# 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 /> | ||

− | * | + | * 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 /> | ||

<html> | <html> | ||

Line 90: | Line 90: | ||

t += p[i].Y() + ';'; | t += p[i].Y() + ';'; | ||

} | } | ||

− | new Ajax.Request('/~ | + | new Ajax.Request('/~mkohl/rserv.php', { |

method:'post', | method:'post', | ||

parameters:'input='+escape(t), | parameters:'input='+escape(t), | ||

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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:' | + | 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}); |

## Revision as of 12:33, 17 December 2008

## Contents

# 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].