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Tukey test differ! Why? In Nested ANOVA and ANOVA with sampling
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IIVANCHUK
Sep 13, 2011, 7:51:24 AM9/13/11
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Hi members:
In this experiment, for example:
· Factor: Treatment, F with f = 3 levels .
· F is fixed.
· Experimental unit for F is a row of four trees, R.
· There are r = 3 experimental units per level of F, that is, each
level of
F is replicated three times.
· R is random, nested in F.
· A tree, E, is an element.
· There are e = 4 trees per row.
· E is random, nested in F and R
Method 1. Analysis of individual data. Use the raw data in the
analysis.
I do a Tukey post hoc test after ANOVA-one-way Table .
Then, I obtain a result 1 comparisons of three means levels.
Method 2. Analysis of experimental unit means. The subsamples within
each
experimental unit are averaged and the analysis is performed on the
means as if there was only one observation for each unit.
I do a Tukey post hoc test after Nested ANOVA Table.
Then I obtain a result 2 comparisons of three means levels.
If the design is balanced, then methods (1) and (2) would result in
the
same F-test for the main effect. Method (2) is quite popular because
it
simplifies the design of an experiment — by using the experimental
unit
means, the element level is removed from the design.
Also, the means are more likely (according to Central Limit Theorem)
to be normally distributed.
My doubt comes when I compare the results 1 with results 2.
They are differents!
Why?
The power Tukey test post nested anova table is superior (higher) than
Tukey test post Anova with means values?
It's possible (reasonable) to do a comparison like that?
Thans in advance
Ivan
In this experiment, for example:
· Factor: Treatment, F with f = 3 levels .
· F is fixed.
· Experimental unit for F is a row of four trees, R.
· There are r = 3 experimental units per level of F, that is, each
level of
F is replicated three times.
· R is random, nested in F.
· A tree, E, is an element.
· There are e = 4 trees per row.
· E is random, nested in F and R
Method 1. Analysis of individual data. Use the raw data in the
analysis.
I do a Tukey post hoc test after ANOVA-one-way Table .
Then, I obtain a result 1 comparisons of three means levels.
Method 2. Analysis of experimental unit means. The subsamples within
each
experimental unit are averaged and the analysis is performed on the
means as if there was only one observation for each unit.
I do a Tukey post hoc test after Nested ANOVA Table.
Then I obtain a result 2 comparisons of three means levels.
If the design is balanced, then methods (1) and (2) would result in
the
same F-test for the main effect. Method (2) is quite popular because
it
simplifies the design of an experiment — by using the experimental
unit
means, the element level is removed from the design.
Also, the means are more likely (according to Central Limit Theorem)
to be normally distributed.
My doubt comes when I compare the results 1 with results 2.
They are differents!
Why?
The power Tukey test post nested anova table is superior (higher) than
Tukey test post Anova with means values?
It's possible (reasonable) to do a comparison like that?
Thans in advance
Ivan
Ray Koopman
Sep 13, 2011, 2:53:00 PM9/13/11
to
Source df Expected Mean Square
F f-1 V_E + e*V_R + r*e*U_F
R|F (r-1)*f V_E + e*V_R
E|R|F (e-1)*r*f V_E
Total f*r*e - 1
(Notation: V is the population variance of a random effects.
U is the quasi-variance of a fixed effect, with denominator =
the df of the effect, not the number of levels of the effect.)
How are you doing Method 1? Treating it as a one-way design
with f levels and r*e observations at each level? That would be
equivalent to pooling the R|F and E|R|F effects. The resulting
error term for testing F would be correct only if V_R = 0.
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