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Reasoning in Psychology
Using Statistics
Psychology 138
2015
• Don’t forget Quiz 5 is due Fri. Mar. 20 at
midnight
Announcements
Reasoning in Psychology
Using Statistics
• Hypothesis testing: a five step program
–
–
–
–
–
Step 1: State your hypotheses
Step 2: Set your decision criteria
Step 3: Collect your data from your sample
Step 4: Compute your test statistics
Step 5: Make a decision about your null hypothesis
Note: In the labs I combine steps 1 & 2, so it is
described as a 4 step program
Testing Hypotheses
Reasoning in Psychology
Using Statistics
• Hypothesis testing: a five step program
–
–
–
–
–
Step 1: State your hypotheses
Step 2: Set your decision criteria
Step 3: Collect your data from your sample
Step 4: Compute your test statistics
Step 5: Make a decision about your null hypothesis
Testing Hypotheses
Reasoning in Psychology
Using Statistics
• A simpler case
– Population:
2
4
6
8
– All possible samples of size n = 2
mean
mean
2
2
4
6
2
5
2
4
2
6
2
8
4
2
4
4
3
4
5
4
8
6
2
6
4
3
4
6
6
6
8
6
4
5
There are 16 of them
mean
8 2
5
8
4
8
6
8
8
6
7
Distribution of sample means
Reasoning in Psychology
Using Statistics
6
7
8
5
4
3
2
1
In long run, the random selection of tiles
leads to a predictable pattern
The distribution of sample means
2 3 4 5 6 7 8
means
2
mean
2
2
4
mean
6
5
8
mean
2
5
2
4
3
4
5
4
8
8
4
2
6
6
2
8
6
2
8
6
4
8
8
4
2
3
4
6
6
4
4
6
8
6
4
5
6
7
Distribution of sample means
Reasoning in Psychology
Using Statistics
6
7
8
5
4
3
2
1
Using the distribution of sample means
• Finding out how likely is a particular sample
2 3 4 5 6 7 8
means
X f
p
8 1 0.0625
7 2 0.1250
6 3 0.1875
5 4 0.2500
4 3 0.1875
3 2 0.1250
• Sample problem:
– What is the probability of getting a sample
(n = 2) with a mean of 6 or more?
P(X > 6) = .1875 + .1250 + .0625 = 0.375
• Same as before, except now we
are asking about sample means
rather than single scores
2 1 0.0625
Distribution of sample means
Reasoning in Psychology
Using Statistics
• Distribution of sample means is a “virtual” distribution
between the sample and population
– Note: There is a different one for each sample size
Population
Distribution of sample means
Sample
• Shape
• Center
• Spread
Distribution of sample means
Reasoning in Psychology
Using Statistics
• Shape
– If population is Normal, then the dist of sample means
will be Normal
– If the sample size is large (n > 30), the DSM will be
approximately Normal (regardless of shape of the population)
Distribution of sample means
Population
n > 30
Properties of the distribution of sample means
Reasoning in Psychology
Using Statistics
• Center
– The mean of the dist of sample means is equal to the mean of the
population
Population
m
Distribution of sample means
same numeric value
different conceptual values
Properties of the distribution of sample means
Reasoning in Psychology
Using Statistics
• Center
– The mean of the dist of sample means is equal to the mean of the
population
– Consider our earlier example
Population
2
4
6
Distribution of sample means
8
μ= 2+4+6+8
4
=5
5
4
3
2
1
2 3 4 5 6 7 8
means
= 2+3+4+5+3+4+5+6+4+5+6+7+5+6+7+8
16
=5
Properties of the distribution of sample means
Reasoning in Psychology
Using Statistics
• Spread
– The Stand. Dev. of the Distrib. of Sample Mean depends on 2 things
• Standard deviation of the population
• Sample size
Properties of the distribution of sample means
Reasoning in Psychology
Using Statistics
• Spread
• Standard deviation of the population
X3 X1μ
X2
X3 X1μ
X2
– The smaller the population variability, the closer
the sample means are to the population mean, so
the smaller the spread of sample means
Properties of the distribution of sample means
Reasoning in Psychology
Using Statistics
• Spread
• Standard deviation of the population
• Sample size
n=1
μ
X
Properties of the distribution of sample means
Reasoning in Psychology
Using Statistics
• Spread
• Standard deviation of the population
• Sample size
n = 10
μ
X
Properties of the distribution of sample means
