Performs a range of all pairwise multiple comparison tests (D.M. Smith).

### Options

`METHOD` = string token |
Test to be performed (`Tukey` , `SNK` , `REGWMR` , `Duncan` , `Scheffe` , `FPLSD` , `FULSD` , `Bonferroni` , `Sidak` ); default `*` |
---|---|

`DIRECTION` = string token |
How to sort means (`ascending` , `descending` ); default `asce` |

`PROBABILITY` = scalar |
The required significance level; default=0.05 |

`ALSD` = string token |
Whether to use the alternative LSD test where the Studentized Range statistic is used instead of Student’s t (`yes` , `no` ); default `no` |

### Parameters

`MEANS` = variates or tables |
Mean values |
---|---|

`REPLICATIONS` = scalars or tables or variates |
Number(s) of observations per mean |

`VARIANCE` = scalars |
Estimate of variance |

`DF` = scalars |
Degrees of freedom |

`LABELS` = texts |
Identifiers of mean values |

### Description

`ALLPAIRWISE`

performs a range of all pairwise multiple comparison tests (see Hsu 1996 and Bechhofer, Santner & Goldsman 1995). The methodology implemented in the procedure closely follows that described in Chapter 5 of Hsu (1996).

The means are input using the `MEANS`

parameter, either in a table saved e.g. from `AKEEP`

, or in a variate. The replication (or number of observations in each mean) is supplied by the `REPLICATIONS`

parameter, either in a scalar (if all the replications are equal) or in a structure of the same type as the means. The estimate of the variance (usually a pooled estimate as given by the residual mean square in `ANOVA`

, and accessible using the `VARIANCE`

parameter of `AKEEP`

) and its corresponding degrees of freedom are input as scalars using the `VARIANCE`

and `DF`

parameters respectively. The `LABELS`

parameter can be used to supply labels for the means.

The type of test to be performed is specified by the `METHOD`

option, with settings `Tukey`

, `SNK`

(Student-Newman-Keuls), `REGWMR`

(Ryan/Einot-Gabriel/Welsch multiple range test), `Duncan`

, `Scheffe`

, `FPLSD`

(Fisher’s Protected Least Significant Difference), `FULSD`

(Fisher’s Unprotected Least Significant Difference), `Bonferroni`

and `Sidak`

.

The `DIRECTION`

option allows the means to be arranged in ascending or descending order.

The `PROBABILITY`

option allows the pair-wise significance level for the intervals intervals from the Fisher tests to be changed from the default 0.05 (e.g. to 0.01). For the other tests, it changes the experiment-wise significance level.

The `ALSD`

allows the LSD test asked for (`FPLSD`

or `FULSD`

) to use the Studentized Range statistic rather than Student’s t (for further information see Hsu, 1996, page 139).

Options: `METHOD`

, `DIRECTION`

, `PROBABILITY`

, `ALSD`

.

Parameter: `MEANS`

, `REPLICATION`

, `VARIANCE`

, `DF`

, `LABELS`

.

### Method

The methodology implemented is based on that described and reviewed in Hsu (1996), and Bechhofer, Santner & Goldsman (1995). For specific details of the tests these books should be referred to.

### References

Bechhofer, R.E., Santner, T.J. & Goldsman, D.M. (1995). *Design and Analysis of Experiments for Statistical Selection, Screening, and Multiple Comparisons*. Wiley, New York.

Hsu, J.C. (1996). *Multiple Comparisons Theory and Methods*. Chapman & Hall, London.

### See also

Procedures: `AMCOMPARISON`

, `AUMCOMPARISON`

, `AMDUNNETT`

, `CONFIDENCE`

, `MCOMPARISON`

, `VMCOMPARISON`

.

Commands for: Analysis of variance.

### Example

CAPTION 'ALLPAIRWISE example',\ 'Data from Duncan (1955) Biometrics paper.'; STYLE=meta,plain VARIATE Mean TEXT Meanid READ [SETNVALUES=YES] Meanid,Mean A 49.6 B 71.2 C 67.6 D 61.5 E 71.3 F 58.1 G 61.0 : FACTOR [LABELS=!t(A,B,C,D,E,F,G)] Labels " means in a variate with accompanying labels " ALLPAIRWISE [METHOD=Bonferroni]\ MEANS=Mean; REPLICATION=6; VARIANCE=79.64; DF=30; LABELS=Meanid TABLE [CLASS=Labels] Meantab; VALUES=Mean " means in a table " ALLPAIRWISE [METHOD=Bonferroni; DIRECTION=descending; PROBABILITY=0.01]\ MEANS=Meantab; REPLICATION=6; VARIANCE=79.64; DF=30