Hello everybody!
Sorry for the long post. I'm not sure if this is the right
place to ask such a question, but here it goes. I've got some
doubts in the use of appropriate planned comparisons.
The problem is that the topic is quite new for me and the
literature does not help a lot (I could not get a copy of
Rosenthal & Rosnow, 1985...)
I've got two possible models of ANOVA to test for differences
in space occupancy between periods.
Lets assume population A as a dominant space occupier. It
outcompete other species, growing over them, but never
monopolizes space (Density < 100%, and is usually below 60%).
The hypothesis is that external disturbance events prevent
it from reaching 100% of space occupancy.
Disturbance events are seasonal. Lets assume W as a winter
disturbance, beginning in November--December and ending
in March--April; S is a summer disturbance, beginning in
June--July and ending in November--December; P stands for
spring season, begins in April--March and ends in June--July,
and no disturbance occurs between these periods.
In each of the above months I have 3 sampling dates (which
are actually 3 different years) and in each date I have
10 estimates of A density.
The hypothesis states that there should be a decrease in
density in winter, an increase in spring (growing season)
and a possible decrease in summer (summer disturbance is
not supposed to be as effective as the winter one).
First model:
Factors are locations (4, random), periods (6, fixed)
and sampling dates (3, nested, random) with 10 replicates
per combination. Periods are:
March (end of winter),
April (beginning of spring),
June(end of spring),
July (beginning of summer),
November (end of summer),
December (beginning of winter)
The model goes like this
Source of Variation DF Test against
--------------------------------------------------
Periods 5 P*L
Between winter months 1 P*L
Between spring months 1 P*L
Between summer months 1 P*L
Winter vs Others 1 P*L
Summer vs Spring 1 P*L
Locations 3 D(P*L)
Periods*Locations 15 D(P*L)
Dates(Periods*Locations) 48 Residual
Residual 648
---------------------------------------------------
TOTAL 719
There is no point in using "unplanned comparisons" because
the interesting contrasts are known before the experiment.
As you see, there is a number of planned comparisons, but
I'm really interested only in the first 3... the others are
there just because they sum up to the SS of "Periods"
They could have been Spring vs Others and Summer vs Winter
or Summer vs Others and Spring vs Winter... whatever...
First question: is it fair to omit these last two
contrasts, since they measure averages between periods
rather than differences within periods? If I omit them
the sums of squares will not add up to "SS Periods" and
the same applies to the dfs. But I read somewhere that
this was valid (was it in Cochran and Cox?)
The second model:
I came out with another simpler model. It is slightly
different from first, because only three periods are
considered. The model goes like this: locations (4, random),
periods (3, fixed) and sampling dates (3, nested, random)
with 10 replicates per combination. Periods are::
November (beginning of winter and end of summer)
March (end of winter and beginning of spring)
June (end of spring and beginning of summer)
Source of Variation DF Test against
--------------------------------------------------
Periods 2 P*L
Between winter months 1 P*L
Between spring months 1 P*L
Between summer months 1 P*L
Locations 3 D(P*L)
Periods*Locations 6 D(P*L)
Dates(Periods*Locations) 24 Residual
Residual 324
---------------------------------------------------
TOTAL 359
Now the planned comparisons are not orthogonal, because each
period is used in two tests. The dfs of the comparisons add up
to more than the df of "Periods". I use the Dunn-Sidak method
to correct the critical value of alpha, because the comparisons
are not independent.
I guess both analyses are correct, the latter being simpler
but less "elegant" than the former. Is there any reason to prefer
one analysis against the other?
Thanks in advance
Antonio
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