statistics for the social sciences psychology 340 spring 2005 statistics & research methods
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Statistics for the Social SciencesPsychology 340
Spring 2005
Statistics & Research Methods
Statistics for the Social Sciences
Variability is key
• A the heart of research methodology and statistics is variability– Variables - characteristics with values that aren’t
constant (across individuals, time, place, etc.)– We’re interested in explaining (predicting) the
variability of variables– We use experimental control to try to constrain
variability to make it easier to see how different variables affect each other
– We use statistical procedures to examine which variables vary together (and which don’t)
Statistics for the Social Sciences
Statistical analysis follows design
Statistical analysis follows from the design of a study
Our decision tree helps us ask the right design questions which will lead us to the appropriate statistical test
Statistics for the Social Sciences
Statistical analysis follows design
Vs.
Decide if there is a difference
Decide if there is a
relationship between variables
Observational studies
Experimental & Quasi-experimental studies
Testing for differences between groups (conditions)
Testing for similarities between variables
This is a generality, there are exceptions. Towards the end of the course we’ll see that the two may be considered essentially the same kinds of analyses
Statistics for the Social Sciences
Basic Research Methods
• Observational study– Researcher observes and measures variables of interest to find
relationships between the variables– No attempt is made to manipulate or influence responses
• Experimental methodology– One (or more) independent variable(s) is manipulated while
changes are observed in another variable (dependent)– Used to establish cause-and-effect relationships between variables– Uses extensive methods of control to minimize extraneous sources
of variability
• Quasi-experimental methodology– One (or more) of the independent variables is a pre-existing
characteristic (e.g., sex, age, etc.)
Statistics for the Social Sciences
Different basic methods
• Experimental versus Observational methods– Experiments involve manipulation of variables
– Observational methods involve examining things as they already are
Statistics for the Social Sciences
Observational Experimental
Example
– Randomly select individuals
– Watch their study habits
– See how they do on a test
– Randomly select individuals
– Randomly assign to groups
• Crammed study group
• Distributed study group
– See how they do on a test
• Issue: What’s the best way to study for a test?
Statistics for the Social Sciences
Experimental Control
• Our goal: – to test the possibility of a relationship between the
variability in our IV and how that affects our DV.
– Control is used to minimize excessive variability.– To reduce the potential of confounds.
Statistics for the Social Sciences
Imprecision in
manipulation (IV)
& measurement (DV)
& random varying
extraneous variables
Imprecision in
manipulation (IV)
& measurement (DV)
& random varying
extraneous variables
Logic of experimental control
• Sources of Total (T) Variability:
T = NonRandomexp + NonRandomother + Random
variables which covary with IV (condfounds)
variables which covary with IV (condfounds)
Manipulatedindependent variables (IV)
Manipulatedindependent variables (IV)
• Study method:– Crammed– Distributed
• Distributed studiers never get to practice problmems
Variability in Test Performance
• Different study times, different study methods, etc.
Statistics for the Social Sciences
Logic of experimental control
• Experimental procedures are used to reduce R and NRother so that we can detect NRexp.
• That is, so we can see the changes in the DV that are due to the changes in the independent variable(s).
• Sources of Total (T) Variability:
T = NonRandomexp + NonRandomother + Random
Constrain variability by carefully levels of IV
Eliminate counfounds
Use good measures
Statistics for the Social Sciences
Weight analogy
• Imagine the different sources of variability as weights
RNRexp
NRother
RNRother
Treatment group control group
Statistics for the Social Sciences
Weight analogy
• If NRother and R are large relative to NRexp then detecting a difference may be difficult
RNRexp
NRother
RNRother
Statistics for the Social Sciences
Weight analogy
• But if we reduce the size of NRother and R relative to NRexp then detecting gets easier
RNRother
RNRexpNR
other
Statistics for the Social Sciences
Logic of observational approaches
Suppose that you wish to predict exam performance using an observational method
• Sources of Total (T) Variability:
Variables that don’t
covary with test
performance
Variables that don’t
covary with test
performance
Variables that do
covary with test
performance
Variables that do
covary with test
performance
Observe and record variables, but don’t know which group they’ll fit into
T = NonRandomother + Random
Total study time
Study topic Test time
Breakfast food
Hours of sleep
That’s what we’ll use statistics to find out
Statistics for the Social Sciences
Logic of observational approaches
Total variability it test performance
Unexplained variance 64%
Total study timer = .6
Some co-variance between the two variables• If we know the total study time, we can predict 36%
of the variance in test performance
Statistics for the Social Sciences
Logic of observational approaches
Total variability it test performance
Unexplained variance 51%
Test timer = .1
Total study timer = .6
A little co-variance between these test performance and test time• If we add it to study time, then we can explain more the of
variance in test performance
Statistics for the Social Sciences
Logic of observational approaches
Total variability it test performance
Unexplained variance 51%
breakfastr = .0
Test timer = .1
Total study timer = .6
No co-variance between these test performance and breakfast food• If we add it to the other two, then we can NOT explain more the
of variance in test performance
Statistics for the Social Sciences
Logic of observational approaches
Total variability it test performance
Unexplained variance 40%
Test timer = .1
Total study timer = .6
breakfastr = .0
Hrs of sleepr = .45
Some co-variance between these test performance and hours of sleep• If we add it to study time, then we can explain more the of variance
in test performance (but notice what happens with the overlap)
Statistics for the Social Sciences
Statistical analysis follows design
Statistical analysis follows from the design of a study
The next question in the tree
Statistics for the Social Sciences
Statistical analysis follows design
Decide if there is a difference
How many separate samples?