Reasoning in Psychology
Using Statistics
• Spread
• Standard deviation of the population
• Sample size
n = 100
- The larger the
sample size the
smaller the spread of
sample means
μ
X
Properties of the distribution of sample means
Reasoning in Psychology
Using Statistics
• Spread
• Standard deviation of the population
• Sample size
– Putting them together we get the standard deviation of
the distribution of sample means
sX =
s
n
- The smaller the population variability,
… the smaller the spread
- The larger the sample size the
smaller the spread
– Commonly called the standard error
Properties of the distribution of sample means
Reasoning in Psychology
Using Statistics
• All three of these properties are combined to form
the Central Limit Theorem
sX =
MEMORIZE THIS
s
n
– For any population with mean μ and standard deviation
, the distribution of sample means for sample size n
will approach a normal distribution with a mean of μ
and a standard deviation of s as n approaches infinity
n
(good approximation if n > 30).
Properties of the distribution of sample means
Reasoning in Psychology
Using Statistics
• The standard error is the average amount that you’d expect
a sample (of size n) to deviate from the population mean
Keep your distributions
– In other words, it is an estimate of the error that you’d expect by
straight by taking care
chance (it is our estimate of the sampling error)
with your notation
Population
Distribution of sample means

sX =
μ
s
n
Sample
s
X
Properties of the distribution of sample means
Reasoning in Psychology
Using Statistics
• Hypothesis testing: a five step program
–
–
–
–
–
Step 1: State your hypotheses
Step 2: Set your decision criteria
Step 3: Collect your data from your sample
Step 4: Compute your test statistics
Step 5: Make a decision about your null hypothesis
Testing Hypotheses
Reasoning in Psychology
Using Statistics
• How do we know which test to use?
– The design of the research: how many groups, how many scores per
person, etc.
Start here
Statistical test decision tree
Reasoning in Psychology
Using Statistics
• How do we know which test to use?
– The design of the research: how many groups, how many scores per
person, etc.
Could be difference between a sample and a
population, or between different samples
observed difference
test statistic =
difference expected by chance
As a result,
the test
statistic
changes
Based on standard error or an
estimate of the standard error
Generic statistical test
Reasoning in Psychology
Using Statistics
Both of these
parts change
as a function
of the design
test statistic =
observed difference
difference expected by chance
• Transform the distribution of sample means into the
appropriate standardized distribution (as determined by the
design features)
Distribution of sample means
Test statistic distribution
We will use 2:
z’s & t’s
sX
Test statistic
Using the distribution of sample means
Reasoning in Psychology
Using Statistics
test statistic =
observed difference
difference expected by chance
Old z-formula
z=
New z-formula
X -m
s
zX =
X - mX
sX
• Same as before,with two differences:
– Uses the distribution of sample means
– Ask questions about samples rather than individual scores
One sample z-test statistic
Reasoning in Psychology
Using Statistics
test statistic =
observed difference
difference expected by chance
Old z-formula
population mean
raw score
z=
sample mean
X -m
population
standard deviation
New z-formula
s
zX =
standard error
One sample z-test statistic
Reasoning in Psychology
Using Statistics
mean of the
distribution of
sample means
X - mX
sX
test statistic =
observed difference
difference expected by chance
Old z-formula
z=
New z-formula
X -m
s
zX =
X - mX
sX
• Same as before,with two differences:
– Uses the distribution of sample means
– Ask questions about samples rather than individual scores
One sample z-test statistic
Reasoning in Psychology
Using Statistics
Old z-formula
What is the probability of getting a 630 or better on
the SAT?
