Lecture16-March+4th-Factorial+design

Lecture16-March+4th-Factorial+design -  ...

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Unformatted text preview:   Exercise
5
due
on
Tuesday
   Questions?
   Extra
credit
will
be
available
today
after
class,
 for
a
week.
   Once
you
start
the
assignment
you
will
have
20
 minutes
to
complete
it.
   Topics
covered
are
the
same
as
midterm
2.

   Midterm
3
next
Thursday.
   Chapters
7,
8,
9,
10,
11
   Lectures
12,
13,
14,
15,
16,
17
   SKIP
CHAPTER
12
   Last
minute
Q&A
session
as
usual
Thursday
11.00
 to
12.30
 Multiple‐group
Experiments

   Efficiency
   Reduce
number
of
experiments
&
participants

   Discovering
relationship
type
   Improve
validity
   Control
for
confounding
variables
   Reduce
participants
guessing
the
hypothesis
   Could
we
use
t‐test?
   Yes…but
tedious,
and
increased
chance
of
 Type
I
error…
   We
could
use
Bonferroni
adjustment,
but
that
 will
increase
chance
of
Type
II
error...
   Better
method
is
ANOVA
   Between
group
variability:
Random
error
 variability
+treatment
variability
   Within
group
variability:
due
only
to
random
 error
within
each
group
 Signal Noise = Variance between groups Variance within groups = F ratio   Between
SS
design
   One‐Way
Analysis
of
variance
(ANOVA;
F‐test)
 ▪  Data
are
interval
or
ratio

 ▪  The
underlying
distribution
is
normally
distributed
 ▪  The
variances
among
the
populations
being
compared
 are
similar

 ▪  The
observations
are
all
independent
of
one
another
 (groups
are
independent)
   One‐way
=
one
factor,
one
IV
   Within
SS
or
matched
design
   One‐Way
repeated
measure
ANOVA
 ▪  One‐way
=
one
factor,
one
IV
   Differences?
 MSB ▪  One‐way
ANOVA
=
 F = MSW ▪  MSB=
between
treatment,
not
groups
(there’s
just
one
 group!)

 € ▪  MSw=
is
MSE
 No treatment Study B Group means 40 42 38 40 40 Meditation Exercise 60 60 58 62 60 78 82 80 80 80   One‐way
RM
ANOVA
 Mean
for
each
group
 2.  Overall
mean
=
60
 3.  Calculate
“b/w
treatment”
 SS
 1.  ( 2 )( 2 )( SSB = n M1 − M + n M 2 − M + n M 3 − M 2 SSB=
4(40‐60)2
+
4(60‐60)€
+
4(80‐60)2 =
3200
 ) 2 No treatment Study B Group means 40 42 38 40 40 dfB=
(k
‐
1)
=
2
 Meditation Exercise 60 60 58 62 60 78 82 80 80 80 €   One‐way
RM
ANOVA
 Mean
for
each
group
 2.  Overall
mean
=
60
 3.  Calculate
“b/w
treat.”
SS
 4.  Calculate
b/w
treat.
MS
 1.  MSBETWEEN SSB = df B MSB=
3200/2=
1600
 No treatment Study B Group means 40 42 38 40 40 0
 2
 ‐2
 0
 Meditation Exercise 60 60 58 62 60 0
 0
 ‐2
 2
 78 82 80 80 ‐2
 2
 0
 0
   One‐way
RM
ANOVA
 5.  Calculate
“w
groups”
SS
 Split
into
2
sources
 80 PP
variance
 SSw=
0+4+4+0+0+0+4+4+4+4+0+0=
24
 error
variance
 No treatment Study B Group means 59
 61
 59
 61
 Meditation Exercise   One‐way
RM
ANOVA
 5.  Calculate
“w
groups”
SS
 40 42 38 40 60 60 58 62 78 82 80 80 6.  Calculate

participants
SS
 40 60 80€ SSerror=
SSw
–
SSPP
=
12
 2 SSPARTICIPANT = ∑ ( M P − M ) K 7.  Calculate

