STATISTICS AND RESEARCH Survey of Modern Psychology.

STATISTICS AND RESEARCH

Survey of Modern Psychology

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 continuousDiscrete

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

MeanMedianMode

Mean

The mean is the most commonly used averageIt 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, 3226 + 27 + 27 + 27 + 28 + 29 + 30 + 31 + 32 =

257257/9 = 28.5The mean age is 28.5 years

Mode

The mode is the most repeated data point in a setThe 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

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

Wrong!

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


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


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 meanUsing z-scores lets us compare the meaning

of data points from different sourcesThe z-score provides information about where

a data point is relative to the averageA 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 jinxThe 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?


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?


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 variablesAn 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 Yes2.Action Movies No----------------------------1.Male2.Female


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


Action Movies Male Female

Like

Count 90 25

Expected 50 50

Dislike

Count 10 75

Expected 50 50

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


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”


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. LongitudinalShort 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 StudiesTwin 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)


Independent Groups (or between subjects design)

Each participant is in only one conditionEach participant is assigned to a group

independently of all other participants

vs. Matched Pair DesignWithin Subjects


Matched Pair DesignEach participant is in only one condition, but

the assignment of one participant dictates the assignment of the second participant.

vs. Within SubjectsIndependent Groups (or between subjects design)


Within Subjects DesignEach participant is studied in multiple

conditionsThe 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


Double BlindThis structure is normally used in drug

studiesSome 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 takingThis 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 questionThe researcher will accurately

interpret the participant’s answer


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


Context and IntentHow the question is framed and who’s askingDesirable 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 doctorEmotional 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.

ORImagine 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


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.


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 memoryTime 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 ImageParticipants 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


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. Sadness0 I do not feel sad.1 I feel sad much of the time2 I am sad all of the time.3 I am so sad or unhappy that I can't stand it.2. Pessimism0 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 Pleasure0 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.


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


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


Condition Treatment Mean

Psych Yes 7.47

No 11.01

Student Yes 21.00

No 8.63


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


Comments Psych Student/Neutral

None

Count 15 48

Expected 21.2 41.8

Yes

Count 15 11

Expected 8.8 17.2

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


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


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’


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 signatureThis 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 BDI-II 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)

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