Download Statistics and Research

Survey of Modern Psychology
STATISTICS AND
RESEARCH
The Scientific Method
The Importance of Statistics and Research
Research requires a testable hypothesis and
systematically gathered data
This approach is important because
Anecdotal evidence is often meaningless
We need a clear and objective way to compare
differences and possible outcomes
Variables
 The independent variable is manipulated to study its
effect


This may be a variable that the experimenter does not actively
control, such as gender.
This may also be the condition a participant is in for an
experiment
 The dependent variable is the participant’s response
Variables
 Quantitative: Numerical variables that represent
quantities

Ex. height, weight, time spent on a task, etc.
vs.
 Categorical/Nominal: A name or a symbol indicating
belonging to a group


Ex. profession, gender, etc.
Numbers are sometimes used as category labels

Ex. calling the first base player “1”, second base “2”, etc.
Using A Number as a Nominal Variable
 When a number is used as a label, the numbers
cannot be added to each other
+
=/=
Quantitative Variables
Quantitative variables can be discrete or continuous
 Discrete


There are a limited number of possible values for the variable
There are gaps between the numerical values of the variable

Ex. The number of pairs of shoes that you have
 Continuous
 The variable can have an infinite number of possible values
 No matter how close the numerical values are, there can be
another value between them

Ex. reaction times of 23.4 seconds and 23.5 seconds
 Values in between can be 23.41, 23.411, 23.412 etc.
Averages
 Mean
 Median
 Mode
Mean
 The mean is the most commonly used average
 It is the sum of the data points, divided by the
number of data points.
 For example, if I wanted to find the average age of a
group of friends:
Ages: 26, 27, 27, 27, 28, 29, 30, 31, 32
26 + 27 + 27 + 27 + 28 + 29 + 30 + 31 + 32 = 257
257/9 = 28.5
The mean age is 28.5 years
Mode
 The mode is the most repeated data point in a set
 The mode is primarily useful for categorical variables
 Ex. if you were buying t-shirts for a large group of people, the
most common size would be useful information
 It may also be used for ordered discrete categories
 Ex. participants are asked to rate a movie on a scale of 1 – 5.
The mean rating may be 4.2, but participants were only
allowed to give whole number answers. Therefore, the mode
would be 4.
Mode
 Sometimes there are two modes. If the modes are far
apart, the data set is considered bimodal.

Ex. t shirt sizes: S, S, S, S, S, S, M, M, L, XL, XL, XL, XL, XL, XL
Median
 The median is the midpoint in an ordered set of data
 It divides a set of data points into two halves, with an
equal number of data points above and below it
 In the example where I was finding the average age
of a group of friends:
Ages: 26, 27, 27, 27, 28, 29, 30, 31, 32
Median
 Note that the numbers MUST be in order for this to
work
Ages: 27, 31, 26, 27, 32, 27, 30, 29, 28
Wrong!
 If there are an even number of data points, the two
middle ones are averaged using the mean
26, 27, 27, 27, 27, 28, 29, 30, 31, 32
(27 + 28)/2 = 27.5
Comparing Mean, Mode, and Median
 Imagine you were trying to determine the average
number of children in a family
 The mode would probably be the best average to use
because one cannot have .5 of a child
Comparing Mean, Mode, and Median
 An outlier is a data point that is far apart from the
rest of your data


Ex. I’m trying to find the average age of the group I’m with,
and my grandmother joins us
Ages: 26, 27, 27, 27, 28, 28, 29, 30, 31, 32, 87
Comparing Mean, Mode, and Median
 The median is unaffected by outliers
 Ages: 26, 27, 27, 27, 28, 28, 29, 30, 31, 32, 87
 The mean is affected by outliers:
 Mean without my grandmother = 28.5
 Mean with my grandmother = 33.82
Standard Deviation
 The standard deviation (SD) tells us how much the
data spreads out from the mean

How much do the data points vary from each other?
Z - Scores
Z-Scores (or standard scores)
 Z-scores are based on standard deviation from the
mean
 Using z-scores lets us compare the meaning of data
points from different sources
 The z-score provides information about where a data
point is relative to the average
 A z-score of 1 means that the data point is 1 standard
deviation above the mean (2 is 2 standard deviations
above the mean, etc.)
Z-Scores
Imagine you and a friend are trying to figure out which
one of you performed better on an aptitude test.
however
You each took a completely different test.
Z-Scores
 You got a score of 36, your friend got a score of 100
 The average score on your test is 30, with a standard deviation
of 3.