error
SS
 SSPP=
3(59‐60)2+3(61‐60)2
+
3(59‐60)2
+
3(61‐60)2
=
12
 No treatment Study B Group means 40 42 38 40 40 0
 2
 ‐2
 0
 Meditation Exercise 60 60 58 62 60 0
 0
 ‐2
 2
 78 82 80 80 ‐2
 2
 0
 0
 80   One‐way
ANOVA
 8.  Calculate
error
MS
 € MSERROR SSE = df E dfE=
(k
‐
1)
(n‐1)
=
2
x
3
=
6
 MSE=
12/6=
2
 No treatment Study B Group means 40 42 38 40 40 0
 2
 ‐2
 0
 Meditation Exercise 60 60 58 62 60 0
 0
 ‐2
 2
 78 82 80 80 80 ‐2
 2
 0
 0
   One‐way
ANOVA
 9.  Calculate
F
ratio
 MSB F= MSE F=
1600/2=
800
 € Look
at
table
for
F
value.
Critical
F
is
4.26
 F=
1600/2.6=
601.5
 How
do
the
groups
differ?
   A
significant
overall
F
requires
follow‐up

 (post
hoc)
analyses
   Bonferroni:
Planned
comparisons
   Tukey:
Unplanned
comparisons
 What
is
the
functional
relationship?
   Post
hoc
trend
analyses
 Multiple‐group
Experiments

   Basic
terminology
   2X2
factorial
designs
   Expanding
on
the
2X2
factorial
   Factorial
Study
Example
   Effects
of
caffeine
and
alcohol
on
people’s
 reaction
time
 Factor 1 No caffeine Level 1 Factor 2 200mg caffeine Level 2 400mg caffeine level3 No alcohol Level 1 Condition 1 Condition 2 Condition 3 Alcohol Level 2 Condition 4 Condition 5 Condition 6 Two-factor design 2X3 factorial design   Simple
experiment
   Multiple‐group
experiment
   2X3
Factorial
design
 No caffeine 200mg caffeine 400mg caffeine No alcohol Reaction Time Reaction Time Reaction Time Alcohol Reaction Time Reaction Time Reaction Time   Basic
terminology
   2X2
factorial
designs
   Expanding
on
the
2X2
factorial
 2 levels of exercise 2 levels of caloric intake Experiment 1: 2 levels of exercise Experiment 2: 2 levels of caloric intake Advantages of factorial designs: –  more ‘realistic’ situation –  Combined effect of the factors on the dependant variable Exercise No Yes Not caloric reduced intake reduced •  Main effects: unique effect of each factor •  Interaction: combined effect of both factors •  Simple effects: effect of a factor in one level of the other factor Exercise No Not caloric reduced intake reduced 2 Yes 7 9 4 11 6 14 20 Two simple effects for ‘caloric intake’ Two simple effects for ‘exercise’ •  Simple effects: effect of a factor in one level of the other factor Exercise No Not caloric reduced intake Yes 2 9 5.5 7.5 6 20 4 reduced 14.5 Not caloric reduced intake reduced 13 5.5 13 Main Effect of ‘caloric intake’ on weight loss Exercise No Not caloric reduced intake reduced Yes 2 9 5.5 6 20 13 4 10.5 14.5 Exercise No Yes 4 14.5 Main Effect of ‘exercise’ on weight loss   Interaction:
combined
effect
of
both
factors
 on
the
dependent
variable
 –  One
shot
of
alcohol
=>
‘2’
 –  One
painkiller
pill




