Transcript Social Science Reasoning Using Statistics

Reasoning in Psychology
Using Statistics
Psychology 138
Spring 2015
• Exam 1 on Wednesday
– In lecture: closed book, scantron
– In labs: open book, open notes
Annoucements
Reasoning in Psychology
Using Statistics
Population
Sampling to
make data
collection
manageable
Inferential
statistics to
generalize
back
Sample
Sampling
Reasoning in Psychology
Using Statistics
Where does “probability”
fit in?
• Randomness in
sampling leads to
variability in sampling
error
• “Randomness” in short
run is unpredictable but
in long run is
predictable
• Allows predictions
about likelihood of
getting particular
samples
Population
Possible Samples
• Examples: Odds in games of chance
Inferential statistics
Reasoning in Psychology
Using Statistics
What are the odds of being
dealt a “Royal Flush”?
Prob. of A = p(A) =
p(Royal Flush) =
Total number of outcomes classified as A
Total number of possible outcomes
4
= 0.000001539
2,598,960
~1.5 hands out of every million hands
Odds in Poker
Reasoning in Psychology
Using Statistics
What are the odds of being
dealt a “Straight Flush”?
Prob. of A = p(A) =
p(straightflush) =
Total number of outcomes classified as A
Total number of possible outcomes
40
= 0.00001539
2,598,960
~15 hands out of every million hands
Odds in Poker
Reasoning in Psychology
Using Statistics
What are the odds of being
dealt a …?
Prob. of A = p(A) =
Total number of outcomes classified as A
Total number of possible outcomes
Odds in Poker
Reasoning in Psychology
Using Statistics
• Draw lettered tiles from bag
– Bag contains:
• A’s B’s and C’s.
• Both upper and lower case letters
b
c
a
A
• What’s the probability of getting an A
(upper or lower case)?
Prob. of A = p(A) =
Total number of outcomes classified as A
Total number of possible outcomes
Sample space
Basics of probability:
Derived from games with all outcomes known
Reasoning in Psychology
Using Statistics
C
B
= 2/6 = 0.33
• What’s the probability of getting an A (upper or lower
case) on the first pick and another on a second pick?
First Pick: Prob. of A = p(A) = 2/6 = 0.33
a
A
1/6
+
b
c
a
A
C
B
2/6
1/6
Second Pick: ? – it depends on how you sample
Sampling with replacement
b
c
a
A
2/6
b
C
B
Sampling without replacement
c
a
b
C
B
1/5
Basics of probability
Reasoning in Psychology
Using Statistics
c
C
A
B
1/5
The
probabilities
of selecting
the titles
change from
1st to 2nd
pick
b
• What’s the probability of getting an A (upper or lower
case) on the first pick and another on a second pick?
a
A
Sampling with replacement
Sampling without replacement
1st picks
1st picks
2nd picks
2nd picks
a
a
A
b
B
c
C
a
A
a
A
b
B
c
C
A
a
b
a
A
b
B
c
C
b
a
A
B
a
A
b
B
c
C
B
a
A
b
c
a
A
b
B
c
C
c
a
A
b
B
C
a
A
b
B
c
C
C
a
A
b
B
A
b
B
c
C
b
B
c
C
B
c
C
c
C
C
c
36 total outcomes
4 outcomes of 2 A’s
30 total outcomes
2 outcomes of 2 A’s
4/36 = 0.11
(2/6)*(2/6) = 0.11
2/30 = 0.06666
(2/6)*(1/5) = 0.0666
1st pick
2nd pick
1st pick
Basics of probability
Reasoning in Psychology
Using Statistics
2nd pick
c
C
B
• Most statistical procedures assume sampling with
replacement
• For large populations it turns out not to matter much
•
e.g., suppose your population is N=1,000,000. Starting
probability of selecting a particular item 1 in 1,000,000.
