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

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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; | ||

− | |||

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; | ||

− | console.log(t); | + | console.log(t, res, m, sd, med, mad, est1, est2); |

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'}); |

## Revision as of 12:33, 21 February 2013

## 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].