Lecture13-February+23rd-Hypothesis+testing

Lecture13-February+23rd-Hypothesis+testing -  

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview:   Tutorial
quiz
10
due
Today
   Last
tutorial
available
today
after
class
   Due
date
is
next
TUESDAY,
march
2nd,
before
 class
   Exercise
4
will
be
available
after
class.
Due
 date
is
Tuesday,
March
2nd,
in
class
   Between
vs.
Within
designs
   Between‐Subjects
Designs
   Advantages
and
disadvantages
   Matched‐pairs
design
   Within‐Subjects
designs
   Threats
to
internal
validity
   Minimizing
threats
   Mixed
designs

   Reduce
number
of
conditions
   Change
sequence
of
conditions
   
Randomized
Within‐Subjects
 ▪  Interview
on
true
and
false
events
   Reduce
number
of
conditions
   Change
sequence
of
conditions
   Randomized
Within‐Subjects
   Randomized
blocks
 ▪  Questions
x
chapter
   Reduce
number
of
conditions
   Change
sequence
of
conditions
   Randomized
Within‐Subjects
   Randomized
blocks
   
Counterbalanced
Within‐Subjects
 Treatment
use
is
COUNTERBALANCED,
so
 it
appear
in
all
possible
orders
             A
B
C
D
 A
C
B
D
 A
D
B
C
 B
D
C
A
 Etc…..
   Change
sequence
of
conditions
   Randomized
Within‐Subjects
   Randomized
blocks
   
Counterbalanced
Within‐Subjects
 ▪  Latin‐square
design
 ▪  Matrix
of
n
elements
were
each
element
appears
 exactly
once
in
each
column
and
in
each
row
 Latin
square
counterbalancing
   A
B
C
D
   B
C
D
A
   C
D
A
B
   D
A
B
C
   Between Within Pros (a) Minimize reactance effects (a) Requires fewer research subjects Cons (a) Requires more research subjects (b) The people in the two conditions may vary for reasons that have nothing to do with your manipulation. (a) Awareness of different levels of independent variable (b) Learning & practice effects   Between‐
and
within‐subjects
designs
 between‐subjects:
different
people
are
exposed
to
 each
level
of
the
IV
 within‐subjects:
the
same
people
exposed
to
each
 level
of
the
IV
   Mixed
design:
one
factor
is
a
between‐ subjects
factor
and
the
other
is
a
within‐ subjects
factor
   A
study
that
combines
between‐
and
within‐
 participants
designs
   One
variable
‘within’

   One
variable
‘between’
 Within Memorability High experimental training control Between Low Number of Number of correct rejection correct rejection Number of Number of correct rejection correct rejection   Hypothesis
   Descriptive
vs.
predictive
   Non‐directional
vs.
directional
   Hypothesis
testing:

   determining
whether
results
of
our
research
 support
our
statement
   Hypothesis
testing:
4
steps
 1.  Convert
research
question
into
NULL
and
 ALTERNATIVE
hypotheses
 2.  Test
statistic
   Hypothesis
testing:
4
steps
 1.  Convert
research
question
into
NULL
and
 ALTERNATIVE
hypothesis
 2.  P
value
and
significance
 3.  Test
statistic
 4.  Decision
   Null
and
alternative
hypotheses
   Test
statistic
   Distribution
of
sample
means
   Single‐sample
inferential
stats
   p
value
and
statistical
significance
   Errors
in
Hypothesis
testing
   Null
hypothesis:
   There
is
no
difference
between
the
groups
being
 compared
   Null
=
nothing,
no
difference
   Alternativehypothesis:
   There
is
a
difference
between
the
groups
being
 compared
   Example:
Practice
questions
affects
students’
 performance
on
test

   Group
A
=
practice
questions
before
test
 (experimental)
   Group
B
=
no
practice
questions
(control)
   Null
hypothesis
(H0)
:
no
difference
b/w
group
A
 and
B
 ▪  H0:
μA

=
μB
   Example:
Practice
questions
affects
students’
 performance
on
test

   Group
A
=
practice
questions
before
test
 (experimental)
   Group
B
=
no
practice
questions
(control)
   Alternative
hypothesis
(H1)
:
there’s
a
difference

 b/w
group
A
and
B
 ▪  H1:
μA

≠
μB
   When
we
use
inferential
stats
we
try
to
reject
 Null
hypothesis
   If
H0
is
not
supported,
alternative
hypothesis
 is
all
that
is
left

 Hypothesis
Testing
 Jury
Trial
 Null
 no
treatment
effects
 defendant
innocent
 hypothesis:
 until
proven
guilty
 Trying
to
refute
 Researcher
gather
 Police
gather
evidence
 the
null
 evidence
to
show
 to
show
defendant
did
 hypothesis:

 treatment
has
an
effect
 the
crime
 If
there
is
 Researcher
rejects
H0
&
 Jury
rejects
H0
&
 enough
 concludes
there
really
is
 concludes
the
 evidence:
 treatment
effect
 defendant

is
guilty
 If
there
is






 Researcher
fails
to
 Jury
fails
to
find
the
 not
enough
 reject
H0

 defendant
guilty
 evidence:
   IMPORTANT:
Failure
to
reject
the
null
 hypothesis
leads
to
its
acceptance
(i.e.
H0
is
 true)
   WRONG!