From the table:
μ = 500, σ = 100, Normal
z(1.3) =.0968
z=
X -m
s
630 - 500
=
=1.3
100
So the probability is 0.0968
New z-formula
What is the probability of getting a sample of n = 4 students with an
average of 630 or better on the SAT?
μ = 500, σ = 100, Normal
From the table:
s 100
sX =
=
= 50
z(2.6) =.0047
n
4
X - m X 630 - 500
=
= 2.6
zX =
50
sX
So the probability is 0.0047
One sample z-test statistic
Reasoning in Psychology
Using Statistics
• Hypothesis testing: a five step program
–
–
–
–
–
Step 1: State your hypotheses
Step 2: Set your decision criteria
Step 3: Collect your data from your sample
Step 4: Compute your test statistics
Step 5: Make a decision about your null hypothesis
Testing Hypotheses
Reasoning in Psychology
Using Statistics
• What are we doing when we test the hypotheses?
– Consider a variation of our memory experiment example
Memory
patients
We test
this one
Memory
treatment
Memory
Test
X
Population of
memory patients
MemoryTest
μ &  known
Compare these
two means
Conclusions:
H0: • The memory treatment sample are the same as those in the
population of memory patients.
HA: • They aren’t the same as those in the population of memory patients
Performing your statistical test
Reasoning in Psychology
Using Statistics
• What are we doing when we test the hypotheses?
Real world (‘truth’)
H0: is true (no treatment effect)
H0: is false (is a treatment effect)
One
population
Two
populations
XA
The memory treatment sample are
the same as those in the population
of memory patients.
XA
They aren’t the same as those in
the population of memory patients
We test this one
Performing your statistical test
Reasoning in Psychology
Using Statistics
• The generic test statistic distribution (a transformation of
the distribution of sample means)
– To reject the H0, you want a computed test statistics that is large
• The probability of having a sample with that mean is very low
– What’s large enough?
• The alpha level gives us the decision criterion
Distribution of the test statistic
α-level determines where
these boundaries go
“Generic” statistical test
Reasoning in Psychology
Using Statistics
• The generic test statistic distribution (a transformation of
the distribution of sample means)
– To reject the H0, you want a computed test statistics that is large
• The probability of having a sample with that mean is very low
– What’s large enough?
• The alpha level gives us the decision criterion
Distribution of the test statistic
If test statistic is
here Reject H0
If test statistic is here
Fail to reject H0
“Generic” statistical test
Reasoning in Psychology
Using Statistics
• The alpha level gives us the decision criterion
Two -tailed
 = 0.05
Reject H0
0.025
split up
into the
two tails
Fail to reject H0
0.025
z
.00
.01
…
-3.4
-3.3
:
-1.9
:
0
:
:
1.0
:
1.9
:
3.4
0.0003
0.0005
:
0.0287
:
0.5000
:
:
0.8413
:
0.9713
:
0.9997
0.0003
0.0005
:
0.0281
:
0.5040
:
:
0.8438
:
.9719
:
0.9997
…
…
.06
.0250
.9750
• Go to the table (unit normal table for z-test) and find the
z that has 0.050 in the tails. Zcritical =
±1.96
“Generic” statistical test
Reasoning in Psychology
Using Statistics
• The alpha level gives us the decision criterion
Two -tailed
One -tailed
 = 0.05
all of it in
one tail
Reject H0
Reject H0
0.05
Fail to reject H0
Reject H0
Fail to reject H0
Fail to reject H0
• Go to the table (unit normal table for z-test) and find the
z that has 0.050 in the tail. Zcritical = +1.645
“Generic” statistical test
Reasoning in Psychology
Using Statistics
• The alpha level gives us the decision criterion
Two -tailed
One -tailed
 = 0.05
Reject H0
all of it in
one tail
Reject H0
0.05
Fail to reject H0
Reject H0
Fail to reject H0
Fail to reject H0
• Go to the table (unit normal table for z-test) and find the
z that has 0.050 in the tail. Zcritical = -1.645
“Generic” statistical test
Reasoning in Psychology
Using Statistics
•
Dr. Mnemonic develops a new treatment for patients
with a memory disorder. He hypothesizes that the
treatment will improve memory performance. To test it
he collects a sample of 16 patients and gives them his
new treatment. Following the treatment he gives them
a standard memory test. His sample averaged 55 errors
(while the typical memory patient averages μ = 60
errors, with σ = 8). Test using α = 0.05.
