Transcript Slide 1

Research Methods for the
Social Sciences:
An Introductory Course
February 23rd, 2010 – Statistics
Sarah Nelson and Julia Braverman
Division on Addictions, Cambridge Health Alliance
Harvard Medical School
The Dissertation Effect – First
Year Project
19
17
15
13
11
9
7
5
3
1
Control
Intervention
M1
M2
M3
M4
The Dissertation Effect Dissertation
2.3
2.25
2.2
2.15
2.1
Control
Intervention
2.05
2
1.95
1.9
1.85
M1
M2
M3
M4
Overview

Descriptive statistics
– Central tendency
– Variability/Dispersion

Inferential statistics
– Hypothesis testing
– Test review
– Effect size and meta-analysis
Adapted from Dr. Braverman’s slides
Descriptive Statistics

Statistics used to summarize or describe
data
– Frequencies
 60% of public high school students say they have
plagiarized papers.
– Mean
 Men who are lost wait an average of 20 minutes
before giving up and asking for directions. Women
– 10 minutes.
– Range
 Romantic love involves chemical changes in the
brain that last 12 – 18 months. After that, you and
your partner are on your own.
Adapted from Dr. Braverman’s slides
Data

Central tendency
Mean
– ΣX/N
– 740/11
– Mean = 67.3
Class A.
60, 80, 90, 80, 75, 90,
95, 30,70, 80, 70

Mode
– Most frequent value
– 80
N = 11.

Median - Center
value when data is
arranged in order
30 60 70 70 75 80 80 80 90 90 95
Dr. Braverman’s slides
Data

Central tendency

– ΣX/N
– 740/11
– Mean = 67.3
Class A.
60, 80, 90, 80, 75, 90,
95, 30,70, 80, 70
Mean

Mode
– Most frequent value
– 80

Median - Center
value when data is
arranged in order
30 60 70 70 75 80 80 80 90 90 95
Dr. Braverman’s slides
Data

Central tendency

– ΣX/N
– 740/11
– Mean = 67.3
Class A.
60, 80, 90, 80, 75, 90,
95, 30,70, 80, 70
Mean

Mode
– Most frequent value
– 80

Median - Center
value when data is
arranged in order
30 60 70 70 75 80 80 80 90 90 95
Dr. Braverman’s slides
Data

Central tendency

– ΣX/N
– 740/11
– Mean = 67.3
Class A.
60, 80, 90, 80, 75, 90,
95, 30,70, 80, 70
Mean

Mode
– Most frequent value
– 80

Median - Center
value when data is
arranged in order
30 60 70 70 75 80 80 80 90 90 95
Dr. Braverman’s slides
Data

Central tendency

– ΣX/N
– 740/11
– Mean = 67.3
Class A.
60, 80, 90, 80, 75, 90,
95, 30,70, 80, 70
Mean

Mode
– Most frequent value
– 80

Median - Center
value when data is
arranged in order
30 60 70 70 75 80 80 80 90 90 95
Dr. Braverman’s slides
Data

Central tendency

– ΣX/N
– 740/11
– Mean = 67.3
Class A.
60, 80, 90, 80, 75, 90,
95, 30,70, 80, 70
Mean

Mode
– Most frequent value
– 80

Median - Center
value when data is
arranged in order
30 60 70 70 75 80 80 80 90 90 95
Dr. Braverman’s slides
Data

Central tendency

– ΣX/N
– 740/11
– Mean = 67.3
Class A.
60, 80, 90, 80, 75, 90,
95, 30,70, 80, 70
Mean

Mode
– Most frequent value
– 80

Median - Center
value when data is
arranged in order
– Median = 80.
30 60 70 70 75 80 80 80 90 90 95
Dr. Braverman’s slides
Mean and Median

Mean
– Reflects ALL values
Dr. Braverman’s slides

Median
– No extreme values
– Exactly 50% above
and below.
Variability
Range
 Standard deviation/dispersion

Dr. Braverman’s slides
Dispersion/standard deviation

Country A
–
–
–
–
–
–
–
15,000
20,000
50,000
60,000
80,000
90,000
100,000

Country B
–
–
–
–
–
–
–
40,000
40,000
50,000
60,000
70,000
70,000
80,000
Standard deviation –
Average distance of all scores from the average.
Dr. Braverman’s slides
Normal Distribution
f
r
e
q
u
e
n
c
y
Dr. Braverman’s slides
values
Normal Distribution
Symmetrical
 Mean = Mode = Median
 Bell-shaped
 Most scores cluster around the mean.