   Failure
to
reject
the
null
hypothesis
ONLY
 implies
insufficient
evidence
for
its
rejection!
   Directional
vs.
non‐directional
   In
statistical
terms
   Directional
=
one‐tailed
hypothesis
   Non‐directional
=
two‐tailed
hypothesis
   Null
and
alternative
hypotheses
   Test
statistic
=
inferential
stats
   Distribution
of
sample
means
   Single‐sample
inferential
stats
   p
value
and
statistical
significance
   Errors
in
Hypothesis
testing
   Descriptive
statistics
   Ways
to
organize,
summarize,
and
simplify
a
set
 of
data
   Inferential
statistics
   Ways
to
use
the
results
obtained
from
samples
to
 help
make
generalizations
about
populations
   Inferential
statistics
   Compare
measure
of
dependent
variable
in
each
 group
   Is
the
difference
b/w
our
groups
meaningful?
   Is
it
large
enough
to
conclude
it
is
due
to
our
 manipulation?
   What
is
the
likelihood
that
it
is
due
to
chance?
   Inferential
statistics
   Compare
measure
of
dependent
variable
in
each
 group
   Null
hypothesis:
 ▪  Difference
is
due
to
chance
(not
to
out
IV)
 ▪  If
result
of
test
stats
occurs
RARELY
by
chance,
we
can
 conclude
that
something
OTHER
than
chance
is
 operative
(i.e.
our
IV)
   Sample
vs.
Population
   Statistics
as
estimates
of
parameters
 Population Population: UCD Students Average GPA µ =2.8 Standard Deviation σ = .80 µ Sample A: 25 Students Average GPA MA =3 Sample B: other 25 Students Average GPA MB =2.7 Sample A Sample B MA MB   Sample
vs.
Population
   Statistics
as
estimates
of
parameters
 ▪  Sampling
error:

 Population the
natural
discrepancy

 between
a
sample
statistic

 and
its
corresponding

 µ population
parameter
 Sample A Sample B MA MB   Sample
vs.
Population
   Statistics
as
estimates
of
parameters
 ▪  Sampling
error:

 Population the
natural
discrepancy

 between
a
sample
statistic

 and
its
corresponding

 µ population
parameter
 ▪  Sampling
distribution:
 a
distribution
of
statistics
obtained
by

 selecting
all
possible
samples
of
a

 specific
size
from
a
population
 Sample A Sample B MA MB   Characteristics
of
Sampling
distribution
 1.  Sample
means
pile
up
around
population
mean
 
mean
of
sampling
distribution=mean
of
population
 2.  Form
a
normal
distribution
 3.  For
larger
samples
–
cluster
close
to
μ

 For
smaller
samples
–
means
would
be
spread
 out
more
   The
Central
Limit
Theorem
   The
sampling
distribution
of
infinite
samples
with
 sample
size
n
   identified
by
the
parameters
μ

and
σ
   Will
be
normally
distributed
with
parameters
μ

 and
σ
/√n
 ▪  Describe
sampling
distribution
for
ANY
population
 ▪  Sampling
distribution
approaches
normal
distribution
 rapidly
(if
N=30,
distribution
almost
perfectly
normal)

   The
Central
Limit
Theorem
   The
sampling
distribution
of
infinite
samples
with
 sample
size
n
   identified
by
the
parameters
μ

and
σ
   Will
be
normally
distributed
with
parameters
μ

 and
σ
/√n

 The standard error How much difference is expected from one sample to another How well an individual sample represents the entire distribution   The
Central
Limit
Theorem
 Larger standard deviation   samples population of the The
sampling
distribution
of
infinite
samples
with
 Larger sample size results in more error sample
size
n
 results in less error   identified
by
the
parameters
μ

and
σ
   Will
be
normally
distributed
with
parameters
μ

 and
σ
/√n

 The standard error How much difference is expected from one sample to another How well an individual sample represents the entire distribution     Z‐score
tells
us
how
many
SD
above
or
below
the
 mean
a
score
falls
 Because
we
know
the
population
mean
and
sd
we
 can
use
z‐score
to
compare
our
sample
mean
to
the
 population
mean

   Using
z‐scores
we
can
find
the
probability
 associated
with
any
specific
sample
   We’ll
use
z‐scores
 (sample
mean‐μ)
 ▪  The
location
of
our
sample
mean
z=