Memory
patients
Memory
treatment
Memory
Test
X
Compare these
two means
1-sample z-test
Reasoning in Psychology
Using Statistics
Population of
memory patients
Memory Test
σ is known
μ is known
•
Dr. Mnemonic develops a new treatment for patients
with a memory disorder. He hypothesizes that the
treatment will improve memory performance. To test it
he collects a sample of 16 patients and gives them his
new treatment. Following the treatment he gives them
a standard memory test. His sample averaged 55 errors
(while the typical memory patient averages μ = 60
errors, with σ = 8). Test using α = 0.05.
Memory
patients
Memory
treatment
Memory
Test
X
Compare these
two means
1-sample z-test
Reasoning in Psychology
Using Statistics
– 1 sample
Population of
memory patients
Memory Test
σ is known
μ is known
•
Dr. Mnemonic develops a new treatment for patients
with a memory disorder. He hypothesizes that the
treatment will improve memory performance. To test it
he collects a sample of 16 patients and gives them his
new treatment. Following the treatment he gives them
a standard memory test. His sample averaged 55 errors
(while the typical memory patient averages μ = 60
errors, with σ = 8). Test using α = 0.05.
Memory
patients
Memory
treatment
Memory
Test
X
Compare these
two means
1-sample z-test
Reasoning in Psychology
Using Statistics
– 1 sample
– 1 score per subject
Population of
memory patients
Memory Test
σ is known
μ is known
•
Dr. Mnemonic develops a new treatment for patients
with a memory disorder. He hypothesizes that the
treatment will improve memory performance. To test it
he collects a sample of 16 patients and gives them his
new treatment. Following the treatment he gives them
a standard memory test. His sample averaged 55 errors
(while the typical memory patient averages μ = 60
errors, with σ = 8). Test using α = 0.05.
Memory
patients
Memory
treatment
Memory
Test
X
Compare these
two means
– 1 sample
– 1 score per subject
– Population mean (μ) and
standard deviation (σ) are
known (assume Normal dist)
Population of
memory patients
Memory Test
σ is known
μ is known
1-sample z-test
zX =
1-sample z-test
Reasoning in Psychology
Using Statistics
X - mX
sX
•
Dr. Mnemonic develops a new treatment for patients
with a memory disorder. He hypothesizes that the
treatment will improve memory performance. To test it
he collects a sample of 16 patients and gives them his
new treatment. Following the treatment he gives them
a standard memory test. His sample averaged 55 errors
(while the typical memory patient averages μ = 60
errors, with σ = 8). Test using  = 0.05.
•
Step 1: State your hypotheses
•
Step 2: Set your decision criteria
•
Step 3: Collect your data
•
Step 4: Compute your test statistics
•
Step 5: Make a decision about your HA:
null hypothesis
One -tailed
H0: the memory treatment
μTreatment > μpop = 60
sample are the same as those
in the population of memory
patients (or even worse).
the memory treatment sample μTreatment <
perform better (fewer errors) than
those in the population of
memory patients
Performing your statistical test
Reasoning in Psychology
Using Statistics
μpop = 60
•
Dr. Mnemonic develops a new treatment for patients
with a memory disorder. He hypothesizes that the
treatment will improve memory performance. To test it
he collects a sample of 16 patients and gives them his
new treatment. Following the treatment he gives them
a standard memory test. His sample averaged 55 errors
(while the typical memory patient averages μ = 60
errors, with σ = 8). Test using α = 0.05.
