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Topic 21  ANOVA (I)
211
Topic 21  Inferences For More Than 2 Populations
EXAMPLES
:
1)
Suppose we want to compare species diversity of
microfauna in three different habitats: desert, caves,
and arctic tundra.
a.
Hypotheses and inferences are related to
determining whether there are differences in
mean diversity among the three habitats and if
so, determining how they differ
2)
Suppose we want to compare the average growth rate
in oysters maintained in four different temperatures.
a.
Hypotheses might be that average growth rate
differs among the four temperatures studied (we
could go further and make hypotheses regarding
whether the means increase or decrease but then
we are moving into the regression setting rather
than the ANOVA setting)
Defn
:
A
Factor
is the variable that separates the groups
of interest into distinct populations.
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Defn
:
A
Treatment
is one level of the Factor under
study. If more than one factor is of interest, then a
treatment is a combination of levels of the factors.
Defn:
The treatments are considered to be
Populations
,
each with its own mean and variance.
EXAMPLE
Oyster experiment.
Factor:
Treatments (levels of
Factor):
Populations under Study:
Completely Randomized Designs (CRD)
Defn
:
A
Completely Randomized Design
is an
experimental design in which the experimental units are
either randomly selected from each of the populations or
are randomly assigned to one of the populations. This
means that each population and sample is considered
independent of all of the other samples and populations.
Topic 21  ANOVA (I)
213
Recall Defn
:
An
Observational Study
is one in which
we cannot control the treatment performed on the
experimental units.
Recall Defn:
A
Planned Experiment
is one in which the
treatment is randomly assigned to each experimental unit.
For example, suppose we are interested in the effect of
three types of submerged aquatic vegetation species on
water clarity. Two approaches:
1)
find locations with only one of the three species and
measure water clarity at those locations.
2)
construct “ponds” and fill each with one of the three
cover species. Leave alone for a while and then
measure water clarity.
Is one method better than the other? why?
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Assumptions of the CRD:
1)
Sampling
:
a.
For observational studies,
independent random
samples are taken from each of the populations
of interest.
b.
For planned experiments, the treatments are
randomly
assigned to the
randomly
chosen
experimental units. Here, the populations refer to
conceptual ones in which there is one population
for each of the treatments in the experiment.
c.
Samples from each population are
independent
.
EXAMPLE
oysters: independent sampling here would
mean that oysters were randomly selected for the
experiment (no clumps of oysters were taken and then
separated, oysters were taken from different locations,
oysters were not selected by size, etc) and further that, if
the experiment was planned, the oysters were randomly
assigned to treatment levels.
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This note was uploaded on 07/22/2011 for the course STA 4702 taught by Professor Staff during the Spring '08 term at University of Florida.
 Spring '08
 Staff

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