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Correlational Research
• Correlational research
– Assess relationships among naturally occurring variables
• Attitudes, preferences, intelligence, personality traits, feelings,
age, sex
– Use correlation coefficients to
• describe a relationship between two variables
• determine a predictive relationship between two variables
– Researchers are not interested simply in the responses of
those surveyed
• inference: use a sample to describe the larger population
• careful selection of a survey sample
• generalize the findings from the sample to the population
Sex, Romance, and Relationships
a survey about sexual attitudes and practices
Correlations: Measuring and Describing Relationships
A correlation is a statistical method used to measure and describe
the relationship between two variables.
A relationship exists when changes in one variable tend to be
accompanied by consistent and predictable changes in the
other variable.
A correlation typically evaluates three aspects of the relationship:
– the direction
– the form
– the strength
Best Fit Line
Figure 15-1 (p. 510)
The relationship between exam grade and time needed to complete the exam. Notice the
general trend in these data: Students who finish the exam early tend to have better grades.
Scatter Plot of Family Income and Student’s average grade
Figure 15.2 page 511
Correlation data showing the relationship between family income (X) and student grades (Y) for a sample
of n=14 high school students. The scores are listed in order from lowest to highest family income and are
shown in a scatter plot.
Correlations: Measuring and Describing Relationships
The direction of the relationship is measured by the
sign of the correlation (+ or -).
A positive correlation means that the two variables
tend to change in the same direction; as one increases,
the other also tends to increase.
A negative correlation means that the two variables
tend to change in opposite directions; as one
increases, the other tends to decrease.
Figure 15-3 (p. 512)
Examples of positive and negative relationships. (a) Beer sales are positively
related to temperature. (b) Coffee sales are negatively related to temperature.
Correlations: Measuring and Describing Relationships
The strength or consistency of the relationship is
measured by the numerical value of the correlation.
Value of r can range from 0 to 1.
A value of 1.00 indicates a perfect relationship
A value of zero indicates no relationship
r value does not have a linear relationship with strength
of the correlation.
Use coefficient of determination ( r2 ) which measures
the proportion of variability instead of r
so if r = 0.80 then r2 = 0.64 which is a better indicator
of strength
Figure 15-4 (p. 513)
Examples of different values for linear correlations: (a) shows a strong positive relationship,
approximately +0.90; (b) shows a relatively weak negative correlation, approximately –0.40;
(c) shows a perfect negative correlation, –1.00; (d) shows no linear trend, 0.00.
Correlations: Measuring and Describing Relationships
To compute a correlation you need two scores, X
and Y, for each individual in the sample.
The Pearson correlation requires that the scores
be numerical values from an interval or ratio
scale of measurement.
Other correlational methods exist for other scales
of measurement.
Survey Research
• Widely used by Social, Political and Psychological scientists
• Surveys are used to
– describe people’s opinions, attitudes, and preferences
– make predictions about people’s behavior
• Scope of surveys
– specific and limited - views about a specific TV program
– global in their goals - about TV habits in general
• Bias in surveys
– determine by examining procedures and analyses
– not just because it is sponsored by an organization with a vested interest
• Typical survey research
– a sample of people completes a questionnaire
– using a predetermined set of questions
Basic Terms of Sampling
• Population: set of all cases of interest. For example:
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current students at your institution
current residents of your city
citizens of the United States
Everyone on the planet
• Sampling Frame: list of the members of a population.
– For example, registrar’s list of all currently registered students
– Frame should reflect the population
– May be difficult to get an adequate frame
• Sample: subset of the population drawn from the frame
– Students in your class as a sample of current students at your
institution (or your city, United States, the planet)
• Element: each member of the population.
Figure 5.1 Illustration of relationship
among four basic terms in sampling
Obtaining a Sample
• Goal: Sample should represent the population.
– Characteristics of participants in the sample should
be similar to those of the entire population.
– Example: Which sample represents a population
that is 30% freshman, 30% sophomore, 20% junior,
20% senior?
Sample A
Sample B
30 freshmen, 30 sophomores,
20 juniors, 20 seniors
60 freshmen, 60 sophomores,
40 juniors, 40 seniors
Both! But note: The samples are representative on one feature only!
Obtaining a Sample
• A biased sample occurs when the characteristics of the
sample differ systematically from those of the target
population.
– under-represent a segment of the population
• Population is 65% female
• Sample is 50% female
– over-represent a segment of the population.
• Population is 35% male
• Sample is 50 % male
– For example, most samples in psychology research
• overrepresent college students
• underrepresent individuals who are not in college.
– Most research underrepresents individuals from diverse cultures
Obtaining a Sample
• Two sources of biased samples:
– Selection bias occurs when the researcher’s
procedures for selecting a sample result in one or more
segments of the population being under- or overrepresented.
• Example: Researcher places sign-up sheets for a research study in a
Psychology Department. Psychology students are likely to be overrepresented because of the selection procedure.
– Response bias occurs when individuals selected for the
initial sample do not complete and return the survey.