•
Step 1: State your hypotheses
•
Step 2: Set your decision criteria  = 0.05
•
Step 3: Collect your data
•
Step 4: Compute your test statistics
•
Step 5: Make a decision about your
null hypothesis
H0: μTreatment > μpop = 60
HA: μTreatment < μpop = 60
One -tailed
Performing your statistical test
Reasoning in Psychology
Using Statistics
•
Dr. Mnemonic develops a new treatment for patients
with a memory disorder. He hypothesizes that the
treatment will improve memory performance. To test it
he collects a sample of 16 patients and gives them his
new treatment. Following the treatment he gives them
a standard memory test. His sample averaged 55 errors
(while the typical memory patient averages 60 errors,
with a σ = 8). Test using α = 0.05.
•
Step 1: State your hypotheses
•
Step 2: Set your decision criteria
•
Step 3: Collect your data n = 16, X = 55
•
Step 4: Compute your test statistics
•
Step 5: Make a decision about your
null hypothesis
H0: μTreatment > μpop = 60
HA: μTreatment < μpop = 60
One -tailed
 = 0.05
Performing your statistical test
Reasoning in Psychology
Using Statistics
•
•
Dr. Mnemonic develops a new treatment for patients
with a memory disorder. He hypothesizes that the
treatment will improve memory performance. To test it
he collects a sample of 16 patients and gives them his
new treatment. Following the treatment he gives them
a standard memory test. His sample averaged 55 errors
(while the typical memory patient averages 60 errors,
with a σ = 8). Test using α = 0.05.
Step 1: State your hypotheses
•
Step 2: Set your decision criteria
•
Step 3: Collect your data
•
Step 4: Compute your test statistics
•
Step 5: Make a decision about your
null hypothesis
zX =
X - mX
sX
=
H0: μTreatment > μpop = 60
HA: μTreatment < μpop = 60
One -tailed
 = 0.05
n = 16, X = 55
55 - 60
æ8
ö
ç
÷
è 16 ø
= -2.5
Performing your statistical test
Reasoning in Psychology
Using Statistics
•
•
H0: μTreatment > μpop = 60
HA: μTreatment < μpop = 60
Dr. Mnemonic develops a new treatment for patients
with a memory disorder. He hypothesizes that the
treatment will improve memory performance. To test it
he collects a sample of 16 patients and gives them his
new treatment. Following the treatment he gives them
a standard memory test. His sample averaged 55 errors
(while the typical memory patient averages 60 errors,
with a σ = 8). Test using α = 0.05.
Step 1: State your hypotheses
•
Step 2: Set your decision criteria
•
Step 3: Collect your data
•
Step 4: Compute your test statistics
•
Step 5: Make a decision about your
null hypothesis
zX =
X - mX
sX
=
One -tailed
 = 0.05
n = 16, X = 55
55 - 60
æ8
ö
ç
÷
è 16 ø
= -2.5
5%
Reject H0
- Support for our HA, the
evidence suggests that the
treatment decreases the
number of memory errors
Performing your statistical test
Reasoning in Psychology
Using Statistics
If time allows:
The following pages give examples of situations that require
different statistical tests.
Performing your statistical test
Reasoning in Psychology
Using Statistics
•
Dr. Mnemonic develops a new treatment for patients
with a memory disorder. He isn’t certain what impact,
if any, it will have. To test it he collects a sample of 25
patients and gives them his new treatment. Following
the treatment he gives them a standard memory test.
His sample averaged 55 errors, with a s = 8 (while the
typical memory patient averages 60 errors).
Memory
patients
Memory
treatment
Memory
Test
X
Population of
memory patients
MemoryTest
 is NOT known
 is known
Compare these
two means
Hypotheses:
H0: • the memory treatment sample are the same as those in the population
of memory patients.
HA: • they aren’t the same as those in the population of memory patients
Performing your statistical test
Reasoning in Psychology
Using Statistics
•
Dr. Mnemonic develops a new treatment for patients
with a memory disorder. He isn’t certain what impact,
if any, it will have. To test it he collects a sample of 25
patients and gives them his new treatment. Following
the treatment he gives them a standard memory test.
His sample averaged 55 errors, with a s = 8 (while the
typical memory patient averages 60 errors).
