Estimates means using the Tukey biweight algorithm (D.B. Baird).

### Options

`CUTPOINT` = scalar |
Cut point after which weight is set to zero; default 5 |
---|---|

`TOLERANCE` = scalar |
Tolerance to avoid division by zero; default 0.00001 |

### Parameters

`DATA` = variates or pointers |
Data values |
---|---|

`GROUPS` = factors |
Groupings of the data values |

`MEANS` = variates |
Saves the means |

`SE` = variates |
Saves standard errors |

### Description

`TUKEYBIWEIGHT`

estimates means using the Tukey biweight algorithm. This weights the data values depending on how far they are from the median, and discards any that are more than a specified number of median absolute distances away. The number of differences is specified by the `CUTPOINT`

, with a default of 5.

The data values are specified by the `DATA`

parameter. They can be in a single variate, with any groupings specified by the `GROUPS`

parameter. Alternatively, they can be in separate variates, one for each group. The `MEANS`

parameter saves the estimated means, and the `SE`

parameter saves standard errors for the means.

Options: `CUTPOINT`

, `TOLERANCE`

.

Parameters: `DATA`

, `GROUPS`

, `MEANS`

, `SE`

.

### Action with `RESTRICT`

`TUKEYBIWEIGHT`

respects any restrictions on `DATA`

or `GROUPS`

.

### See also

Commands for: Calculations and manipulation.

### Example

CAPTION 'TUKEYBIWEIGHT example','Mean vs. Tukey BiWeight';\ STYLE=meta,minor FACTOR [LEVELS=100; VALUES=(1...100)100] Group "Create X as a mixture of 2 normals, 10% with SE of 10 vs 1" CALCULATE [SEED=498725] X1,X2 = GRNORMAL(9000,1000;10;1,100) APPEND [NEWVECTOR=X] X1,X2 TABULATE [CLASS=Group] X; MEANS=AMeans VTABLE AMeans; VARIATE=Average TUKEYBIWEIGHT [CUTPOINT=3] X; GROUPS=Group; MEANS=TukeyBiWt DHISTOGRAM [TITLE='Distribution of Mean vs Tukey Biweight'; NGROUPS=15]\ Average,TukeyBiWt