Correlational and Causal
Comparative Research
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.
Correlational Research
Concerned with examining the strength of
associations (or relations) among two or
more variables.
Strength is expressed as a correlation
coefficient between -1.0 and +1.0.
The relationship can be positive or negative.
Correlations with absolute values close to 1.0
imply strong relationships; close to 0.0
imply weak (or no) relationships.
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.
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.
More on 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
Analysis
Correlation coefficients (rxy) describe both the
size and direction of the relationship between
two variables, x and y.
Positive correlations close to +1.0 indicate that two
variables are strongly positively related (scores on
one variable can be used to predict scores on the
other).
Negative correlations close to -1.0 indicate that the
two variables are strongly negatively correlated.
Again scores on one can be used to predict scores
on the other.
Analysis
Assuming all or most of the coordinates (points)
fall within the ellipse (of a scatter graph), the
figure below represents a weak (near zero)
correlation.
Analysis
This figure represents a weak positive
correlation:
Analysis
Here we have a strong positive correlation:
Analysis
This would be a representation of a weak
negative correlation.
Analysis
Finally, a graphic representation of a strong
negative correlation.
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
Var 2
Var 3
Var 4
1.00
.32
.78
.66
1.00
.89
.21
1.00
.11
1.00
A Table of Correlations
The lower triangular half.
Correlations Among Four Variables
Var 1
Var 2
Var 3
Var 1
1.00
Var 2
.32
1.00
Var 3
.78
.89
1.00
Var 4
.66
.21
.11
Var 4
1.00
A Table of Correlations
Often the diagonal is replaced by dashes.
Correlations Among Four Variables
Var 1
Var 2
Var 3
Var 1
---
Var 2
.32
---
Var 3
.78
.89
---
Var 4
.66
.21
.11
Var 4
---
How large should a
correlation be?
Correlations where Abs(rxy ) > .50 are
typically useful for prediction purposes
The square of the correlation coefficient
(rxy2) gives the percent of variation x
and y have in common.
The size of the correlation required in
order to be useful depends on the
purpose.
Statistical significance and
Practical significance
Correlation coefficients should not be
interpreted unless it is first shown that the
coefficient is statistically significant (i.e.,
until we can state that there is sufficient
statistical evidence that the correlation is
NOT zero).
With large enough samples, even small
correlations can be statistically significant.
Statistically significant correlations may not be
practically significant. A low correlation is
still a low correlation.
Linear correlations vs Curvilinear
correlations
The chart below indicates a correlation
between two variables that has a nearzero linear correlation but a strong
curvilinear correlation.
Causal-Comparative Research
Also called ex post facto research.
An attempt is made to find the cause or
explanation for existing differences
between (or among) groups.
Two or more existing groups are compared
retrospectively.
Note that in correlational research we had
one group and two or more variables. Here
we have two or more groups and one
variable.
Causal-Comparative research vs
Experimental research
In experimental research (or quasiexperimental research) the researcher
controls the administration of the
independent variable.
In causal-comparative research the groups
being formed have already been
differentiated according to the independent
variable (e.g., either they have been exposed
to pre-school or not).
Causal Comparative Research
Groups…
are classified according to common
preexisting characteristic, and
compared on some other measure
There is NO
intervention,
manipulation, or
random assignment
Major difficulty:
Establishing the cause.
Three conditions for establishing causeeffect relationships:
1.
The presumed cause must precede the
effect.
2. The relationship between the cause and
effect must be statistically significant.
3. Other probable causes must be eliminated
(most difficult condition to meet).
Spurious Causation
Here are two examples of
spurious causation.
In the top example, the
correlation between A and
C requires the mediator, B.
In the bottom example the
correlation between B and
C exists because both
variables are caused by A.
A
B
B
C
C
A
Reaching Conclusions
At best, causal-comparative research produces
evidence that supports a theoretical
conjecture.
The strength of evidence relies heavily on two
things:
1. The extent to which rival causes can be
ruled out.
2. The extent to which the results can be
predicted (according to theory) beforehand.
Conducting a
Causal-Comparative Study
Identify two or more populations (or groups)
that differ on some independent variable (IV)
of interest (e.g., novice teachers and veteran
teachers).
Formulate some theory about how the groups
should perform differently on some
dependent variable (DV) of interest (e.g.,
classroom management).
Select representative samples from the
populations and compare them on the
dependent variable.
Two Variations of Causal
Comparative Studies
There are two ways to approach causalcomparative research:
• Prospective: start with a presumed cause
an investigate effects (not very common in
social science/education research).
• Retrospective: start with a presumed
effect and investigate possible causes
(these are more prevalent in social
science/education research).
Examples of the Two Variations
Investigate the relationship between
gender and career aspirations or career
choice.
• Retrospective: Groups identified on the
basis of career choice and then compared
by gender.
• Prospective: Groups formed on the basis of
gender, and compared on strength of
career aspirations.
Examples of the Two Variations
Investigate the relationship of time
watching TV (the IV) on academic
achievement (the DV)
• Prospective: Form groups on the basis of how much
TV they watch and compare them on academic
achievement (say, GPA).
• Retrospective: Form groups on the basis of
academic achievement (say, class rank) and
compare this to hours of TV watched.
Examples of the Two Variations
Investigate the effect of time parents
spend reading to children and children’s
reading readiness when entering 1st
grade.
• Retrospective: Groups formed on the basis of a
reading-readiness test score, and compare in terms of
time parents spend reading to their children.
• Prospective: Form groups of children in terms of time
their parents spent reading to them and compare the
children on reading readiness scores.
Examples of the Two Variations
Investigate the effect of mentoring and
tendency to drop out of high school.
• Prospective: Groups formed on the basis of
whether they enjoyed a mentoring relationship
while in high school and compared in terms of
whether they dropped out of high school
• Retrospective: Groups formed on the basis of
whether they dropped out of high school, and
compared on whether they enjoyed a mentoring
relationship prior to dropping out.
Example Causal-Comparative
Study: What causes lung cancer?
Finding: People with lung cancer smoke
more than people without lung cancer.
There are no other differences in
lifestyle characteristics between the
groups.
Conclusion: Smoking is a possible cause of
lung cancer.
Caution: Is there a third factor that
might explain lung cancer AND smoking?
Weaknesses and Controls
Lack of randomization, inability to manipulate
the independent variables, lack of controls
of extraneous variables are all weaknesses
in causal-comparative research.
Three approaches that help ameliorate some of
the problems are:
1. Matching,
2. Comparing homogeneous groups, and
3. Analysis of covariance (to be discussed
later).
Strengthening Causal
Comparative Designs
Strong inference (theory plays a major role).
Time sequence (presumed cause precedes
presumed effect).
Incorporate other, possible, causes in the
design (measure common antecedents) .
Use designs that control for possibl extraneous
causes:
• matched group design
• Extreme groups design
• Statistical control (Analysis of Covariance)
Establishing Causal Relationships
From John Stuart Mills
• Establish a temporal sequence (the presumed cause
must precede the presumed effect).
• Establish a statistical relation ship between the
presumed cause and effect (correlations among
variables or differences among groups).
• Rule-out possible rival causes (control for, or
eliminate extraneous sources of influence).
• This is often the most difficult condition.
• Strong theory plays an important role here.
Wide Variety of Statistical
Procedures
t tests, ANOVA, ANCOVA when two or more
groups are being compared.
Regression analysis when there are multiple
independent variables.
MANOVA, and multivariate regression, when
there are multiple dependent variables.
Path analysis and structural equation modeling
when the theoretical causal paths are being
investigated.
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Correlational and Causal Comparative Research