Therefore, your z-score is 2
The average score on your friend’s test was 80, with a standard
deviation of 20.

Therefore, their z-score is 1
Therefore, you performed well above the mean,
whereas your friend performed slightly above the
mean
The Normal Distribution
 The mean is in the
center
 Approximately 68% of
data points are within
1 SD of the mean
 95% of data points are
within 2 SD of the
mean
 Almost all data is
within 3 SD of the
mean
Notes on the Standard Deviation
 If you are dealing with large number values, it is OK
if the SD is larger.

i.e., the standard deviation may seem small or large relative to
the numbers your are dealing with
Notes on the Standard Deviation
For example, you are catering a dinner party and 10
extra people show up.
 If you were expecting 100 people, the 10 more will
not be a problem and you’ll still have enough food.
 If you were expecting 20 people, 10 more is a
relatively large number of extra guests and you will
not have enough food.
Mistakes We Make in Statistics
 Regression fallacy
 We look for patterns to make sense of things, and
sometimes see patterns when there is really no
pattern or relationship there
Regression Fallacy
 “Lucky” items
 You will have success at times when you have the item.
 You will also have failure at times when you have the item.
 It’s also quite likely that the item will “make” you
more successful by boosting your confidence (self
fulfilling prophecy)
 If you attribute too much to luck, you may also be
less likely to put in effort (therefore making it seem
unlucky!)
Regression Fallacy
Example: The Sports Illustrated cover jinx
 The idea that an athlete will have a run of bad luck
after appearing on the magazine cover
 What really may be happening:


Athletes fluctuate; more people may notice after the athlete is
brought to their attention
An athlete will probably be featured on the cover at the peak of
his or her career; at some point, they are bound to stop
performing so well
Regression Fallacy
Example: We attribute major changes to whomever
holds office when something good or bad happens
 There are natural fluctuations (in the economy,
crime, etc.) that have nothing to do with who’s in
charge
Calculating Odds
 Imagine that you have flipped a (fair) coin
three times, and gotten heads each time.
 How likely do you think it is that the next
flip will be heads?
Coin Flips
 The next toss is no more or less likely to be
heads than tails
 Each toss, there is the same chance of
getting heads or tails
The Monty Hall Problem
 On the old game show Let’s Make a Deal, a prize was
hidden behind one of three doors.
 The contestant would choose a door; Monty Hall
then eliminated a no prize door and offered the
contestant the chance to change their choice.
Do you think it was better to change doors, keep the
first choice, or no difference?
The Monty Hall Problem
 Initially, you had a 1 in 3 chance of getting the prize
 After a door is eliminated, what are your chances of
winning a prize?
The Monty Hall Problem
 People generally believe that after a door is
eliminated you have a 1 in 2 chance of winning
 In reality, you have a 2 in 3 chance of winning
Statistics - Humor
A headline shown on Jay Leno’s show said “The
average American is getting older.” His addition was
“the average American doesn’t have a choice!”
 Statistically, the statement does make sense. The
headline was actually stating that the mean age of
Americans is increasing.
Statistics - Humor
Studies find that 3 in every 4 people make up 75% of
the population
Statistics - Humor
They say that 1 in every 4 people suffers from some
form of mental illness. Look at your three closest
friends. If it’s not them, it’s you.
Types of Error
 Type 1 Error:
 A false positive
 Finding a difference when there really is none
 Type 2 Error
 A false negative
 Finding no difference when there really is a difference
Conditions
Participants in a study are usually in a control
condition or experimental condition
 In the control condition, there is no manipulation
 In the experimental condition, there is a
manipulation or extra information given
The Null Model vs. Full Model
 The Null model says that the experimental
conditions will give a result no different from
average/chance
 The full model says that the experimental conditions
will give cause a different outcome
Basic Research
The goal of basic research is to increase
understanding of human behavior.
Applied Research
The goal of applied research is to increase
understanding of real world needs and
contribute to the solution of problems
Types of Research
Naturalistic
observations
 The
researcher
observes but does
not manipulate or
become actively
involved with the
subjects
Types of Research
 Case studies
 Observational
research in which one person is
studied intensively
Types of Research
 Experimental
 The
researcher obtains a group of participants
and manipulates conditions
 Establishes cause and effect
 Often uses self-report measures
Types of Research
 Correlational
 Examines
the association between two variables
 Correlations can be used for predicting and
generating hypotheses
 Correlations are often useful when one cannot
manipulate variables
CORRELATION
 In a positive correlation, as one variable
increases the other variable increases
 In a negative correlation, as one
variable increases the other variable
decreases
Correlation
 Worksheet
CORELATION
CORRELATION
IS NOT
CAUSATION!
T- Tests
 T-tests are used to compare the null and full models.
ANOVA
 ANalysis Of VAriance
 An ANOVA is used instead of a t-test if there are 3 or
more variables
 An ANOVA can be used to look at subcategories of
variables
Chi Square
 The chi square is used with categorical variables
 It looks at how many observed data points fit in a
category compared to the number of expected data
points in that category.
 For example, if you were trying to find out if there is
a difference in the number of men and women who
like action movies.
Chi Square - Example
Imagine you are doing a survey on whether there is a
difference in the number of men and women who
like action movies.
Your categories are:
1. Action Movies Yes
2. Action Movies No
---------------------------1. Male
2. Female
Chi Square - Example
Imagine you are doing a survey on whether there is a difference in the number of men and
women who like action movies.
The null hypothesis says that the numbers of men and
women who like action movies are equal.
Therefore, one might expect that if everything were
left completely to chance, half of each group would
like action movies, half of each group would dislike
action movies.
You have 100 participants, 50 male and 50 female
Chi Square - Example
Action Movies
Male
Female
Like
Count
Expected
90
50
25
50
Count
Expected
10
50
75
50
Dislike
Defining Variables
 When constructing an experiment, you need to
clearly define what you are going to study and how
Statistics in Advertising:
 Many commercials
use statistics.
 For example,
everything seems
to be
recommended by
“4 out of 5”
members of a
profession
Statistics in Advertising:
However, they never explicitly define what the given
alternatives were
 “4 out of 5 dentists recommend this brand of
sugarless gum”



In some of these studies, the dentists were asked what they
recommend for patients who chew gum.
They were given the multiple choice answers: regular,
sugarless, or none
The 1 in 5 recommended “no gum”
 “4 out of 5 doctors favored this brand of pain
reliever”
Statistics in Advertising:
However, they never explicitly define what the given
alternatives were
 “4 out of 5 doctors favored this brand of pain
reliever”



What were the other options?
Reportedly, in some of these surveys the possible answers were
“our brand” or “none”
This really means that doctors did not necessarily favor a given
brand, but they find it more effective than nothing at all
Defining Variables
 Another example of defining variables comes from a
former classmate who wanted to study when parents
start teaching their sons vs. daughters about money.
Defining Variables
She did not explain what she meant by money:
 “This is a dime, it’s worth 10 cents; this is a quarter,
it’s worth 25 cents; etc.”
 “Money needs to be earned and saved.”
 “Money is used to buy things.”
 “We do have money, they don’t./We don’t have
money, they do.”
Cautions in Research
All research methods used must be reliable and valid!
Validity
Does the
method
measure
what you
are trying
to
measure?
Reliability
 Will the measure give you (approximately) the same
results each time?