Memory
patients
Memory
treatment
Memory
Test
X
– 1 sample
Population of
memory patients
MemoryTest
 is NOT known
 is known
Compare these
two means
Hypotheses:
H0: • the memory treatment sample are the same as those in the population
of memory patients.
HA: • they aren’t the same as those in the population of memory patients
Performing your statistical test
Reasoning in Psychology
Using Statistics
•
Dr. Mnemonic develops a new treatment for patients
with a memory disorder. He isn’t certain what impact,
if any, it will have. To test it he collects a sample of 25
patients and gives them his new treatment. Following
the treatment he gives them a standard memory test.
His sample averaged 55 errors, with a s = 8 (while the
typical memory patient averages 60 errors).
Memory
patients
Memory
treatment
Memory
Test
X
– 1 sample
– One score per subject
Population of
memory patients
MemoryTest
 is NOT known
 is known
Compare these
two means
Hypotheses:
H0: • the memory treatment sample are the same as those in the population
of memory patients.
HA: • they aren’t the same as those in the population of memory patients
Performing your statistical test
Reasoning in Psychology
Using Statistics
•
Dr. Mnemonic develops a new treatment for patients
with a memory disorder. He isn’t certain what impact,
if any, it will have. To test it he collects a sample of 25
patients and gives them his new treatment. Following
the treatment he gives them a standard memory test.
His sample averaged 55 errors, with a s = 8 (while the
typical memory patient averages 60 errors).
Memory
patients
Memory
treatment
Memory
Test
X
– 1 sample
– One score per subject
– Population mean (μ) is
known
Population of
memory patients
MemoryTest
 is NOT known
 is known
Compare these
two means
Hypotheses:
H0: • the memory treatment sample are the same as those in the population
of memory patients.
HA: • they aren’t the same as those in the population of memory patients
Performing your statistical test
Reasoning in Psychology
Using Statistics
•
Dr. Mnemonic develops a new treatment for patients
with a memory disorder. He isn’t certain what impact,
if any, it will have. To test it he collects a sample of 25
patients and gives them his new treatment. Following
the treatment he gives them a standard memory test.
His sample averaged 55 errors, with a s = 8 (while the
typical memory patient averages 60 errors).
Memory
patients
Memory
treatment
Memory
Test
X
– 1 sample
– One score per subject
– Population mean (μ) is
known
– Population standard
deviation () is NOT known
Population of
memory patients
MemoryTest
 is NOT known
 is known
Compare these
two means
Hypotheses:
H0: • the memory treatment sample are the same as those in the population
of memory patients.
HA: • they aren’t the same as those in the population of memory patients
Performing your statistical test
Reasoning in Psychology
Using Statistics
• The single sample t-test
can be used when:
– 1 sample
– One score per subject
X - mX
t=
sX
– Population mean ()
is known
– Population standard
deviation () is NOT
known
Which test do we use?
Reasoning in Psychology
Using Statistics
•
Dr. Mnemonic develops a new treatment for patients
with a memory disorder. He isn’t certain what impact,
if any, it will have. To test it he collects a sample of 25
patients and gives them his new treatment. Before the
treatment he gives them a pre-treatment memory test
and after the treatment a post-treatment memory test.
His sample averaged 60 errors before the treatment and
55 errors after the treatment.
Pre-test
Memory
patients
Memory
Test
X
Post-test
Memory
treatment
Memory
Test
X
Compare these
Hypotheses:
two means
H0: Memory performance at the post-test is equal to memory performance
at the pre-test.
HA: Memory performance at the post-test is NOT equal to memory performance
at the pre-test
Performing your statistical test
Reasoning in Psychology
Using Statistics
•
Dr. Mnemonic develops a new treatment for patients
with a memory disorder. He isn’t certain what impact,
if any, it will have. To test it he collects a sample of 25
patients and gives them his new treatment. Before the
treatment he gives them a pre-treatment memory test
and after the treatment a post-treatment memory test.
His sample averaged 60 errors before the treatment and
55 errors after the treatment.
