Hi
As shown in following example, significant omnibus and nonsignificant Tukeys is
not strictly speaking a simple product of small sample size (the 4 groups below
each have 90 subjects). It also depends on magnitude of difference relative to
variation within groups (MSE) and the specific pattern of the difference.
Below, groups 1 and 2 are different than groups 3 and 4 IN THE POPULATION.
Although maximum difference is almost significant by Tukey (p = .055) that
really does not capture the pattern in the data, as shown by the subsequent
contrast analysis. The contrast between 1&2 vs 3&4 is highly significant (p =
.008). The lesson, analyses for predicted patterns in data are more sensitive
than omnibus or post hoc analyses (as long as the predicted pattern is in fact
observed in the data, of course).
Rick should post a description of the conditions for the factor (WITHOUT MEANS)
to see if we could agree on a predicted pattern that could be tested by a
single df contrast.
Take care
Jim
set seed = 435678234.
input program.
loop o = 1 to 360.
end case.
end loop.
end file.
end input program.
comp group = trunc((o-1)/90)+1.
comp dep = rnd(rv.norm(50,10.5)).
if group > 2 dep = dep + 5.
glm dep by group /posthoc = group(tukey).
Tests of Between-Subjects Effects
Dependent Variable: dep
Source Type III Sum of df Mean Square F Sig.
Squares
Corrected Model 1027.744(a) 3 342.581 2.687 .046
Intercept 990360.900 1 990360.900 7767.647 .000
group 1027.744 3 342.581 2.687 .046
Error 45389.356 356 127.498
Total 1036778.000 360
Corrected Total 46417.100 359
a R Squared = .022 (Adjusted R Squared = .014)
Post Hoc Tests
group
Multiple Comparisons
Dependent Variable: dep
Tukey HSD
(I) (J) Mean Difference Std. Sig. 95% Confidence Interval
group group (I-J) Error Lower Bound Upper Bound
1.000 2.000 -1.43333 1.683239 .830 -5.77812 2.91145
3.000 -4.27778 1.683239 .055 -8.62256 .06701
4.000 -3.51111 1.683239 .160 -7.85590 .83368
2.000 3.000 -2.84444 1.683239 .331 -7.18923 1.50034
4.000 -2.07778 1.683239 .605 -6.42256 2.26701
3.000 4.000 .76667 1.683239 .969 -3.57812 5.11145
Homogeneous Subsets
Tukey HSD
group N Subset
1
1.000 90 50.14444
2.000 90 51.57778
4.000 90 53.65556
3.000 90 54.42222
Sig. .055
glm dep by group /contr(group) = spec(-1 -1 1 1 -1 1 0 0 0 0 -1 1).
Source Type III Sum of df Mean Square F Sig.
Squares
Corrected Model 1027.744(a) 3 342.581 2.687 .046
Intercept 990360.900 1 990360.900 7767.647 .000
group 1027.744 3 342.581 2.687 .046
Error 45389.356 356 127.498
Total 1036778.000 360
Corrected Total 46417.100 359
Custom Hypothesis Tests
group Special Dependent
Contrast Variable
dep
L1 Contrast Estimate 6.356
Std. Error 2.380
Sig. .008
L2 Contrast Estimate 1.433
Std. Error 1.683
Sig. .395
L3 Contrast Estimate -.767
Std. Error 1.683
Sig. .649
James M. Clark
Professor of Psychology
204-786-9757
204-774-4134 Fax
[EMAIL PROTECTED]
---
To make changes to your subscription go to:
http://acsun.frostburg.edu/cgi-bin/lyris.pl?enter=tips&text_mode=0&lang=english