For example, if within a matter of 3 minutes a thermometer
gives temperatures of 98.6, 101.3, and 95.4 it is not reliable.
 Will other researchers using the same method agree
with your results?
Structures of Studies
Short Term vs. Longitudinal
 Short term research gathers data over a short
amount of time (generally one incident)
 Longitudinal research collects data over extended
periods of time, sometimes following the same
participants from birth to adulthood
Structure of Studies
Twin Studies
 Twin studies use pairs of twins (identical or
fraternal)

Some use twins who were raised separately and then compare
them to each other (to study the impact of genetics vs.
environment)
Structure of Studies
Independent Groups (or between subjects design)
 Each participant is in only one condition
 Each participant is assigned to a group
independently of all other participants
vs.
 Matched Pair Design
 Within Subjects
Structure of Studies
Matched Pair Design
 Each participant is in only one condition, but the
assignment of one participant dictates the
assignment of the second participant.
vs.
 Within Subjects
 Independent Groups (or between subjects design)
Structure of Studies
Within Subjects Design
 Each participant is studied in multiple conditions
 The participant obtains two scores, which are
compared

Ex. if each student was in the reward and no reward condition for the
boring task
vs.
 Independent Groups (or between subjects design)
 Matched Pair Design
Structure of Studies
Double Blind
 This structure is normally used in drug studies
 Some participants are given the actual drug, others
are given a placebo (an inactive pill)
 Neither the participant nor the experimenter knows
what the participant is taking
 This prevents the experimenter from treating
participants differently based on which condition
they’re in
Placebo Effect
 In the placebo effect, a person who is given an
inactive pill experiences benefits and side effects
from the “drug”
•Placebos are used as a
control condition in
drug studies
Placebo Effect
There are multiple theories about what makes the
placebo effect work
The participant wants
to please the
researcher, so they
respond accordingly
•(“The doctor gave me
a pill to make me feel
better, so I will.”)
Placebo Effect
There are multiple theories about what makes the
placebo effect work
 The participant expects the treatment to have certain
outcomes, and therefore produces those outcomes.
(This is based on internal motivation, not the external motivation of
pleasing someone else.)
 The brain expects a certain reaction to a pill and
causes the body to physiologically react that way.
Class Demonstration: IQ
 How we answer self-report questions usually doesn’t
depend on our own personal answer in a vacuum; we
look for comparison points
Self Report Research
Self-reports rely on the following
happening:
 The participant will accurately
interpret the researcher’s question

The participant then honestly answers the
question
 The researcher will accurately interpret
the participant’s answer
Self Report Research
How do people answer self-report questions?
 One theory on the steps taken when answering a question
include that one interprets what is being asked, finds an answer
and possibly adjusts it to fit a series of given choices, and
finally may edit the answer to make it desirable
Self Report Research
Context and Intent
 How the question is framed and who’s asking
 Desirable vs. undesirable responses

What is “normal” or socially acceptable?
 Threatening vs. Non-Threatening
Context and Intent
 Interpreting what is being asked requires an
understanding of the questioner’s intent.
 Imagine being asked to rate your health as
being excellent, good, fair, or poor.
 The examinee is required to think in the
following terms:
Understanding Intent and Answering
 Counting
the number of visits to the doctor
 Emotional health vs. physical health
 “Relative” health/comparisons to:
One’s
usual state of health
The health of people in general
The health of peers
Groves, Fultz & Martin (1992)
Desirability
 People want to appear desirable to
whomever is asking the question.
 Ex.
asking teenagers about drug use
Answering Desirably
 If a teenager is questioned by an adult, he or she
is less likely to admit to drug use.

It would be threatening to report drug use.
 If a teenager is questioned by another teenager,
he or she might exaggerate drug use to appear
“cool.”

