Performs t-tests for pairwise differences (P.W. Goedhart).
Options
PRINT = string tokens |
What to print (differences, sed, tvalues, tprobabilities); default diff, sed, tval |
|---|---|
DF = scalar or symmetric matrix |
Degrees of freedom for calculation of TPROBABILITIES from TVALUES; default 10000, approximates to the normal distribution |
SORT = string token |
Whether ESTIMATES (and other output) are sorted in ascending order (yes, no); default no |
Parameters
ESTIMATES = variates |
Estimates to be compared |
|---|---|
VCOVARIANCE = symmetric matrices |
Symmetric matrix containing the variance-covariance matrix of the estimates |
LABELS = texts |
Text vector naming the elements of ESTIMATES; if unset, the numbers 1, 2… are used as labels |
DIFFERENCES = symmetric matrices |
To save the pairwise differences (ESTIMATES on the diagonal) |
SED = symmetric matrices |
To save the standard errors of the pairwise differences (missing values on the diagonal) |
TVALUES = symmetric matrices |
To save the t-values (missing values on the diagonal) |
TPROBABILITIES = symmetric matrices |
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.
See also
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
READ 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