Correlational and Causal Comparative Research

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


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



Var 1 1.00 .32 .78 .66

Var 2 1.00 .89 .21

Var 3 1.00 .11

Var 4 1.00


The lower triangular half.



Var 1 1.00

Var 2 .32 1.00

Var 3 .78 .89 1.00

Var 4 .66 .21 .11 1.00


Often the diagonal is replaced by dashes.



Var 1 - - -

Var 2 .32 - - -

Var 3 .78 .89 - - -

Var 4 .66 .21 .11 - - -

How large should acorrelation be?

Correlations where Abs(rxy ) > .50 are typically useful for prediction purposes

The square of the correlation coefficient (rxy

2) 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 andPractical 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 near- zero 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 quasi-experimental 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 cause-effect 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 CausationHere 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 C

A

B C

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 aCausal-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 causal-comparative 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.


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.


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.


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, and3. 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