.org/projects/robast/ RobASt project on R-Forge]
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$input = $_POST["input"];
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* [http://en.wikipedia.org/wiki/Robust_statistics Wikipedia on Robust Statistics]
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$cmd = "/usr/bin/Rscript LokSkala.R '" . $input ."'";
 
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passthru($cmd);
 
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?>
 
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</source>
 
  
 
[[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

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