Pre-test
Memory
patients
Memory
Test
X
– 1 sample
Post-test
Memory
treatment
Memory
Test
X
Compare these
Hypotheses:
two means
H0: Memory performance at the post-test is equal to memory performance
at the pre-test.
HA: Memory performance at the post-test is NOT equal to memory performance
at the pre-test
Performing your statistical test
Reasoning in Psychology
Using Statistics
•
Dr. Mnemonic develops a new treatment for patients
with a memory disorder. He isn’t certain what impact,
if any, it will have. To test it he collects a sample of 25
patients and gives them his new treatment. Before the
treatment he gives them a pre-treatment memory test
and after the treatment a post-treatment memory test.
His sample averaged 60 errors before the treatment and
55 errors after the treatment.
Pre-test
Memory
patients
Memory
Test
X
– 1 sample
– Two scores per
subject
Post-test
Memory
treatment
Memory
Test
X
Compare these
Hypotheses:
two means
H0: Memory performance at the post-test is equal to memory performance
at the pre-test.
HA: Memory performance at the post-test is NOT equal to memory performance
at the pre-test
Performing your statistical test
Reasoning in Psychology
Using Statistics
• The related sample ttest can be used when:
– 1 sample
– Two scores per
subject
D - mD
t=
sD
Which test do we use?
Reasoning in Psychology
Using Statistics
•
Dr. Mnemonic develops a new treatment for patients with a memory disorder.
He isn’t certain what impact, if any, it will have. To test it he collects a sample
of 25 patients and matches them to a sample of similar individuals. He then
gives them one sample the new treatment (but not the other). Following the
treatment period he gives both groups a memory test. His treatment sample
averaged 55 errors after the treatment and his matched sample averaged 60
errors over the same time period.
No Memory
treatment
Memory
patients
related
Memory
treatment
On a pair-by-pair basis
every person in the No
Treatment group is
related to or matched to
a person in the Memory
Treatment group
Performing your statistical test
Reasoning in Psychology
Using Statistics
•
Dr. Mnemonic develops a new treatment for patients with a memory disorder.
He isn’t certain what impact, if any, it will have. To test it he collects a sample
of 25 patients and matches them to a sample of similar individuals. He then
gives them one sample the new treatment (but not the other). Following the
treatment period he gives both groups a memory test. His treatment sample
averaged 55 errors after the treatment and his matched sample averaged 60
errors over the same time period.
No Memory
treatment
Memory
patients
Memory
Test
X
related
Memory
treatment
Memory
Test
X
Compare these
two means
Hypotheses:
H0: Memory performance by the treatment group is equal to memory
performance by the no treatment group.
HA: Memory performance by the treatment group is NOT equal to memory
performance by the no treatment group.
Performing your statistical test
Reasoning in Psychology
Using Statistics
•
Dr. Mnemonic develops a new treatment for patients with a memory disorder.
He isn’t certain what impact, if any, it will have. To test it he collects a sample
of 25 patients and matches them to a sample of similar individuals. He then
– 2 samples
gives them one sample the new treatment (but not the other). Following the
treatment period he gives both groups a memory test. His treatment sample
averaged 55 errors after the treatment and his matched sample averaged 60
errors over the same time period.
No Memory
treatment
Memory
patients
Memory
Test
X
related
Memory
treatment
Memory
Test
X
Compare these
two means
Hypotheses:
H0: Memory performance by the treatment group is equal to memory
performance by the no treatment group.
HA: Memory performance by the treatment group is NOT equal to memory
performance by the no treatment group.
Performing your statistical test
Reasoning in Psychology
Using Statistics
•
Dr. Mnemonic develops a new treatment for patients with a memory disorder.
He isn’t certain what impact, if any, it will have. To test it he collects a sample
of 25 patients and matches them to a sample of similar individuals. He then
– 2 samples
gives them one sample the new treatment (but not the other). Following the
treatment period he gives both groups a memory test. His treatment sample
– Samples are
averaged 55 errors after the treatment and his matched sample averaged 60
matched with
errors over the same time period.
one score per
No Memory
treatment
Memory
patients
Memory
Test
X
related
Memory
treatment
Memory
Test
X
subject
Compare these
two means
Hypotheses:
H0: Memory performance by the treatment group is equal to memory
performance by the no treatment group.
