Hi
I like to use small, artificially generated data sets with
integer parameters to introduce analyses. Often, however, I find
it difficult to avoid undesirable contingencies among the scores
(e.g., linear dependencies in within-subject designs). Is there
an algorithmic way to generate such scores and avoid such
dependencies? Here is a small example with 4 scores for each of
5 subjects. The following analysis reveals the undesirable
linear dependencies. I'm assuming the dependencies arise from
the noise vectors that I used to generate the cell scores by
adding them to the main effect of the factor and the subject
effects. Is there a systematic way to create such noise vectors
to avoid linear dependencies?
data list free / subj vl lo hi vh
begin data
1 3 3 5 5 2 1 3 7 9 3 6 8 8 10 4 7 8 6 7 5 3 3 9 9
end data
manova vl lo hi vh /wsf = conc(4) /print = cell
/contr(conc) = poly
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Cell Means and Standard Deviations
Variable .. VL
Mean Std. Dev. N 95 percent
Conf. Interval
For entire sample 4.000 2.449 5 .959
7.041
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Variable .. LO
Mean Std. Dev. N 95 percent
Conf. Interval
For entire sample 5.000 2.739 5 1.600
8.400
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Variable .. HI
Mean Std. Dev. N 95 percent
Conf. Interval
For entire sample 7.000 1.581 5 5.037
8.963
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Variable .. VH
Mean Std. Dev. N 95 percent
Conf. Interval
For entire sample 8.000 2.000 5 5.517
10.483
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Tests of Between-Subjects Effects.
Tests of Significance for T1 using UNIQUE sums of squares
Source of Variation SS DF MS F Sig of F
WITHIN CELLS 40.00 4 10.00
CONSTANT 720.00 1 720.00 72.00 .001
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Estimates for T1
--- Individual univariate .9500 confidence intervals
CONSTANT
Parameter Coeff. Std. Err. t-Value Sig. t
Lower -95% CL- Upper
1 12.0000000000 1.41421 8.48528 .00106
8.07351 15.92649
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* * * * * * * * * * * * * * * * * A n a l y s i s o f V a r i a n c e -- Design
1 * * * * * * * * * * * * * * * * *
Tests involving 'CONC' Within-Subject Effect.
Mauchly sphericity test, W = .00000
Chi-square approx. = . with 5 D. F.
Significance = .
Greenhouse-Geisser Epsilon = .40650
Huynh-Feldt Epsilon = .49123
Lower-bound Epsilon = .33333
AVERAGED Tests of Significance that follow multivariate tests are equivalent to
univariate or split-plot or mixed-model approach to repeated measures.
Epsilons may be used to adjust d.f. for the AVERAGED results.
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* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
* * *
* W A R N I N G * The WITHIN CELLS error matrix is SINGULAR. *
* * These variables are LINEARLY DEPENDENT *
* * on preceding ones .. *
* * T3 *
* * Multivariate tests will be skipped. *
* * *
* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
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07:51:26 The University of Winnipeg SUN SPARC Solaris
* * * * * * * * * * * * * * * * * A n a l y s i s o f V a r i a n c e -- Design
1 * * * * * * * * * * * * * * * * *
EFFECT .. CONC
Tests involving 'CONC' Within-Subject Effect.
AVERAGED Tests of Significance for MEAS.1 using UNIQUE sums of squares
Source of Variation SS DF MS F Sig of F
WITHIN CELLS 40.00 12 3.33
CONC 50.00 3 16.67 5.00 .018
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Estimates for T2
--- Individual univariate .9500 confidence intervals
CONC
Parameter Coeff. Std. Err. t-Value Sig. t
Lower -95% CL- Upper
1 3.1304951685 . . .
. .
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Estimates for T3
--- Individual univariate .9500 confidence intervals
CONC
Parameter Coeff. Std. Err. t-Value Sig. t
Lower -95% CL- Upper
1 .0000000000 . . .
. .
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Estimates for T4
--- Individual univariate .9500 confidence intervals
CONC
Parameter Coeff. Std. Err. t-Value Sig. t
Lower -95% CL- Upper
1 -.4472135955 . . .
. .
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Best wishes
Jim
============================================================================
James M. Clark (204) 786-9757
Department of Psychology (204) 774-4134 Fax
University of Winnipeg 4L05D
Winnipeg, Manitoba R3B 2E9 [EMAIL PROTECTED]
CANADA http://www.uwinnipeg.ca/~clark
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