 σ/√n   Single
sample
inferential
stats:
Z‐test
 Test
of
null
hypothesis
for
single
sample,
when
 population
variance
is
known
   Parametric
test:
population
parameters
(μ,
σ)
 are
known
     Z‐test:
uses
sample
data
to
evaluate
a
 hypothesis
about
a
population
 Does a treatment has an effect on the population mean? Known population before treatment σ = 15 µ = 100 T r e a t m e n t Unknown population after treatment σ = 15 µ =?   Statistical
method
that
uses
sample
data
to
 evaluate
a
hypothesis
about
a
population
 Does a treatment has an effect on the population mean? Known population before treatment σ = 15 µ = 100 sample
 T r e a t m e n t Unknown population after treatment σ = 15 µ =? treated
 sample
   Four
steps
 1.  State
the
hypotheses
 2.  Set
the
criteria
for
a
decision
 3.  Collect
data
and
compute
sample
statistics
 4.  Make
a
decision
   Do
practice
questions
improve
performance
 on
test?
   Distribution
of
test
score
is
normal
   μ
=
38,
σ
=
4
   Provide
group
(N=25)
with
practice
questions
 before
test
   If
μpractice
is
noticeably
different
from
38,
we
can
 conclude
practice
questions
have
an
effect
   Stating
the
hypotheses
   Null
hypothesis
(
H0):
Practice
questions
 have
no
effects
on
test
performance
 ▪  H0:
μpractice
=
38
   Alternative
hypothesis
(H1):
Practice
 questions
DO
have
an
effect
on
test
 performance
 ▪  H1:
μpractice
≠
38
(non‐dir/two‐tailed
hypothesis)
 Setting
the
criteria
for
a
decision
   Determine
the
sample
means
that
are
consistent
 with
the
null
hypothesis
   Determine
the
sample
means
that
are
at
odds
 with
the
null
hypothesis
   Practice questions have no effect on test performance H0: µpractice = 38 If true sample means should be near 80 If false sample means should be very different from 80 What
does
it
mean
to
be
“near”
or
“different
 from”?
 How
different?
     We
need
to
examine
all
the
possible
means
 that
could
be
obtained
if
H0
were
true
     Distribution
of
sample
means
for
N=25
 68% 95% 99%   Setting
the
criteria
for
a
decision
   Based
on
probabilities
 ▪  Level
of
significance
 (α
):
determines

 the
low‐prob
 sample
means
 The distribution of sample means if the null hypothesis is true (all the possible outcomes) Sample means close to H0: High probability values if H0 is true Extreme, low-probability values if H0 is true µ from H0 Extreme, low-probability values if H0 is true   Setting
the
criteria
for
a
decision
   Based
on
probabilities
 ▪  Level
of
significance
 (α
):
determines
the
low‐prob
 sample
means
 ▪  The
critical
region:
 Region
of
extreme

 values;
boundaries

 Reject H 0 determined
by
α

 Middle 95%: high-prob values if H0 is true µ from H0 Reject H0 Critical Region: Extreme 5%   Statistical
Significance
test:
Z‐test
 1.  Calculate
critical
values
set
by
α
 ▪  Calculate
sample
z‐score
 (sample
mean‐μ)
 z= σ/√n Z=-1.96 Middle 95%: high-prob values if H0 is true µ from H0 Reject H0 Reject H0 Z= (41-38) 4/√25 = 3.75 Z=1.96 Critical Region: Extreme 5%   Statistical
Significance
test
 1.  Calculate
critical
values
set
by
α
 ▪  Calculate
sample
z‐score

 (=sample
statistic)
 Middle 95%: ▪  If
Z>1.96
or
Z<‐1.96
then

 we
reject
the
null
hypothesis
 ▪  If
‐1.96<Z<1.96
then

 Z=-1.96 we
fail
to
reject
the

 Reject H0 null
hypothesis
 Z= (39-38) 4/√25 = 1.25 high-prob values if H0 is true µ from H0 Z=1.96 Reject H0 Critical Region: Extreme 5%   Statistical
Significance
test
 1.  Calculate
critical
values
set
by
α
 2.  Calculate
probability
of

 getting
your
sample
mean:
 p‐value
 ▪  If
p‐value
<
α
then

 reject
null
hypothesis
 ▪  If
p‐value
>
α
then

 fail
to
reject
null
hypothesis
 P-value for M = 39 P-value: Likelihood of getting the sample mean that we got if H0 is true P-value for M = 41   Type
I
error
   Rejecting
null
hypothesis
that
is
actually
true
   Equals
to
the
alpha
level
   Type
II
error
   Failing
to
reject
a
null
hypothesis
that
is
really
 false
 True State of Affairs Ho True Reject Ho Decision Do not reject Ho Ho False Type I error Correct decision (= α ) Correct decision (confidence level=1- α) (power=1- β) Type II error (=β ) True State of Affairs Not Guilty Guilty Decision Not Guilty Guilty Type I error Correct decision (= α ) Correct decision (confidence level=1- α) (power=1- β) Type II error (=β )   Power
   Probability
that
the
test
will
correctly
reject
a
false
 null
hypothesis
   Increase
power
by
larger
sample
size
   Increase
power
by
greater
precision
of
the
 research
design
   Effect
size
   How
substantial
is
the
effect?
   Measure
the
absolute
magnitude
of
a
treatment
 independent
of
the
sample
size
 ▪  Cohen’s
d=(M‐μ)/σ
 ...
View Full Document

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.

Ask a homework question - tutors are online