=>
‘2’
 –  One
shot
of
alcohol+
one
pill
=>
‘7’
   Interaction:
combined
effect
of
both
factors
 Exercise No Not caloric reduced intake reduced 2 Yes 7 9 4 11 6 14 20   Possible
outcomes:
   The
2
factors
combined
have
an
intensified
effect
 on
the
dependent
variable
   The
2
factors
combined
have
a
weakening
effect
 on
the
dependent
variable
   The
2
factors
combined
have
a
reversed
effect
on
 the
dependent
variable
   One
main
effect,
no
interaction
   Two
main
effects,
no
interaction
   No
main
effects,
no
interaction
   One
main
effect,
interaction
   Two
main
effects,
interaction
   No
main
effects,
interaction
   Are
there
gender
differences
in
diet
efficacy?
 Gender Males Diet No diet diet 1 Females 0 1 9 1 9 10 0 10 5.5 0 5.5 9 10 Amount of weight loss diet no diet 12 10 8 6 4 2 0 males females Gender   Effects
of
alcohol
and
caffeine
on
reaction
time?
 Caffeine 0mg No alcohol Alcohol 2 shots of alcohol 225 400mg -50 175 50 200 50 275 -50 225 250 -50 200 50 250 Reaction Time (in Msec) no alcohol 300 275 250 225 200 175 150 0mg 400mg Level of Caffeine 2 shots   Effect
of
flowers
&
dating
status
on
happiness?
 Receiving Flowers no flowers Single Dating Status 1 flowers 8 9 4 Dating 5 -4 5 0 5 3 4 7 0 5   Effects
of
team
allegiance
and
game
result
on
happiness?
 Game Outcome Kings win Kings fans Team Allegiance Lakers fans 9 Lakers win -8 1 -8 5 8 1 8 9 5 0 5 0 5   Analyses
of
Variance
   For
single
factor:
one‐way
ANOVA
 ▪  Multiple
group
study
(1
IV,
more
than
2
groups
of
scores)
   For
two
factors
design:
two‐way
ANOVA
 ▪  We
get
F‐ratio
for
each
of
the
components:
 ▪  For
main
effect
of
factor
1
 ▪  For
main
effect
of
factor
2
 ▪  For
the
interaction
   For
three
factors:
three‐way
ANOVA
etc…
   Main
effect
   On
average
the
factor
has
an
effect
   Interaction
   Effect
of
one
factor
moderated
by
the
other
 Receiving Flowers no flowers Single Dating Status Dating flowers 1 9 5 5 3 5 7 5   Is
there
an
interaction
between
the
2
factors?
   If
the
difference
in
groups’
means
changes
within

 each
pair
of
simple
effects

   Or
when
graphing
–
lines
are
NOT
parallel
 There
is
an
interaction
 *
Assuming
all
differences
are
statistically
significant
   If
there
is
an
interaction,
what
kind?
   Ordinal
 ▪  lines
in
graphs
have
same
direction
of
slope
 ▪  Or
one
line
is
horizontal
(the
other
is
slanted)

   Disordinal
 ▪  lines
in
graph
have
different
direction
of
slopes
   Ordinal
Interaction:
same
direction
of
slope
 level 2 level 1 80 Dependent variable Dependent variable level 1 70 60 50 40 level 2 80 70 60 50 40 30 30 20 20 10 10 0 0 level 1 level 2 Factor 1 level 1 level 2 Factor 1   Disordinal
Interaction:
different
direction
of
 slopes
 Kings fans Lakers fans 10 Happiness 8 6 4 2 0 Kings win Lakers win Game Outcome   Basic
terminology
   2X2
factorial
designs
   Expanding
on
the
2X2
factorial
 No caffeine   Experimental
   Factors
are
manipulated
 caffeine R.T. R.T. R.T. R.T. Male Female Single Hap Hap Dating Hap Hap Male Female No alcohol R.T. R.T. alcohol R.T. R.T. No alcohol alcohol   Quasi‐experimental
   Factors
are
not
manipulated
 ▪  Participant
variable
   Combined
strategies
   Some
factors
are
manipulated
   Some
factors
are
not
manipulated
   All
examples
were
of
between‐participants
 factorials
designs
   We
can
also
do
factorial
designs
within
 participants
   Every
participant
goes
through
the
different
 conditions
   Or
–
we
can
do
a
mixed
factorial
 Imaginar   One
between
one
within
 3-yearolds 5-yearolds Real y How afraid How afraid How afraid How afraid   More
than
two
factors
   The
complexity
of
the
experimental
design
 increases
   More
main
effects
   More
interactions
   Example
‐
With
3
factors
we
have
   3
main
effects
(A;
B;
C)
   3
two‐way
interactions
(A
x
B;
B
x
C;
A
x
C)
   1
three‐way
interaction
(A
x
B
x
C)
 YES NO ONE GROUP? YES Z test t test Population parameters known? NO YES TWO GROUPS YES Independent groups t-test Are scores independent? NO Correlated groups t-test YES NO 3 or more GROUPS? YES ONE-WAY ANOVA ONE-WAY RM ANOVA Are scores independent? YES More than 1 factor? TWO-WAY (3-way..) ANOVA NO RM ANOVA Are scores independent? ...
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This note was uploaded on 06/21/2011 for the course PSYCHOLOGY Psych 41 taught by Professor Castelli during the Winter '10 term at UC Davis.

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