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




              Chapter 13

      Correlational Research




                                                 1
    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)


                                                           2
      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

                                                             3
     Cautions about Cause-and-Effect…


•   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




                                                             4
     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




                                                                  5
      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



                                                             6
      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



                                                             7
      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)
                                                          11
     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)




                                                           12

				
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