1
Testing for a difference between a sample and a known population value
Or within-groups designs
Testing for a difference between two samples
Various “t-tests”
2
>2
Testing for a difference between two samples
Various “ANOVA” designs
Statistics for the Social Sciences
What are samples?
• Who do we test?– Population
• The set of all individuals of interest
– Sample• A subset of the population from whom data is collected
• Typically we don’t have access to all of the population
We test these folks and then generalize the results to the population as a whole
Statistics for the Social Sciences
What are samples?
– “Sample”• may also be used to refer to the participants (randomly) assigned to a particular condition of the experiment
condition A
condition B condition C
condition D
Statistics for the Social Sciences
Statistical analysis follows design
Statistical analysis follows from the design of a study
Next question in the tree
Statistics for the Social Sciences
Statistical analysis follows design
… Are the samples
related or independent?
related
There is a pre-existing relationship between the groups – “non-independent groups”– “matched samples”
Or the same subjects participate in multiple conditions– “within-groups”– “repeated-measures”
independent There is no pre-existing relationship between the groups
“between-groups”
Statistics for the Social Sciences
Example
Dr. Charles investigated the
impact of three types of
video taped teaching programs
for two types of subjects (math
and Spanish). 12 participants
were randomly assigned to one
type of teaching program and
one subject. After two weeks
of training Dr. Charles assessed
their learning. What test should
he use to analyze his data (which
program works best for which
subject)?
Dr. Charles investigated the
impact of three types of
video taped teaching programs
for two types of subjects (math
and Spanish). 12 participants
were randomly assigned to one
type of teaching program and
one subject. After two weeks
of training Dr. Charles assessed
their learning. What test should
he use to analyze his data (which
program works best for which
subject)?
Statistics for the Social Sciences
Example
Dr. Charles investigated the
impact of three types of
video taped teaching programs
for two types of subjects (math
and Spanish). 12 participants
were randomly assigned to one
type of teaching program and
one subject. After two weeks
of training Dr. Charles assessed
their learning. What test should
he use to analyze his data (which
program works best for which
subject)?
Dr. Charles investigated the
impact of three types of
video taped teaching programs
for two types of subjects (math
and Spanish). 12 participants
were randomly assigned to one
type of teaching program and
one subject. After two weeks
of training Dr. Charles assessed
their learning. What test should
he use to analyze his data (which
program works best for which
subject)?
Statistics for the Social Sciences
Example
Dr. Charles investigated the
impact of three types of
video taped teaching programs
for two types of subjects (math
and Spanish). 12 participants
were randomly assigned to one
type of teaching program and
one subject. After two weeks
of training Dr. Charles assessed
their learning. What test should
he use to analyze his data (which
program works best for which
subject)?
Dr. Charles investigated the
impact of three types of
video taped teaching programs
for two types of subjects (math
and Spanish). 12 participants
were randomly assigned to one
type of teaching program and
one subject. After two weeks
of training Dr. Charles assessed
their learning. What test should
he use to analyze his data (which
program works best for which
subject)?
Statistics for the Social Sciences
Example
Dr. Charles investigated the
impact of three types of
video taped teaching programs
for two types of subjects (math
and Spanish). 12 participants
were randomly assigned to one
type of teaching program and
one subject. After two weeks
of training Dr. Charles assessed
their learning. What test should
he use to analyze his data (which
program works best for which
subject)?
Dr. Charles investigated the
impact of three types of
video taped teaching programs
for two types of subjects (math
and Spanish). 12 participants
were randomly assigned to one
type of teaching program and
one subject. After two weeks
of training Dr. Charles assessed
their learning. What test should
he use to analyze his data (which
program works best for which
subject)?
Statistics for the Social Sciences
Example
Dr. Charles investigated the
impact of three types of
video taped teaching programs
for two types of subjects (math
and Spanish). 12 participants
were randomly assigned to one
type of teaching program and
one subject. After two weeks
of training Dr. Charles assessed
their learning. What test should
he use to analyze his data (which
program works best for which
subject)?
Dr. Charles investigated the
impact of three types of
video taped teaching programs
for two types of subjects (math
and Spanish). 12 participants
were randomly assigned to one
type of teaching program and
one subject. After two weeks
of training Dr. Charles assessed
their learning. What test should
he use to analyze his data (which
program works best for which
subject)?
Statistics for the Social Sciences
Using SPSS
• The design of a study also has an impact on how you need to set up your SPSS data file
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Brief review of SPSS
Two view windows:
Data view
This is where you type in all of the data
To switch between the views click on the tabs
Statistics for the Social Sciences
Brief review of SPSS
Two view windows:
Variable view
This is where you specify the details about the variables
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Variable view
Name of the variable, limited to 8 characters
Type of variable: numeric, text, monetary, date, etc.
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The Data View
Each row corresponds to an experimental unit(called “cases” in SPSS lingo)
So each column in the data view corresponds to a row in the variable view
Each column corresponds to a variable
Statistics for the Social Sciences
In-class lab
• With the remaining time, go ahead and work through the lab– A few study descriptions, using the decision tree try to
determine the appropriate statistical test
– Download the “majors.sav” datafile and open it up in SPSS.