Displays results of t-tests for pairwise differences in compact diagrams (P.W. Goedhart, H. van der Voet & D.C. van der Werf).
|What to print (
||Level of significance of pairwise comparison tests; default 0.05|
||Probabilities of tests of pairwise comparisons|
||What to print alongside the labels of
||Text vector labelling the output; if unset the row labels of
||Saves the letters showing the items not significantly different from each item|
||Saves the letters showing groups of items not significantly different from each other|
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.
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
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
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
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
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.
LABELS are ignored.
Commands for: Regression analysis.
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