Dr. Braverman’s slides
The normal distribution
The area under the normal curve represents
100% of the scores
 A property of the normal curve is that
approx. 99% of scores fall within 3 standard
deviations of the mean

– Specifically
 ~34.13% within one SD in one direction
 ~68.26% within one SD
 ~95.44% within two SD
Dr. Braverman’s slides
Normal and z-scores
Dr. Braverman’s slides
Normal distribution of IQ
 = 100
  = 15
 Mode = 100
 Median = 100

Number of people
Frequency of IQ
30 40 50 60 70 80 90 100 110 120 130 140 150 160 170
IQ
Dr. Braverman’s slides
Central Tendency
Dr. Braverman’s slides
Inferential statistics

Drawing a conclusion about general
population based on a sample.
Dr. Braverman’s slides
A Quick Aside

Population computations:
– Often provided in text books for pedagogical reasons.
– Requires that you have every subject, i.e. you are not
making any inferences to a more general population
– Uses Greek letters:  

Sample computations:
– Often presented as computational formulas
– Allows one to make inferences to a more general
population
– Uses Arabic letters: M S X
– Uses degrees of freedom
Dr. Braverman’s slides
Hypothesis Testing

9 Step procedure
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–
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–
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State the hypotheses
Determine the nature of variables
Choose the appropriate test statistic
Set Type I error rates (alpha)
Determine your sample size
Collect data
Run appropriate statistical test
Calculate observed effect size
Make a decision and conclusions
Dr. Braverman’s slides
Hypotheses

Null hypothesis: H0
– States that nothing special is happening in
respect to some characteristic of the
underlying population

Alternative hypothesis H1
– The opposite of the null hypothesis, also
called the research hypothesis
Dr. Braverman’s slides
Example

Students participate in an SAT prep class
in English. The experimenter thinks that
this class will improve the students scored
compared to the national average of 500.
– Null: There will be no difference in the
performance of the participants in the prep
group. X- <= 0
– Alternative: Student in the prep group
perform better than the national average. X-
>0
Dr. Braverman’s slides
Rejecting Null hypothesis

With the given set of data, how likely (p)
is it that the null hypothesis is true?
α = .05/ .01/ .001 (Arbitrary setting)
If p < α
Reject H0

Dr. Braverman’s slides
Error
Type I error: Probability of rejecting a null
hypothesis when there is no effect
present. Alpha level, generally set to .05
 Type II error: Probability of retaining a
false null, i.e., missing an effect. Beta

– Power is the opposite of Beta and is the
probability of detecting a present effect.
Power is useful for determining a sample size
Dr. Braverman’s slides
Significance of significance

1.
2.
What significance does NOT mean..
The effect is IMPORTANT
The effect is LARGE
Dr. Braverman’s slides
Effect size
Effect size = (mean of experimental group mean of control group)/standard deviation
 Cohen’s d (can be bigger than 1)

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–
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Less than .1 trivial
.1-.3 small
.3-.5 moderate
Greater than .5 large
r - correlation coefficient
– <.2 - small
– .5 - large
Dr. Braverman’s slides
Power
The probability to reject null hypothesis
when it is, in fact, false.
 Power is bigger if

– Effect size is bigger
– Sample size is bigger
– Alpha is bigger
Dr. Braverman’s slides
What Kind of Test to Use?
1.
Define your variables.
– Independent Variables:

what you manipulate
– Dependent Variables:

what you measure
Dr. Braverman’s slides
Numerical or Categorical

Numerical
– Values defined by numbers.
– You can calculate mean and standard
deviation.

Categorical
– Values defined by labels.
– You can calculate frequency (how many of
each category).
Dr. Braverman’s slides
Tests to Use if All Variables are
Numerical

Examples:
– How SAT is related to the average GPA during the senior year of
college.
– How attitudes toward George Bush related to the attitudes
toward abortion.

Test to use:
– Regression/Correlation analysis
 Statistics: r
Dr. Braverman’s slides
Linear Correlation
Examining the relationship between height
and self esteem
 Examining the relationship between
emotional intelligence and social skills.

Dr. Braverman’s slides
Linear Correlation
Positive (r > 0)

Negative (r < 0)
Help
Performance

Hours of sleep before the exam
Dr. Braverman’s slides
Number of bystanders
Dr. Braverman’s slides
r=?
Performance
r=0
Anxiety
1>r>0
r- correlation

A social scientist wishes to determine
whether their is a relationship between
the attractiveness scores (on a 100-point
scale) assigned to college students by a
panel of peers and their score on a paperand-pencil test of anxiety.
– Variable 1 (numerical): attractiveness
– Variable 2 (numerical): anxiety
Dr. Braverman’s slides
Tests to Use if Variables are
Mixed: Categorical + Numerical

Examples:
1.
2.

Do females experience more empathy toward a stranger than
males do?
Which religious group gives more support toward the
president.
Test to use:
– t-test or different kinds of ANOVA.
the number of groups and variables.
Dr. Braverman’s slides
Depends on
t-test for independent samples.

A school psychologist compares the
reading comprehension score of migrant
children who, as a result of random
assignment, are enrolled in either a
special bilingual reading program or a
traditional reading program.
– IV( categorical, 2 levels): Reading program
– DV (numerical): Reading score.
Dr. Braverman’s slides
t-test for matched samples.

