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Y603
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Lecture
#11
1. Review of Interaction
graphs based on Two-Way Factorial Designs
--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 (on PINK sheet).
2. Three types of
interactions defined and discussed by Kirk
The simple
main-effect interactions
-- Simple main
effects are defined as (p. 377):
-- Test of simple main
effects (alphas) at b1 or b2 or b3 levels is a test
of A effect + AB interaction because
SSA+ SSAB=SSA at b1 + SSA
at b2 + SSA at b3.
Turn to p. 380 and Table
9.6-2 for a verification.
-- Likewise, test of
simple main effects (betas) at a1, a2, or a3 levels
is a test of B effect +AB interaction.
Use p. 380 and Table 9.6-2
to verify this.
-- For these reasons, the
notion of testing simple main effects is not
endorsed by your instructor.
The treatment-contrast
interactions
--
Treatment-contrast interactions are defined on
p.383.
-- Test of
treatment-contrast interactions is once again
confounded by test of main effects
Turn to p. 388 and examine
F tests of line # 4-8.
-- For the reason stated
above, this type of interaction is also not
endorsed by your instructor.
The contrast-contrast
interactions
-- Contrast-contrast
interactions are defined on p. 384 (middle).
-- They are differences of
differences based on cell means.
-- This is the only type
of interactions which directly follow from the
definition of (a
b
)jk.
-- Can be implemented into
SAS via the CONTRAST statement in PROC GLM such
as
PROC GLM;
CLASS a
b;
MODEL score=a b
a*b;
CONTRAST 'psy5-on
ab' a*b 1 1 -2 -1 -1 2 0 0 0;
CONTRAST 'psy6-on
ab' a*b 1 -1 0 -1 1 0 0 0 0;
CONTRAST 'psy7-on
ab' a*b 1 1 -2 1 1 -2 -2 -2 4;
CONTRAST 'psy8-on
ab' a*b 1 -1 0 1 -1 0 -2 2
0;
3.
Assignments:
(1) Review Sections
9.3, and 9.6 in Kirk.
(2) Do questions 5(a), 5(b),
6(a), 6(b), 6(e), 6(g), 7(a), and 7(b-i) in Chapter 9
of Kirk.
(3) For questions 5, 6, and
7, conduct all contrast-contrast interaction tests by
SAS.
(4) Preview Sections 9.8 and
5.6 in Kirk.
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