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```									Introduction to Educational Research (5th ed.)
Craig A. Mertler & C.M. Charles

Chapter 13

Correlational Research

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Correlations

•   Human (logical) thought tends to reflect linearity

If “A”                then “B”

• Measures of relationship between variables
• Can permit future predictions of one variable from
knowledge of another
• Can raise questions about cause-and-effect patterns
(can only be established with experimental research)

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The Nature of Correlational Research

•   Purpose is to discover corelationships between two or
more variables; seeks out conditions that covary, or
correlate, with each other
•   Corelationship is when an individual’s status on one
variable tends to reflect the status on another
•   Correlations help us:
» Understand related events, behaviors, etc.

» Predict future events, etc. from what we know about

another
» Sometimes obtain strong suggestions that one

variable may be causing another

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•   Post hoc fallacy—post hoc ergo propter hoc (“after the

fact, because of the fact”

»   The “cause” can actually be the “effect” (or vice

versa)

»   This is a common fallacy of logical thinking

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Topics for Correlational Research

•   If a relationship is suspected

•   If you wish to predict values on one variable from

another

•   If you need to establish instrument validity or reliability

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Correlational Research Design

•   Typically oriented by research questions or hypotheses
•   A relatively straightforward design:
» Identify variables for inclusion

» Formulate questions or hypotheses

» Select a random sample (preferably with n > 30)

» Obtain data for each member of the sample on each

variable being investigated
» Compute correlations in order to determine degree

of relationship

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Types of Bivariate (2 variables)
Correlation Coefficients

•   Pearson product-moment correlation (a.k.a., Pearson r
or r)—correlation between two continuous variables
•   Biserial correlation—one continuous variable and one
artificial dichotomous variable
•   Point-biserial correlation—one continuous variable and
one natural dichotomous variable
•   Phi correlation ()—two natural dichotomous variables
•   Tetrachoric correlation—two artificial dichotomous
variables

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Types of Bivariate (2 variables)
Correlation Coefficients (cont’d.)

•   Spearman rho (rs)—two ranked variables, with larger
samples
•   Kendall’s tau ()—two ranked variables, with
samples < 10

8
Types of Multivariate (> 2 variables)
Correlation Coefficients

•   Partial correlation (partial r)—correlation between two
variables with the effects of a third variable “partialed
out”
•   Multiple regression—used to determine degree of
relationship between one continuous dependent
variable (“criterion variable”) and a combination of
independent variables (“predictor variables”)
•   Discriminant analysis—analogous to MR, but criterion
variable is categorical (e.g., “pass-fail”)
•   Factor analysis—used with a large number of correlated
variables; variables are statistically grouped into
clusters, known as “factors”

9
Interpretation of Correlation
Coefficients

•   Most coefficients range from -1.00 to +1.00 (some range
from 0 to +1.00)
•   1.00 = a perfect correlation/relationship; 0 = no
correlation/relationship
•   General rule of thumb for interpretation:

-1.00         -.70           -.30          0            +.30        +.70       +1.00
|------|------|------|------|------|------|
weak relationship
moderate                               moderate
relationship                           relationship

strong
strong
relationship
relationship

10
A Published Example of Correlational
Research

Coates, L. & Stephens, L. (1990). Relationship of computer
science aptitude with selected achievement meaures
among junior high students. Journal of Research and
Development in Education, 23(3), 162–164.

See “Additional Examples of Published Correlational
Research Studies” for 8 additional articles, available
through Research NavigatorTM
(http://www.researchnavigator.com)
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Applying Technology…
Web sites covering topics related to correlational
research

• Dr. Rousey’s discussion of "Correlational Research"

(http://www.fractaldomains.com/devpsych/corr.htm)

• A second page of examples from Dr. Rousey

(http://www.fractaldomains.com/devpsych/corr2.htm)

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