# Analyze data with the Statistics software R

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# 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].