• Example: People who receive the survey aren’t interested,
they’re worried about privacy, have vision or other problems,
don’t have time, etc.
• Final sample will only represent the population of people who
are interested, not worried, have good vision, time, etc.
Examples of response bias
• Survey of sexual attitudes
– for example, should sex be more openly discussed in schools?
• Whom is most likely to return survey?
• Whom is most likely to not return the survey?
Approaches to Sampling
• Sampling refers to the procedures used to obtain a sample.
• Two basic approaches to sampling are
– Nonprobability sampling
– Probability sampling
Approaches to Sampling
• Nonprobability sampling: No guarantee that each
member of the population has an equal chance of being
included in the sample.
– “Convenience sampling” occurs when the researcher selects
individuals who are available and willing to respond to the
survey.
• Magazine surveys, Internet surveys, Call-In surveys
– Can have very large sample size
• Students in a classroom
– Lots of psychological research uses convenience samples
• but this can be OK
• How do you know if the sample is representative?
Approaches to Sampling
• Probability sampling: All members of a population have an
equal chance of being selected for the survey
– Simple random sample
• Random selection from a sampling frame (list) of people in the
population
• Effective Sample size is related to variability of the population
– Stratified random sample
• Divide population into strata and sample proportionally
• Random samples are then drawn from the strata.
• For example, strata from a university population potentially
include freshmen, sophomores, juniors, seniors
• Stratified random sampling increases the likelihood that the
sample will represent the population.
Survey Methods
• Four methods for obtaining survey data are:
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mail surveys,
personal interviews,
telephone interviews, and
Internet surveys.
• Each method has advantages and disadvantages.
• Choose depending method based on research question.
Survey Methods
• Mail surveys
– quick and convenient, self-administered, best for highly personal
or embarrassing topics.
– may have the problem of response bias when people selected
for the survey sample don’t complete and return their survey.
– Due to response bias, the final sample may not be
representative of the population.
– Because mailed surveys are self-administered
• respondents are free to interpret questions as they see fit
• leading to possible differences in how people respond to questions.
• Questions must be self explanatory
Survey Methods (continued)
• Personal Interviews
– are costly, but researchers gain more control over how the
survey is administered, and how people interpret survey
questions.
– Interviewers can seek clarification of answers.
– potential problem: interviewer bias.
– Interviewer bias occurs when interviewer records only selected
portions of respondents’ answers, or interviewer words questions
differently to fit particular respondents.
– Interviewers must be highly motivated, carefully trained, and
supervised.
Survey Methods (continued)
• Telephone Interviews
– brief surveys can be completed efficiently and with greater
access to the population.
– Random-digit dialing technology allows researchers to select
random samples.
– Interviewers can be supervised easily from one location
– Potential problems include
• selection bias because only people with phones can be included
• response bias in that people may refuse solicitations to complete
surveys over the phone
• interviewer bias
Survey Methods (continued)
• Internet Surveys
– The Internet allows for efficient, low-cost means to survey very
large samples.
– Samples can be very diverse and access typically
underrepresented samples.
– Potential problems include
• selection bias because access to computers and Internet required
• response bias
• lack of control over the research environment
Survey Methods
• Ways to increase survey response rate (and lessen
problems associated with response bias):
– Questionnaire has a “personal touch” (e.g., respondent are
addressed by name and not simply “Dear student”)
– Responding requires a minimum of effort
– Topic of survey is intrinsically interesting to respondent
– Respondent identifies with the organization or researcher who is
sponsoring the survey.
Survey Research Designs
• A research design is a plan for conducting a research
project.
• There are three types of survey research designs:
– Cross-sectional design
– Successive independent samples design
– Longitudinal design
• The survey design researchers choose depends on their
research question.
Survey Research Designs
• Cross-sectional Survey Design
– A sample is selected from one or more populations at one time point.
– The responses are used to describe and make predictions for the
population at that point in time.
– If two or more samples are drawn from different populations, the
populations can be compared.
– Researchers cannot assess changes over time with cross-sectional
designs.
Survey Research Designs
• Successive Independent Samples Design
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A series of cross-sectional surveys over time.
A different sample of people completes the survey each time.
Each sample is selected from the same population.
Responses from the sample are used to describe the population at
each point in time.
– Researchers can compare the survey responses from each sample to
see how the population changes over time.
• Successive independent samples designs don’t tell us whether
individuals change over time (because different individuals complete the
survey each time).
– Problem of noncomparable samples:
• If different populations are sampled at each time, we don’t know if
responses differ because of true changes over time, or because different
populations were sampled.
Survey Research Designs
• Longitudinal Research Designs
– The same sample of individuals completes the survey at different
points in time.
– This allows researchers to assess how individuals change over
time.
– Responses from the sample of respondents are generalized to
describe changes over time in the population from which the
sample was drawn.
• Problems with longitudinal designs:
– Just because people change over time, surveys can’t tell us why
people change.
– Attrition occurs when people drop out of the study.
– Reactivity: Respondents may strive to be consistent or become
sensitized to the topic.