Y603
Lectures Online
Lecture
#10
1. Two-way fixed-effects,
factorial design (Sections 9.1-9.4 in
Kirk)
Factorial
Design-- a design in which levels of two or more
treatments occur together in the same design.
Completely crossed
factorial design (or CRF) -- a design in which
each and every combination of all levels of all
treatments occur together in the same
design.
Notational system:
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Treatments or
Factors or Independent Variables:
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A
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B
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C
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D
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E
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F
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G
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Conditions or levels
within each treatment
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Treatment effects
associated with factors
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?
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?
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?
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Subscripts from
1,..., to
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P
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Q
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R
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T
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U
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V
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W
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S is used to denote blocks or
samples of subjects (experimental units).
N is used to denote the total
sample size.
n denotes the number of
subjects per cell or subgroup.
The foundation for a
factorial design is the CR design with additional
factor(s) or independent variable(s).
Triplets of null/alternative
hypotheses, alpha level (familywise), critical
regions, F-tests, and decisions.
Box, Hunter, and Hunter
(1978) proved that all three F-tests are orthogonal to
each other under null hypothesis; hence, three F-tests
are also independent from each other.
The underlying mathematical
model is as follows:
2. Introduction to
Interaction Effect in Two-Way Factorial
Design
--How to graph the cell
means to reflect the presence (or absence) of a
significant interaction effect--p. 369 data.
--How to interpret the
significant interaction effect in light of a graph--
the exercise with a 3 by 3 factorial design based on
school attendance records of Elementary, Junior High,
and Senior High School students from three ethnic
backgrounds.
3. Analysis of a two-way
problem (based on p. 369 data)
--Three null hypotheses
corresponding to the column effect, the row effect,
and the interaction effect.
--Three familywise alpha
levels, each set for testing a separate null
hypothesis.
--Three F-ratios with degrees
of freedom derived from columns, rows, and the two
combined.
--Three decisions to make
following the rejection or retention of the null
hypothesis.
To analyze a two-way analysis
of variance problem, follow the syntax
below:
PROC GLM
DATA=data_set_name;
CLASS a b;
MODEL score=a b
a*b;
MEANS a b a*b/SIDAK
TUKEY;
4.
Assignments:
(1) Review Sections
9.3, 9.6 in Kirk
(2) Do questions 2, 3, 4,
5(a), 5(b), 5(f), 6(a), 6(b), 6(g), 7(a), 7(b-i), 7(f)
of Chapter 9 in Kirk.
(3) Preview Section 9.6
(interactions in a factorial design) in
Kirk.
(4) Answer all open-ended
questions on the pink sheet.
