Displays results of t-tests for pairwise differences in compact diagrams (P.W. Goedhart, H. van der Voet & D.C. van der Werf).

### Options

`PRINT` = string token |
What to print (`items` , `groups` ); default `grou` |
---|---|

`PROBABILITY` = scalar or symmetric matrix |
Level of significance of pairwise comparison tests; default 0.05 |

### Parameters

`TPROBABILITIES` = symmetric matrices |
Probabilities of tests of pairwise comparisons |
---|---|

`DIFFERENCES` = symmetric matrices, variates or tables |
What to print alongside the labels of `TPROBABILITIES` ; default * |

`LABELS` = texts |
Text vector labelling the output; if unset the row labels of `TPROBABILITIES` and the diagonal of `DIFFERENCES` (if set) are used |

`ITEMLETTERS` = texts |
Saves the letters showing the items not significantly different from each item |

`GROUPLETTERS` = texts |
Saves the letters showing groups of items not significantly different from each other |

### Description

Procedures `RPAIR`

and `PAIRTEST`

produce a symmetric matrix of two-sided t-probabilities for tests of all pairwise differences of estimates. `PPAIR`

displays this matrix at a specified level of significance in two compact schematic diagrams. This is especially useful when the number of estimates is large.

Input to `PPAIR`

is a symmetric matrix `TPROBABILITIES`

containing probabilities of the set of pairwise comparisons. The level of significance can be set by the `PROBABILITY`

option. A common level is specified by a scalar, while a symmetric matrix specifies a level for each comparison separately (which may be useful for some multiple comparison methods). Output is labelled by the row labels of `TPROBABILITIES`

. If parameter `DIFFERENCES`

is set to a symmetric matrix the diagonal of this matrix is printed alongside these labels (with number of decimals as defined at declaration of `DIFFERENCES`

). This is especially useful if `DIFFERENCES`

is saved by `RPAIR`

or `PAIRTEST`

because it then contains the estimates on the diagonal. `DIFFERENCES`

can also be set to a variate or table. Alternatively the output can be labelled by specifying parameter `LABELS`

.

`PRINT`

controls which diagram is printed. `PRINT=items`

produces a diagram which should be read line by line. Each item (represented by a letter) is followed by those items (again represented by letters) not significantly different from that item. When there are more than 52 items, letters are repeated. `PRINT=groups`

is only useful when the `TPROBABILITIES`

are sorted in a sensible order, for example by specifying `SORT=yes`

in `RPAIR`

or `PAIRTEST`

. This produces a diagram in which items followed by a common letter are not significantly different. Such items are said to form a homogeneous group. This is similar to common underlining of items with non-significantly different estimates. In constructing this diagram the philosophy of multistage testing is followed, see the Method section. The letters can be saved, in texts, by the `ITEMLETTERS`

and `GROUPLETTERS`

parameters.

Options: `PRINT`

, `PROBABILITY`

.

Parameters: `TPROBABILITIES`

, `DIFFERENCES`

, `LABELS`

, `ITEMLETTERS`

, `GROUPLETTERS`

.

### Method

The construction of the diagram for `PRINT=groups`

is as follows. First the difference between the first and last item of the complete set of n items is checked for significance. Then the first and last item of all subsets of *n*-1 consecutive items are checked, followed by all subsets of *n*-2 items, and so on. If non-significance is found between the first and last item of a subset, all items of the subset are said to form a homogeneous group and they receive the same letter. This is only sensible when the `TPROBABILITIES`

are sorted according to the estimates. The diagram only consists of homogeneous groups which are not a part of a larger group.

It is obvious that items in a homogeneous group can be significantly different. This is not displayed in the diagram, although a message is printed if this occurs. If there are no significant differences within homogenous groups, both diagrams essentially contain the same information; `PRINT=groups`

then gives a more concise representation.

### Action with `RESTRICT`

Restrictions on `DIFFERENCES`

and `LABELS`

are ignored.

### See also

Procedures: `ALLDIFFERENCES`

, `AMCOMPARISON`

, `AUMCOMPARISON`

, `PAIRTEST`

, `RPAIR`

.

Commands for: Regression analysis.

### Example

CAPTION 'PPAIR example',\ !t('1. Comparison of variety means in a 5x5 lattice experiment.',\ 'Data from Cochran, W.G. & Cox, G.M. (1957), Experimental',\ 'Designs, 2nd Ed. Wiley, New York, page 406. There are no',\ 'significant differences within homogenous groups.',\ 'PRINT=groups only would then be sufficient.');\ STYLE=meta,plain FACTOR [LEVELS=2; VALUES=25(1,2)] Rep FACTOR [LEVELS=5; VALUES=5(1...5)2] Block FACTOR [LEVELS=25; VALUES=(1...25), (1,6...21), (2,7...22), (3,8...23),\ (4,9...24), (5,10...25)] Variety VARIATE [VALUES= 6,7,5,8,6, 16,12,12,13,8, 17,7,7,9,14, 18,16,13,13,14,\ 14,15,11,14,14, 24,13,24,11,8, 21,11,14,11,23, 16,4,12,12,12,\ 17,10,30,9,23, 15,15,22,16,19] Yield MODEL Yield FIT [PRINT=accumulated] Rep/Block + Variety RPAIR [SORT=yes; PRINT=*] !P(Variety); TPROBABILITIES=YieldPr;\ DIFFERENCES=YieldDif PRINT YieldPr; FIELDWIDTH=7; DECIMALS=3 PPAIR [PRINT=items,groups] YieldPr; DIFFERENCES=YieldDif CAPTION !t('2. Comparison of unequally replicated treatments with',\ 'significant differences within homogenous groups.') FACTOR [LABELS=!t(Aap, Noot, Mies, Wim, Zus, Jet, Vuur, Gijs);\ VALUES=7(1), 8(2), 4(3), 9(4), 1(5), 8(6), 9(7), 2(8)] Label VARIATE [VALUES=4.58, 3.66, 4.05, 6.24, 5.70, 5.13, 5.65, 6.56, 5.24,\ 6.09, 3.53, 5.77, 4.04, 4.18, 5.40, 5.93, 6.00, 6.78, 4.89,\ 7.17, 5.91, 5.22, 5.34, 6.87, 7.25, 6.91, 5.26, 5.86, 6.30,\ 6.89, 7.79, 7.41, 5.58, 7.17, 7.90, 6.14, 5.50, 6.58, 8.17,\ 8.19, 7.55, 9.58, 7.38, 7.72, 8.00, 7.92, 7.59, 8.41] Response MODEL Response FIT Label RPAIR [SORT=yes; PRINT=*] !P(Label); TPROBABILITIES=LabelPr;\ DIFFERENCES=LabelDif PRINT LabelPr; FIELDWIDTH=7; DECIMALS=3 PPAIR [PRINT=items,groups] LabelPr; DIFFERENCES=LabelDif