Lecture15-March+2nd-Beyond+simple+experiment

Lecture15-March+2nd-Beyond+simple+experiment -  

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Unformatted text preview:   Getting
to
the
end!
   Last
exercise
available
after
class
   Due
date
is
NEXT
Tuesday,
March
9th
   Null
hypothesis:
   There
is
no
difference
between
the
groups
being
 compared
   Null
=
nothing,
no
difference
   Alternative
hypothesis:
   There
is
a
difference
between
the
groups
being
 compared
   What
kind
of
inferential
statistics?
   Single
group
experiment
 ▪  Z‐test=
when
population
parameters
(μ
and
σ)
are
 known

 M −µ z= σn ▪  T‐test
=
when
population
parameters
are
unknown
 € M −µ t= sn   What
kind
of
inferential
statistics?
   Two
groups
experiment
 ▪  Independent
group
t‐test
=
when
scores
are
 independent
(between
ss
design)
 t = M1 − M 2 s1 s +2 n1 n 2 ▪  Correlated
groups
t‐test
=
when
scores
are
correlated
 (matched
design,
within
ss
design)
 MD − 0 € € t= Σ( D − M D ) 2 N −1 n Multiple‐group
Experiments

   Advantages
of
the
Multiple‐group
design
   Statistical
analysis
of
multiple
group
studies
   Deciding
on
the
inferential
statistics
tests
   Compare
more
than
two
treatments
   Compare
two
treatments
to
no
treatment
   Compare
three
or
more
levels
of
a
treatment
   Compare
treatment
to
two
different
control
 groups
(placebo
and
no
treatment)
   Efficiency
   Reduce
number
of
experiments
(1
instead
of
3)
   Reduce
number
of
participants
(3
groups
instead
 of
6)
 Low vs. medium stress medium vs. high stress Low vs. high stress low vs. medium vs. high   Efficiency
   Reduce
number
of
experiments
&
participants
   Discovering
relationship
type
   Functional
relationship
 Memory performance   Discovering
U‐shaped
Relationship
 low medium Stress level high Memory Performance   Discovering
U‐shaped
Relationship
 low medium Stress level high   Discovering
U‐shaped
Relationship
 Linear Dependent Variable Curvilinear (nonlinear) Independent Variable   Discovering
Nonlinear
Relationship
 Quadric(U-shape) DV Cubic (double U-shape) DV IV IV S-shape J-shape DV DV IV IV   Efficiency
   Reduce
number
of
experiments
&
participants
   Discovering
relationship
type
   Improve
validity
   External
and
internal
   Efficiency
   Reduce
number
of
experiments
&
participants

   Discovering
relationship
type
   Improve
validity
   Control
for
confounding
variables
   Efficiency
   Reduce
number
of
experiments
&
participants

   Discovering
relationship
type
   Improve
validity
   Control
for
confounding
variables
   Reduce
participants
guessing
the
hypothesis
   Reduce
participants
guessing
the
hypothesis
   Example:
Lee,
Fredrick,
&
Ariely
(2006)

 ▪  Participants
were
asked
to
rate
the
tastiness
of
a
new
 beer
(the
beer
was
mixed
with
vinegar)

 condition Not told about vinegar Told about vinegar before tasting Told about vinegar after tasting Rating of beer tastiness (1-7) 6 2 6   Advantages
of
the
Multiple‐group
design
   Statistical
analysis
of
multiple
group
studies
   Deciding
on
the
inferential
statistics
tests
   Could
we
use
t‐test?
   Yes…but
tedious,
and
increased
chance
of
 Type
I
error…
   Type
I
error:
Reject
H0
when
it’s
true
(false
+)
 ▪  For
any
single
t‐test
probability
of
type
I
error
is
α
 ▪  For
multiple
comparison,
probability
of
type
I
error
 increases:
1
‐
(1
–
α)c
 ▪  c
=
number
of
comparisons
 ▪  1
–
(1
‐
.05)3
=
1
–
(.95)
3
=
1
‐
.86
=
.14

   To
reduce
type
I
error,
we
can
adopt
more
 stringent
criterion
:
Bonferroni
adjustment
   Divide
α
by
number
of
comparisons
   .05/3
=.017
   Adopt
more
stringent
criterion
increases
 chance
of
type
II
error!!!!