• Sampling with replacement, odds stay at 1 in 1,000,000
• Sampling without replacement, odds change to 1 in 999,999
the change is so small that it may not matter
• In experiments, you typically don’t want to use sampling with
replacement because of the potential for lasting effects of your
independent variable
Basics of probability
Reasoning in Psychology
Using Statistics
• Scientific method
• Research methods
– Observation methods
– Experimental methods
– Quasi-experimental
• Variables
– Types
– Operational definitions
• Sampling
– Samples and populations
– Statistics and parameters
– Techniques
• Measurements
– Continuous and discrete
– Scales of measurement
– Instrument
• Errors in Measurement
– Validity & Reliability
– Confounds
– Bias
• Reliability
• Experimental control
• Basic probability
Reviewing Producing Data
Reasoning in Psychology
Using Statistics
The researchers used a questionnaire to interview a random sample
of 351 people ages 20 to 80 in the Vancouver, British Columbia, area,
asking about their dog ownership and level of physical activity.
Dog owners walked almost twice as many minutes per week as
people who did not own dogs, and the dog owners spent more time in all
forms of mild and moderate physical activity.
People who own dogs
appear to get more exercise
than those who do not …
Neither the sex of the owner nor the size of the dog made a
difference: men and women who owned dogs participated in increased
amounts of moderate exercise compared with those who had no dog. But
no statistically significant difference between the two groups was
evident in the amount of strenuous exercise performed.
The authors concede that the study, published in the February issue
of The American Journal of Preventive Medicine, does not determine
whether owning a dog itself makes people exercise more.
Shane Brown, the study's lead author and a graduate student at the
Behavioral Medicine Laboratory of the University of Victoria, called this
"the million-dollar question."
When the researchers subtracted the time spent walking the dog
from total physical activity, dog owners actually walked less than their
counterparts without dogs.
This, the researchers say, may suggest that the dog makes the
difference. When dog owners choose to engage in moderate physical
exercise, the reason may be that a four-legged member of the household
is insisting on a walk. Now.
Report (NY Times 2006): dog a more reliable exercise partner than a human.
In the news
Reasoning in Psychology
Using Statistics
Background
Dog ownership may be an effective tailored
intervention among adults for promoting physical
activity. This study examined the relationship
between walking, physical activity levels, and
potential psychological mediators between people
who owned dogs and those who did not own dogs
in the Capital Region District of Greater Victoria,
British Columbia, Canada. Data were collected in
September 2004; analyses were conducted in
January 2005.
Methods
A random sample of men (n=177) and women
(n=174) aged 20 to 80 years participated.
Questionnaires were mailed out in 2004 to collect
information about demographics, dog ownership,
leisure-time walking, physical activity levels, and
theory of planned behavior (TPB) constructs.
Results
The analyses revealed that dog owners spent more time in
mild and moderate physical activities and walked an average
of 300 minutes per week compared to non–dog owners who
walked an average of 168 minutes per week. A mediator
analysis suggests that dog obligation acts as a mediator
between dog ownership and physical activity. Moreover, the
theory of planned behavior constructs of intention and
perceived behavioral control explained 13% of the variance in
walking behavior with an additional 11% variance in walking
behavior being explained by dog obligation. Regarding
intention to walk, the TPB explained 46% of the variance in
intention to walk with dog obligation adding an additional 1%
variance.
Conclusions
In this group of Canadians, those who owned a dog
participated in more mild to moderate physical activity than
those who did not. Acquiring a dog should be explored as an
intervention to get people more physically active.
Shane G. Brown, Bed. and Ryan E. Rhodes PhD
School of Physical Education, University of Victoria, Victoria, British Columbia, Canada
Available online 2 February 2006. American Journal of Preventive Medicine
In the research literature
Reasoning in Psychology
Using Statistics
• Research process
Regimens: Pounding the
Pavement, Stopping at
Fire Hydrants
People who own dogs appear to get more
exercise than those who do not …
In the news
Reasoning in Psychology
Using Statistics
– Ask research question
– Identify variables &
formulate hypothesis
– Define population
– Select research methodology
– Collect data from a sample
– Analyze data
– Draw conclusions based on
data
– Repeat
Regimens: Pounding the
Pavement, Stopping at
Fire Hydrants
People who own dogs appear to get more
exercise than those who do not …
In the news
Reasoning in Psychology
Using Statistics
– Ask research question
– Identify variables &
formulate hypothesis
– Define population
– Select research methodology
– Collect data from a sample
– Analyze data
– Draw conclusions based on
data
– Repeat
Context for our numbers
• Research process
• Research process
Regimens: Pounding the
Pavement, Stopping at
Fire Hydrants
People who own dogs appear to get more
exercise than those who do not …
In the news
Reasoning in Psychology
Using Statistics
– Ask research question
– Identify variables &
formulate hypothesis
– Define population
– Select research methodology
– Collect data from a sample
– Analyze data
– Draw conclusions based on
data
– Repeat
• Research process
Variables
– Ask research question
– Operational level
Regimens:
– Identify variables &
– Conceptual
level Pounding the
formulate hypothesis
Pavement, Stopping at
Fire Hydrants
– Define your population
Variables
– Select a research
The researchers …, asking about their dog
–
Independent
(explanatory) variables
ownership and level of physical activity.
