Statistics for the Social SciencesPsychology 340

Spring 2010

Introductions &

Review of some basic research methods

PSY 340Statistics for the

Social Sciences This course

• How is this course different from PSY 138?– Format: Longer lectures, but no separate lab times– Content: review of PSY 138 and beyond

(remember the “beyond 138” in the decision tree)• Dealing with more complex situations (more than 2

variables)• Hypothesis testing with:

– Correlation and regression

– Multiple regression

– Tests for differences with more than two groups

PSY 340Statistics for the

Social Sciences PSY 138

PSY 340Statistics for the

Social Sciences

This course

PSY 340Statistics for the

Social Sciences Course Format

• Syllabus: Blackboard – try logging in now

• Lectures - will take up most of class time

• Homework (30%) - practice items, ARE collected for credit (typically due Tuesdays)

• Exams (50%)– three cumulative mid-semester exams (10% each)– 1 final exam (20%)

• Quizzes (5%) - on-line Blackboard quizzes, based primarily on textbook readings (typically due Thurs)

• Final project (15%) – large data set, multiple analyses, write up a “results” section

• Labs – additional practice items, NOT collected for credit– Two parts:

• By hand step-by-step example(s)• Large SPSS dataset practice question(s)

PSY 340Statistics 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 research methods (like 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)

PSY 340Statistics 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

PSY 340Statistics for the

Social SciencesStatistical 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

PSY 340Statistics 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.)

PSY 340Statistics 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

PSY 340Statistics 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?

PSY 340Statistics 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.

PSY 340Statistics 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 • Different study

times, different study methods, etc.

Variability in Test Performance

PSY 340Statistics 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

PSY 340Statistics for the

Social Sciences Weight analogy

• Imagine the different sources of variability as weights

RNRexp

NRother

RNRother

Treatment group control group

PSY 340Statistics 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

PSY 340Statistics 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

PSY 340Statistics for the

Social SciencesLogic 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

PSY 340Statistics 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

PSY 340Statistics 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

PSY 340Statistics 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

PSY 340Statistics 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)

PSY 340Statistics for the

Social Sciences

Statistical analysis follows design

Statistical analysis follows from the design of a study

The next question in the tree

PSY 340Statistics 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

PSY 340Statistics 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

PSY 340Statistics 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

PSY 340Statistics for the

Social Sciences

Statistical analysis follows design

Statistical analysis follows from the design of a study

Next question in the tree

PSY 340Statistics for the

Social SciencesStatistical 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”

PSY 340Statistics 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)?

PSY 340Statistics 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)?

PSY 340Statistics 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)?

PSY 340Statistics 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)?

PSY 340Statistics 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)?