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# PAIRTEST procedure

Performs t-tests for pairwise differences (P.W. Goedhart).

### Options

`PRINT` = string tokens What to print (`differences`, `sed`, `tvalues`, `tprobabilities`); default `diff`, `sed`, `tval` Degrees of freedom for calculation of `TPROBABILITIES` from `TVALUES`; default 10000, approximates to the normal distribution Whether `ESTIMATES` (and other output) are sorted in ascending order (`yes`, `no`); default `no`

### Parameters

`ESTIMATES` = variates Estimates to be compared Symmetric matrix containing the variance-covariance matrix of the estimates Text vector naming the elements of `ESTIMATES`; if unset, the numbers 1, 2… are used as labels To save the pairwise differences (`ESTIMATES` on the diagonal) To save the standard errors of the pairwise differences (missing values on the diagonal) To save the t-values (missing values on the diagonal) To save the t-probabilities (missing values on the diagonal)

### Description

`PAIRTEST` can be used to test all pairwise differences in every situation in which a vector of estimates and a corresponding variance-covariance matrix are available. `PAIRTEST` is particularly useful for tests of all pairwise differences of slopes after fitting a model with an interaction between a factor and a variate. In most other situations procedure `RPAIR` will be more suitable.

All pairwise differences of entries in `ESTIMATES` with variance-covariance matrix `VCOVARIANCE` are calculated and tested. The results of these tests can be saved in symmetric matrices `DIFFERENCES`, `SED`, `TVALUES` and `TPROBABILITIES`. The matrices are labeled by text vector `LABELS` or, if `LABELS` is unset, by the numbers 1, 2, 3…

`PRINT` controls the output of `PAIRTEST`. The t-probabilities are based on `DF` degrees of freedom; by default, if `DF` has not been set, Normal probablitities are calculated. Option `SORT` controls whether the estimates on the diagonal of `DIFFERENCES` are sorted in ascending order. The other output is sorted accordingly.

Options: `PRINT`, `DF`, `SORT`.

Parameters: `ESTIMATES`, `VCOVARIANCE`, `LABELS`, `DIFFERENCES`, `SED`, `TVALUES`, `TPROBABILITIES`.

### Method

The calculations are all relatively straightforward.

### Action with `RESTRICT`

The variate `ESTIMATES` and the text `LABELS` can be restricted; the analysis is restricted according to restrictions on `ESTIMATES`. The lengths of the unrestricted vectors `ESTIMATES` and `LABELS` must be identical.

Procedures: `ALLDIFFERENCES`, `AMCOMPARISON`, `AUMCOMPARISON`, `PPAIR`, `RPAIR`.

Commands for: Regression analysis.

### Example

```CAPTION 'PAIRTEST example',\
!t('Comparison of slopes following a regression with grouped data.',\
'Data from Wetherill, G.B. (1981), Intermediate Statistical',\
'Methods, Chapman & Hall, London, page 247.'); STYLE=meta,plain
TEXT    [VALUES=OwnRoots,ComPlum,ComMussel,Myrobalan] Labels
FACTOR  [LABELS=Labels; VALUES=9(1...4)] Plumtree
VARIATE [NVALUES=36] CirBase,CirTop,Weight
1.690  1.663  2.318     1.583  1.568  2.100     1.693  1.643  2.225
1.648  1.609  2.140     1.628  1.599  2.107     1.600  1.603  2.049
1.677  1.640  2.228     1.588  1.535  2.029     1.645  1.606  2.140
1.525  1.515  1.940     1.517  1.501  1.940     1.582  1.542  2.045
1.537  1.529  1.919     1.504  1.487  1.869     1.589  1.562  2.049
1.567  1.548  1.954     1.480  1.449  1.820     1.498  1.490  1.892
1.604  1.540  2.104     1.650  1.633  2.233     1.591  1.581  2.090
1.598  1.579  2.079     1.672  1.629  2.255     1.585  1.555  2.064
1.645  1.610  2.185     1.628  1.612  2.068     1.653  1.642  2.201
1.747  1.712  2.382     1.769  1.754  2.413     1.763  1.747  2.446
1.766  1.738  2.450     1.739  1.719  2.387     1.749  1.742  2.396
1.738  1.710  2.310     1.731  1.689  2.332     1.707  1.650  2.204 :
MODEL     Weight
TERMS     [FULL=yes] CirBase + Plumtree * CirTop
FIT       [CONSTANT=omit; PRINT=estimates] CirBase + Plumtree / CirTop
RKEEP     ESTIMATES=Est; VCOVAR=Vcov; DF=Df
TEXT      [VALUES=5(no),#Labels] NewLabel
RESTRICT  Est; CONDITION=NewLabel .NI. 'no'
PAIRTEST  [DF=Df] ESTIMATES=Est; VCOVAR=Vcov; LABELS=NewLabel
```
Updated on March 6, 2019