methodology
– Dependent (response) variable
Methods
– Collect your data from a
–
Control
variables
…. Questionnaires were mailed out in 2004 to
sample
collect information about demographics, dog
– Random
variables
– Analyze
your data
ownership, leisure-time walking, physical
– Confound
variables
activity levels, and theory of planned behavior
–
Draw
conclusions based on
(TPB) constructs.
your data
– Repeat
In the news
Reasoning in Psychology
Using Statistics
• Research process
– Ask research question
Regimens: Pounding the
– Identify variables &
formulate hypothesis
Pavement, Stopping at
Instrument used?
Fire Hydrants
– Define your population
Scales of measurement
– Select a- research
The researchers …, asking about their dog
men & women, own dog or not
–
Nominal
ownership and level of physical activity.
methodology
- mild, strenuous
– –Ordinal
Methods
Collect your data from a
…. Questionnaires were mailed out in 2004 to
– Interval
sample
collect information about demographics, dog
- time spent exercising
– –Ratio
Analyze
your data
ownership, leisure-time walking, physical
activity levels, and theory of planned behavior
– Draw conclusions based on
(TPB) constructs.
data
– Repeat
In the news
Reasoning in Psychology
Using Statistics
• Research process
– Ask the research question
Is the sample representative?
Regimens: Pounding the
– Identify variables &
Is there
Pavement, Stopping
at bias in sample?formulate hypothesis
Fire Hydrants
– Define population
The researchers used a questionnaire to
– Select research methodology
interview a random sample of 351 people ages
– Collect data from sample
20 to 80 in the Vancouver, British Columbia,
– Analyze data
area, (i.e., mailed out questionnaires)
– Draw conclusions based on
data
Was it simple random sampling?
Stratified random sampling?
– Repeat
Etc.?
In the news
Reasoning in Psychology
Using Statistics
• Research process
– Ask research question
Regimens: Pounding the
– Identify variables &
formulate hypothesis
Pavement,Causal
Stopping
at
Claims??
Fire Hydrants
– Define population
The researchers used a questionnaire to
– Select research methodology
interview a random sample of 351 people ages
– Collect data from sample
20 to 80 in the Vancouver, British Columbia,
– Research
Analyze your
data
Which
Method??
area,
The authors concede that the study… does
Draw conclusions
– –Observational
studybased on
not determine whether owning a dog itself
your data
– Experimental methodology
makes people exercise more.
– Repeat
This may suggest that .. when dog owners
– Quasi-experimental
choose to engage in moderate physical
methodology
exercise, the reason may be that [the dog] is
insisting on a walk.
Gather 2 pieces of data for each person: dog ownership, exercise
In the news
Reasoning in Psychology
Using Statistics
• Research process
– Ask research question
Regimens: Pounding the
– Identify variables &
formulate hypothesis
Pavement, Stopping at
Fire Hydrants
– Define population
– Select research methodology
Possible confounds?
– Collect data from sample
Threats to internal validity?
– Analyze your data
If follow-up experiment were
– Draw conclusions based on
designed,
yourwhat
data would you do?
– Repeat
In the news
Reasoning in Psychology
Using Statistics
• Scientific method
• Research methods
– Observation methods
– Experimental methods
– Quasi-experimental
• Variables
– Types
– Operational definitions
• Sampling
– Samples and populations
– Statistics and parameters
– Techniques
• Measurements
– Continuous and discrete
– Scales of measurement
– Instrument
• Errors in Measurement
– Validity & Reliability
– Confounds
– Bias
• Reliability
• Experimental control
• Basic probability
Reviewing Producing Data
Reasoning in Psychology
Using Statistics