It would be non-threatening to report real incidences
of drug use
Schwarz & Oyserman, 2001
Answering Desirably
 Pepsi Challenge

A Pepsi representative would set up a table and offer
people a sample of coke and a sample of Pepsi and
then ask which they preferred
 Supposedly, more people preferred Pepsi
Answering Desirably
 A person might be
more tempted to
say they preferred
Pepsi to appease
the Pepsi
representative
 When I took the
Pepsi challenge,
people were
offered a prize if
they reported
preferring Pepsi,
further skewing
the result
Answering Relevantly
 It is assumed that anything said is said for a
reason and is therefore relevant to your
interpretation of the question.
 Clearly, it is also desirable to answer relevantly.
Answering Relevantly
Researchers identifying themselves as
personality psychologists or as social
psychologists asked participants to explain
hypothetical behavior.
Answering Relevantly
(continued)
 Participants who believed they were answering
for social psychologists gave social
explanations.
 Participants who believed they were answering
for personality psychologists gave trait
explanations.
Schwarz, 1999
Context
 The context behind a question provides clues
to the questioner’s intention.
 Understanding the context and intention gives
information about what would make a
desirable answer.
Answering Contextually
 Imagine being asked to report your daily levels
of stress.
OR
 Imagine being asked to report your daily levels
of stress leading up to a stressful event.
Answering Contextually (continued)
 Reporting increased stress is appropriate and
“desirable” in the context of a stressful event.
 Acknowledgement of a stressful event in a
question implies that the event is relevant to
your response.
Eisenkraft, 2004
Retrospective Self-Reports
 Two week long study using undergraduate students in an
intro psych class
 Participants were given a “daily diary” to complete every
night before going to bed and two “weekly diaries” to
complete once a week


The daily diaries asked participants how many hours they
had spent since the previous day in class, sleeping,
socializing, and studying
The weekly diaries asked participants on average how many
hours they’d spent per day in each activity over the previous
week
Retrospective Self-Reports
Results were obtained by calculating the
arithmetic means of daily hours spent in
activities (daily average) and the arithmetic
mean of the weekly estimates (weekly average).
Daily average reports were compared to weekly
average reports.
Retrospective Self-Reports
 In weekly diaries, participants reported having spent
significantly more time in class than in daily diaries
Participants reported fewer hours sleeping in weekly
diaries
 Participants reported more time studying in weekly
diaries

 There was no difference in reports of time spent
socializing
Explanations
An honest error in memory
 Time spent socializing was usually concentrated over
a few days, making it easier to keep track of the total
number of hours for the week
 Participants may have estimated hours spent in class
per week based on their schedules and how much
time should have been spent in class

Forgetting times when a professor dismissed the class
early, or a student came in late
Explanations
Protecting Image
 Participants reported spending more time studying
(desirable behavior) and less time sleeping

This interprets sleeping as a less desirable behavior –
less time spent sleeping would imply more time spent
studying
 There is less motivation to alter the report of hours
spent socializing
Less socializing implies the person is not popular
 More time socializing implies the person is neglecting
their studies

Self Report and Depression
Self Report depression measures are often used in
large screenings, such as at university health centers
Self Report and Depression
 Participants were divided into three conditions
 All used the same questionnaire, BDI-II
 The conditions varied by the title put on the questionnaire:
 Student
condition said “Student Responses to the Depression
Questionnaire for Students”
 Psychiatric condition said “Student Responses to the
Depression Questionnaire for Psychiatric Patients”
 Neutral condition said “Student Responses to a Depression
Questionnaire”
Participants completed the questionnaire online
BDI-II Sample Questions
Pick out the one statement in each group that best describes the way you have been feeling
during the past two weeks, including today.
1. Sadness
0 I do not feel sad.
1 I feel sad much of the time
2 I am sad all of the time.
3 I am so sad or unhappy that I can't stand it.
2. Pessimism
0 I am not discouraged about my future.
1 I feel more discouraged about my future than I used to be.
2 I do not expect things to work out for me.
3 I feel my future is hopeless and will get only worse.
4. Loss of Pleasure
0 I get as much pleasure as I ever did from the things I enjoy.
1 I don't enjoy things as much as I used to.
2 I get very little pleasure from the things I used to enjoy.
3 I can't get any pleasure from the things I used to enjoy.
Self Report and Depression
 After completing the questionnaire, participants
were asked demographic questions, including:
Whether the participant had seen the BDI previously
 If the participant was in treatment for a mood disorder
 The participant’s major

