Correlational Research: An overview

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Correlational Research An overview
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Definition and Purpose

• Correlational research involves the collection of
  data to determine the extent to which two (or
  more) variables are related.
• If a relationship exists, we say that the two
  variables covary in some non-random way.
• The strength of the relationship is expressed as
  a correlation coefficient, r.

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Purpose of Correlation Research

• Descriptive Show (or describe) the associations
  among variables.
• Hypothesis testing Test whether variables
  expected to be related are, in fact, related.
• Theory driven.
• Correlations often occur spuriously.
• Should not examine correlations, first, and then
  construct a theory to explain them.

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The Correlation Coefficient, r

• The coefficient, r, better known as the Pearson
  product moment coefficient, gives a quantitative
  measure of the linear relationship between two
  variables, X and Y, say.
• To indicate which variables are being correlated,
  we sometimes write rXY.
• An r of -1 (or close to -1) indicates a strong
  negative or inverse relationship.
• An r of 1 (or close to 1) indicates a strong
  positive (or direct) relationship.
• An r of 0 (or close to 0) indicates a lack (or at
  least a weak) relationship.

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A Table of Correlations

• Correlations among several variables are usually
  given in a correlation table.

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A Table of Correlations

• Only one half of a correlation table need be
  displayed. The upper triangular half or

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A Table of Correlations

• The lower triangular half.

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A Table of Correlations

• Often the diagonal is replaced by dashes.

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Correlation ? Causation

• The more highly correlated (i.e. the closer r is
  to or 1) the more accurate are predictions
  based on the relationship.
• This, however, does not necessarily imply that
  one variables is the cause of the other.
• Implying causation from correlation is what
  causal comparative research is all about.

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Correlational Research Design

• Collect data on two or more variables for each
  participant in the research study.
• Minimally accepted sample size is 30.
• If the measures have low reliability, larger
  sample sizes are needed.
• If participants are to be subdivided (say, into
  males and females) larges sample sizes are needed.

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Sample Sizes

• Depends on the reliability of the measures.
• With reasonable reliability a minimum of 30 cases
  with bivariate measures is usually acceptable.
• The statistical test is a t test of the null
  hypothesis H0 ?xy 0.0

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Interpreting Correlations

• Correlations close to -1 or to 1 indicate the
  same high degree of relationship, but in
  different directions.
• E.g., an r of -.87 between hours of TV watched
  and GPA indicates that higher GPSs are associated
  with lower hours watching TV.
• Question Does this mean that more hours spent
  watching TV leads to lower GPSs?

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Interpreting Correlations

• Correlations lower than .5 typically are not very
  interpretable.
• Correlations in the 60s and 70s are considered
  adequate for interpreting relationships among
  variables within groups.
• Correlations in the 80s and higher are good for
  interpreting relationships among variables for
  individuals.
• In the end, however, the interpretability of a
  correlation coefficient depends upon the purpose
  of the study.

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The END