Calculates effective standard errors that give good approximate standard errors of differences (R.W. Payne).

### Option

`PRINT` = string token |
Controls printed output (`ese` , `discrepancy` , `maxdiscrepancy` , `%discrepancy` , `%accounted` ); default `*` i.e. none |
---|

### Parameters

`SED` = symmetric matrices |
Standard errors of differences to be approximated |
---|---|

`ESE` = variates or tables |
Saves the effective standard errors |

`DISCREPANCY` = symmetric matrices |
Saves the discrepancies between the standard errors of differences and the approximate values calculated from the effective standard errors |

`%ACCOUNTED` = scalars |
Percentage of variation amongst the standard errors of differences accounted for by the approximate values calculated from the effective standard errors |

`TEMPLATE` = tables |
Table that can be duplicated to provide a table to store the effective standard errors |

### Description

In the analysis of variance of many balanced designs it is possible to provide a succinct description of the variability of a table of means, by giving an effective standard error (ese) for each mean. This can be used to calculate the standard error for the difference (sed) between any pair of means (i and j) using the usual formula:

sed* _{ij}* = √(ese

_{i}^{2}+ ese

_{j}^{2})

In unbalanced designs, however, the standard errors may not possess such a simple structure. So it may be necessary to present the full symmetric matrice of sed’s. This matrix has as many rows (and columns) as the number of means, and can be too large for many reports. The temptation therefore is to print just an average sed, but this can be very misleading. An alternative, provided by the `SED2ESE`

procedure, is to estimate approximate ese’s that allow good approximations to the sed’s to be calculated using the usual formula.

The sed’s to be approximated are supplied using the `SED`

parameter, in a symmetric matrix. (This is the form in which they are saved from `AKEEP`

, `AUKEEP`

or `PREDICT`

). The ese’s can be saved using the ESE parameter. If no further information is supplied, they will be formed as a variate, with unit labels taken from the row labels of the `SED`

symmetric matrix. Alternatively, you can predefine `ESE`

as a table (which should have exactly the same form as the table of means to which the sed’s refer). Or you can use the `TEMPLATE`

parameter to provide a table (which could be the table of means itself) to act as a template for an `ESE`

table. The `DUPLICATE`

directive is then used to form `ESE`

as a table with the same attributes as the template. The `DISCREPANCY`

parameter can save a symmetric matrix containing the discrepancies between the sed’s and the approximate values calculated from the ese’s, and the `%ACCOUNTED`

parameter can save a scalar indicating the percentage of the variation amongst the sed’s accounted for by the approximate values calculated from the ese’s.

Printed output is controlled by the `PRINT`

option, with settings:

`ese` |
the approximate effective standard errors; |
---|---|

`discrepancy` |
discrepancies between the sed’s and the approximate values calculated from the ese’s; |

`maxdiscrepancy` |
maximum discrepancy; |

`%discrepancy` |
maximum discrepancy between any sed and the approximate value calculated from the corresponding ese’s, expressed as a percentage of the sed; |

`%accounted` |
percentage of the variation amongst the sed’s accounted for by the approximate values calculated from the ese’s. |

By default, nothing is printed.

Option: `PRINT`

.

Parameters: `BLOCKFACTORS`

, `TREATMENTFACTORS`

, `LEVELS`

.

### Method

The ses’s are estimated by fitting the equation in the formula by least squares using the standard Genstat regression facilities (see Menezes & Firth 1998).

### Reference

Menezes, R. & Firth, D. (1998). More useful standard errors for group and factor effects. In: *COMPSTAT 1998, Proceedings in Computational Statistics, Short Communications and Posters* (ed. R. Payne & P. Lane), 79-80. IACR-Rothamsted, Harpenden.

### See also

Procedures: `AUNBALANCED`

, `SEDLSI`

.

Commands for: Calculations and manipulation.

### Example

CAPTION 'SED2ESE example'; STYLE=meta VARIATE Y FACTOR [LEVELS=3] A,B & [LEVELS=2] C,Day READ [SETNVALUES=yes] Day,A,B,C,Y 1 1 3 2 91 1 2 2 1 79 1 3 2 2 118 1 2 2 1 113 1 2 1 2 107 1 2 2 2 77 1 1 1 2 96 1 2 1 1 105 1 2 3 1 104 1 1 1 2 119 1 3 3 1 130 1 3 1 1 98 1 1 2 1 128 1 1 3 1 116 1 3 1 2 98 1 2 1 2 108 1 1 1 1 148 1 3 3 2 90 1 3 1 2 112 1 2 3 2 100 1 1 2 2 104 1 1 2 1 131 1 2 1 1 106 1 1 3 2 120 1 3 2 1 120 1 3 3 1 111 1 2 2 2 119 1 1 3 1 116 1 1 1 1 133 1 2 3 1 94 1 1 2 2 94 1 3 1 1 108 1 2 3 2 119 1 3 2 2 135 2 2 1 2 91 2 2 1 2 69 2 2 3 1 85 2 2 2 2 89 2 3 2 1 101 2 3 2 2 110 2 2 2 2 107 2 1 1 2 95 2 3 1 1 113 2 1 3 2 115 2 2 3 1 122 2 3 3 1 113 2 1 1 1 143 2 1 1 1 120 2 1 2 2 80 2 3 1 1 50 2 2 1 1 97 2 3 1 2 105 2 3 3 2 126 2 1 1 2 70 2 1 2 1 107 2 2 3 2 121 2 1 2 1 130 2 2 3 2 105 2 1 3 1 120 2 2 2 1 105 2 2 1 1 100 2 2 2 1 110 2 3 1 2 89 2 3 2 2 100 2 3 3 1 96 2 1 2 2 125 2 3 3 2 84 : BLOCKSTRUCTURE Day TREATMENTSTRUCTURE C*A*B AUNBALANCED [PRINT=aov,means; PSE=alldifferences,differences;\ FPROBABILITY=yes] Y AUKEEP A.C; MEANS=ACmeans; SEDMEANS=ACsed SED2ESE [PRINT=ese,discrepancy,%discrepancy,maxdiscrepancy,%accounted]\ ACsed; TEMPLATE=ACmeans