Correlational and Causal Comparative Research

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Correlational and Causal Comparative Research
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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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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.

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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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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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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

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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.

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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.

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Analysis

• This figure represents a weak positive
  correlation

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Analysis

• Here we have a strong positive correlation

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Analysis

• This would be a representation of a weak negative
  correlation.

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Analysis

• Finally, a graphic representation of a strong
  negative correlation.

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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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How large should acorrelation be?

• Correlations where Abs(rxy ) gt .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.

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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.

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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.

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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.

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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).

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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

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Major difficulty Establishing the cause.

• Three conditions for establishing cause-effect
  relationships
• The presumed cause must precede the effect.
• The relationship between the cause and effect
  must be statistically significant.
• Other probable causes must be eliminated (most
  difficult condition to meet).

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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
C
B
C
A
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Reaching Conclusions

• At best, causal-comparative research produces
  evidence that supports a theoretical conjecture.
• The strength of evidence relies heavily on two
  things
• The extent to which rival causes can be ruled
  out.
• The extent to which the results can be predicted
  (according to theory) beforehand.

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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.

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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).

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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.

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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.

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Examples of the Two Variations

• Investigate the effect of time parents spend
  reading to children and childrens 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.

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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.

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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?

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More Examples of Causal Comparative Research

• A researcher measured the mathematical reasoning
  ability of young children who had enrolled in
  Montessori schools and compared the scores with a
  group of similar children who had not been to
  Montessori schools.
• A researcher measured the frequency of students
  misbehavior at schools which use corporal
  punishment and compared the frequency to schools
  which did not use corporal punishment.

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More Examples of Causal Comparative Research

• A researcher compared the high school dropout
  rate among students who had been retained (held
  back) in elementary school with similar students
  who had not been retained
• A researcher formed 3 groups of preschoolers
  those who never watched Sesame Street, those who
  watched it sometimes, and those who watched it
  frequently and then compared the 3 groups on a
  reading readiness test.

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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
• Matching,
• Comparing homogeneous groups, and
• Analysis of covariance (to be discussed later).

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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)

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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.

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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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• END