To determine whether speed reading influences
reading comprehension, a researcher obtains
two reading comprehension scores for each
student in a group of high school students, once
before and once after training in speed reading.
– IV (categorical, 2 levels) : training
– DV (numerical): reading comprehension score
Dr. Braverman’s slides
One-way ANOVA

In a study of problem solving, a
researcher randomly assigns college
students to one of three groups: highstatus leader, equal-status leader or no
leader, and measure the amount of time
required to solve a complex puzzle.
– IV (categorical, 3 levels): type of leader
– DV (numerical): time
Dr. Braverman’s slides
2-way ANOVA

To determine whether cramming can increase GRE
scores a researcher randomly assigns college students to
either a specialized GRE test-taking workshop, a general
test-taking workshop, or a control (non-test-taking)
workshop. Furthermore, to check the effect of
scheduling, students are randomly assigned, in equal
number, to experience their workshop either during one
long marathon weekend or during weekly sessions.
– DV (numerical): GRE score
– IV (categorical, 3 levels): kind of workshop
– IV (categorical, 2 levels): session
Dr. Braverman’s slides
Tests to Use if There are No
Numerical Variables
 Example:
– Is there a different frequency of rainy days in the four
seasons?
 Test
to use:
– One variable
 One-way Chi-square
– Two variables
 Two-way Chi square
Dr. Braverman’s slides
One-Way Chi-Square.

A random sample of 90 college students
indicates whether they most desire love,
wealth, power, health, fame, or family
happiness.
– Variable 1 (categorical): desire.
Dr. Braverman’s slides
2-way Chi-Square

A social scientist cross-classifies the
responses of 100 randomly selected
people on the basis of gender and
whether or not they favor strong gun
control laws.
– Variable 1 (categorical, 2 levels): gender
– Variable 2 (categorical, 2 levels): opinion
toward gun control.
Dr. Braverman’s slides
Article 1: Meghany et al., 2009. Predictors of
resolution of aberrant drug behavior in chronic pain
patients treated in a structured opioid risk
management program

Research Question:
– For chronic pain patients prescribed opioids
who are at risk for developing addiction to
opioids, what predicts success in a program
designed to manage those risks?

This is a question about moderators of a
supposed treatment effect
Article 1: Meghany et al., 2009. Predictors of
resolution of aberrant drug behavior in chronic pain
patients treated in a structured opioid risk
management program

Sample:
– Consecutive referrals to the Opioid Renewal
Clinic for aberrant drug related behaviors
(ADRBs) over the course of two and a half years
(N = 195 [49% of the 401 total referred])
– All participants had chronic non-cancer-related
pain
Article 1: Meghany et al., 2009. Predictors of resolution of
aberrant drug behavior in chronic pain patients treated in a
structured opioid risk management program

Measures: Predictors
– Demographics: Age, Race, Gender, Marital
Status, Employment, Veteran Status/Impairment
– Pain: Primary Diagnosis, # of Pain Diagnoses
– Comorbidity: Medical and Psychiatric

Measures: Outcome
– Staying in the program vs. Discharge/Drop-out
 Assumes resolution of ADRBs and negative urine
screens for illicit drugs
Article 1: Meghany et al., 2009. Predictors of
resolution of aberrant drug behavior in chronic pain
patients treated in a structured opioid risk
management program

Predictors are:
– Categorical
– Continuous

Outcome is:
– Categorical
 Specifically, dichotomous
Article 1: Meghany et al., 2009. Predictors of resolution of
aberrant drug behavior in chronic pain patients treated in a
structured opioid risk management program

Analysis Plan
1. Descriptives
–
51% (106) did not complete the program
–
–
–
–
58% (61) discharged
19% (20) moved into addiction treatment
23% (25) self-discharged/dropped out
General tendencies on the predictors for the sample
2. Comparison of groups (89 vs. 106) on predictor
variables
–
–
No demographic differences
Successful completers had higher medical comorbidity and
more pain diagnoses, were more likely to have a history of
depression, and were less likely to have abused cocaine
Article 1: Meghany et al., 2009. Predictors of resolution of
aberrant drug behavior in chronic pain patients treated in a
structured opioid risk management program

Analysis Plan
3. Multivariate Test: Logistic Regression
– Point of multivariate test: Takes the correlation
between variables into account so you learn which
variables have unique effects
– Certain relationships disappear because of those
correlations and others emerge
– # of pain diagnoses and history of cocaine abuse
remained significant independent predictors; marital
status emerged as a protective factor
Resources
• Gonick & Smith (1993). The Cartoon Guide to
•
•
•
Statistics.
Grimm & Yarnold (1995). Reading and
Understanding Multivariate Statistics
Grimm & Yarnold (2000). Reading and
Understanding More Multivariate Statistics
Abelson (1995). Statistics as Principled Argument.