# Correlational Research: An overview

Document Sample

```					Correlational Research:
An overview
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.
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.
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.
A Table of Correlations
Correlations among several variables are usually
given in a correlation table.

Correlations Among Four Variables
Var 1     Var 2     Var 3    Var 4
Var 1     1.00      .32       .78      .66
Var 2     .32       1.00      .89      .21
Var 3     .78       .89       1.00     .11
Var 4     .66       .21       .11      1.00
A Table of Correlations
Only one half of a correlation table need be
displayed. The upper triangular half or……

Correlations Among Four Variables
Var 1     Var 2     Var 3    Var 4
Var 1     1.00      .32       .78      .66
Var 2               1.00      .89      .21
Var 3                         1.00     .11
Var 4                                  1.00
A Table of Correlations
The lower triangular half.

Correlations Among Four Variables
Var 1     Var 2    Var 3     Var 4
Var 1     1.00
Var 2     .32       1.00
Var 3     .78       .89      1.00
Var 4     .66       .21      .11       1.00
A Table of Correlations
Often the diagonal is replaced by dashes.

Correlations Among Four Variables
Var 1     Var 2    Var 3     Var 4
Var 1     ---
Var 2     .32       ---
Var 3     .78       .89      ---
Var 4     .66       .21      .11       ---
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
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.
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
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?
Interpreting Correlations
• Correlations lower than .5 typically are not
very interpretable.
• Correlations in the 60’s and 70’s are
relationships among variables within groups.
• Correlations in the 80’s 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.
The END

```
DOCUMENT INFO
Shared By:
Categories:
Tags:
Stats:
 views: 40 posted: 6/11/2012 language: English pages: 14
How are you planning on using Docstoc?