Self Report and Depression
 Participants who were in the psychiatric condition
and in treatment for a mood disorder had the lowest
score
 Participants who were in the student condition and
in treatment for a mood disorder had the highest
score
Self Report and Depression
Condition
Treatment
Mean
Psych
Yes
7.47
No
11.01
Yes
21.00
No
8.63
Student
Self Report and Depression
 Participants who were in the psychiatric condition
were significantly more likely to leave comments
than participants in the student or neutral
condition
50% of participants in the psychiatric condition left
comments vs. 18.6% of the participants in the student/neutral
condition
Sample Comments
 Needs more range between “completely fine” and 1st
degree of “I feel crappy”
 Ridiculously negative. I feel better about myself than
I used to, and yet my only choices were between
feeling the same as ever or three stages of feeling
worse.
 There should be more middle ground between the 1st
and 2nd selections. For instance, I feel sad sometime
wasn’t an answer it was either I feel sad never or
much of the time
Self Report and Depression
Comments
Psych
Student/
Neutral
None
Count 15
Expected 21.2
48
41.8
Count 15
Expected 8.8
11
17.2
Yes
Self Report and Depression
 For participants who were not in treatment and in the
psychiatric condition:
The title of the condition was not threatening and they
did not hesitate to report some level of actual symptoms
 While as a non-psychiatric patient the participant
should not have a high score, if the questionnaire was
being used with students then it must be somewhat
relevant to them

Self Report and Depression
 For participants who were in treatment and in the
psychiatric condition:
The title was more threatening and primed thoughts
about stigma
 The participant would then refrain from reporting
depressive symptoms in order to distance him or herself
from the negative impressions of what a psychiatric
patient is

Self Report and Depression
 For participants who were in treatment and in the
student condition:
The participant would identify with the symptoms and
not feel threatened by reporting them
 The participant may have compared him or herself to
the other people completing the questionnaire
 The participant would over report symptoms because
any symptom should be more severe than other
students’

Self Report and Depression
 Participants in the Psych condition leaving more
comments suggests that they did find the process of
completing the BDI-II more disturbing.


Many comments reflected on the gap between the first and
second answer choices, complaining that the first option was
no symptoms and there was no middle ground
This supports the idea that participants in the Student and
Neutral conditions felt that the questionnaire gave more
appropriate options, and therefore a “no symptoms” answer
in the Student or Neutral conditions meant something
different from a “no symptoms” answer in the Psych
condition.
Consent Form
 Note: this would normally require a signature
This study is examining students’ responses to a Depression
Questionnaire.
There is no anticipated risk involved in participating in this study,
but questions are about a sensitive topic and you may decide to
discontinue your participation at any time without penalty.
Responses are anonymous.
Please answer each question honestly.
Please click here to verify that you are over the age of eighteen years
and choose to participate.
Button: (No) and (Yes. Continue to Depression Questionnaire)
Debriefing
The questionnaire that you completed is called the Beck Depression Inventory II (or
BDI-II). The purpose of this study is to look at whether the description of the
questionnaire and heading will influence participants’ answers. In reality, the BDIII is used in a variety of settings and is not intended solely for a specific population.
If you choose to forward the main webpage link to others, please do not disclose the
purpose of the study because that may influence the results. If you have any
questions, or are interested in the results, you may contact me at [email protected].
Everyone occasionally feels blue or sad, but these feelings are usually fleeting and pass
within a couple of days. When a person has a depressive disorder, it interferes with
daily life, normal functioning, and causes pain for both the person with the disorder
and those who care about him or her. Depression is a common but serious illness,
and most who experience it need treatment to get better.
Many people with a depressive illness never seek treatment. But the vast majority,
even those with the most severe depression, can get better with treatment.
Intensive research into the illness has resulted in the development of medications,
psychotherapies, and other methods to treat people with this disabling disorder.
(from http://nimh.nih.gov/health/publications/depression/introduction.shtml)