HA: Memory performance by the treatment group is NOT equal to memory
performance by the no treatment group.
Performing your statistical test
Reasoning in Psychology
Using Statistics
• The related sample ttest can be used when:
– 2 samples
– Samples are matched
with one score per
subject
D - mD
t=
sD
Which test do we use?
Reasoning in Psychology
Using Statistics
•
Dr. Mnemonic develops a new treatment for patients with a memory disorder.
He isn’t certain what impact, if any, it will have. To test it he randomly assigns
50 patients to one of two samples. He then gives one sample the new treatment
but not the other. Following the treatment period he gives both groups a
memory test. His treatment sample averaged 55 errors after the treatment and
his control sample averaged 60 errors over the same time period.
No Memory
treatment
Memory
patients
Memory
treatment
Memory
Test
X
Memory
Test
X
Compare these
two means
Hypotheses:
H0: Memory performance by the treatment group is equal to memory
performance by the no treatment group.
HA: Memory performance by the treatment group is NOT equal to memory
performance by the no treatment group.
Performing your statistical test
Reasoning in Psychology
Using Statistics
•
Dr. Mnemonic develops a new treatment for patients with a memory disorder.
He isn’t certain what impact, if any, it will have. To test it he randomly assigns
50 patients to one of two samples. He then gives one sample the new treatment
but not the other. Following the treatment period he gives both groups a
– 2 samples
memory test. His treatment sample averaged 55 errors after the treatment and
his control sample averaged 60 errors over the same time period.
No Memory
treatment
Memory
patients
Memory
treatment
Memory
Test
X
Memory
Test
X
Compare these
two means
Hypotheses:
H0: Memory performance by the treatment group is equal to memory
performance by the no treatment group.
HA: Memory performance by the treatment group is NOT equal to memory
performance by the no treatment group.
Performing your statistical test
Reasoning in Psychology
Using Statistics
•
Dr. Mnemonic develops a new treatment for patients with a memory disorder.
He isn’t certain what impact, if any, it will have. To test it he randomly assigns
50 patients to one of two samples. He then gives one sample the new treatment
but not the other. Following the treatment period he gives both groups a
– 2 samples
memory test. His treatment sample averaged 55 errors after the treatment and
– Samples are
his control sample averaged 60 errors over the same time period.
independent
No Memory
treatment
Memory
patients
Memory
treatment
Memory
Test
X
Memory
Test
X
Compare these
two means
Hypotheses:
H0: Memory performance by the treatment group is equal to memory
performance by the no treatment group.
HA: Memory performance by the treatment group is NOT equal to memory
performance by the no treatment group.
Performing your statistical test
Reasoning in Psychology
Using Statistics
•
Dr. Mnemonic develops a new treatment for patients with a memory disorder.
He isn’t certain what impact, if any, it will have. To test it he randomly assigns
50 patients to one of two samples. He then gives one sample the new treatment
but not the other. Following the treatment period he gives both groups a
– 2 samples
memory test. His treatment sample averaged 55 errors after the treatment and
– Samples are
his control sample averaged 60 errors over the same time period.
No Memory
treatment
Memory
patients
Memory
treatment
Memory
Test
X
Memory
Test
X
independent
– One score per
subject
Compare these
two means
Hypotheses:
H0: Memory performance by the treatment group is equal to memory
performance by the no treatment group.
HA: Memory performance by the treatment group is NOT equal to memory
performance by the no treatment group.
Performing your statistical test
Reasoning in Psychology
Using Statistics
• The independent sample ttest can be used when:
– 2 samples
– Samples are independent
(X A - X B ) - (mA - mB )
t=
sX A -X B
– One score per subject
Which test do we use?
Reasoning in Psychology
Using Statistics
• In lab
– Make hypotheses (both null & alternative)
– Test hypotheses using 1-sample z-test
• Questions?
Wrap up
Reasoning in Psychology
Using Statistics