   false
negative:
fail
to
reject
H0
when
false
   Bottom
line:
better
to
use
other
statistics!
 No treatment Study A Group means 50 51 52 51 51 No treatment Meditation Exercise 51 53 52 52 52 54 53 53 52 53 Study B Group means More variability between groups Meditation Exercise 40 42 38 40 60 60 58 62 78 82 80 80 40 60 80 No treatment Study C Group means 10 80 60 10 40 No treatment Meditation Exercise 10 90 60 80 60 100 80 60 80 80 Study B Group means More variability within groups Meditation Exercise 40 42 38 40 60 60 58 62 78 82 80 80 40 60 80 More random error!!!   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
group
variability:
Random
error
 variability
+treatment
variability
   Within
group
variability:
due
only
to
random
 error
within
each
group
 F ratio= Random error variance + treatment variance Random error variance =1   The
distribution
of
F‐ratios
   Requires
calculations
of

 ▪  Between
group
df
 ▪  Within
groups
df
 ▪  As
sample
size
increases
&
F‐ratio
is
 larger,
p‐value
decreases
=>

 more
likely
to
be
significant
   Between
SS
design
   One‐Way
Analysis
of
variance
(ANOVA;
F‐test)
   Tests
whether
the
means
of
three
or
more
groups
 are
statistically
different
from
each
other
 H0 : µ1 = µ2 = µ3 Ha : µ1 < > µ2 < > µ3 or Ha : µ1 > µ2> µ3 or…   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
 No treatment Study B Group means Meditation Exercise   One‐way
ANOVA
 Calculate
mean
for
each
 group
 2.  Calculate
overall
mean
 3.  Calculate
“b/w
groups”
SS
 1.  40 42 38 40 60 60 58 62 78 82 80 80 40 60 80 Grand
mean=
M
=
40+60+80/3
=
60
 No treatment Study B Group means 40 42 38 40 40 Meditation Exercise   One‐way
ANOVA
 Calculate
mean
for
each
 group
 2.  Calculate
overall
mean
 3.  Calculate
“b/w
groups”
SS
 1.  60 60 58 62 60 78 82 80 80 80 ( 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 Meditation Exercise   One‐way
ANOVA
 Calculate
mean
for
each
 group
 2.  Calculate
overall
mean
 3.  Calculate
“b/w
groups”
SS
 4.  Calculate
b/w
groups
MS
 1.  40 42 38 40 60 60 58 62 78 82 80 80 40 60 80 MSBETWEEN = SSB df B dfB=
(k
‐
1)
=
2
 € 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   One‐way
ANOVA
 5.  Calculate
“w
groups”
SS
 ‐2
 2
 0
 0
 80 SSw=
0+4+4+0+0+0+4+4+4+4+0+0=
24
 No treatment Study B Group means 40 42 38 40 40 0
 2
 ‐2
 0
   One‐way
ANOVA
 Meditation Exercise 60 60 58 62 60 0
 0
 ‐2
 2
 78 82 80 80 5.  Calculate
“w
groups”
SS
 ‐2
 6.  Calculate
w
groups
MS
 2
 SSW MSWITHIN = 0
 df W 0
 80 € dfW=
k
(n
‐
1)
=
3
(4‐1)=
9

or
(N
‐
k)
=
12
–
3
=
9
 MSW=
24/9=
2.6
 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   One‐way
ANOVA
 5.  Calculate
“w
groups”
SS
 ‐2
 6.  Calculate
w
groups
MS
 2
 7.  Calculate
F
ratio
 0
 MSB 0
 F= 80 MSW F=
1600/2.6=
601.5
 Look
at
table
for
F
value.
Critical
F
is
4.26
 €   Possibility
1:
   High
treatment
>
Control
   High
treatment
>
low
treatment
   Control
=
Low
treatment
   Possibility
2:
   High
treatment
>
Control
   Low
treatment
>
Control
   High
Treatment
=
Low
treatment

 How
do
the
groups
differ?
   A
significant
overall
F
requires
follow‐up

 (post
hoc)
analyses
   Bonferroni:
Planned
comparisons
   Tukey:
Unplanned
comparisons
 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
   Advantages
of
the
Multiple‐group
design
   Statistical
analysis
of
multiple
group
studies
   Deciding
on
the
inferential
statistics
tests
   Parametric
vs.
Nonparametric
Statistics
   Parametric
statistics
used
if:
 ▪  the
variable
is
normally
distributed
in
the
population
 AND
 ▪  Dependent
measures
should
be
at
least
interval
   Nonparametric
statistics
 ▪  Used
if
the
variable
is
not
distributed
normally
 OR
 ▪  Dependent
measures
are
ordinal
or
nominal
 YES ONE GROUP? YES Z test NO t test Population parameters known? 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 ONE GROUP? YES Z test t test Population parameters known? NO YES TWO GROUPS YES Are scores independent? NO MORE GROUPS Independent groups t-test ANOVAs Correlated groups t-test   Repeated
measure
ANOVA
   Factorial
designs
 ...
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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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