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Correlational Research
Stephen E. Brock, Ph.D., NCSP
California State University, Sacramento
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Correlational Research
A quantitative methodology used to determine whether,
and to what degree, a relationship exists between two or
more variables within a population (or a sample).
The degree of relationships are expressed by correlation
coefficients.
Coefficients range from +1.00 to -1. Higher correlations (coefficients closer to +1.00 or -1.00) indicate stronger relationships.
Positive correlations indicate that as the values associated
with one variable go up, so do the values associated with
the other.
e.g., higher grades are associated with higher ???.
Negative correlations indicate that as the values
associated with one variable go up, the values associated
with the other go down
e.g., higher grades are associated with lower ???.
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Correlational Research:
Scatter Plots
http://www.mste.uiuc.edu/courses/ci330ms/youtsey/scatterinfo.html
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Correlational Research:
Scatter Plots
http://www.mste.uiuc.edu/courses/ci330ms/youtsey/scatterinfo.html
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Portfolio Activity # 7: Mini-proposal 2
Briefly describe a correlational research
project relevant to one of your identified
research topics.
Small group discussion
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Correlation vs. Causation
A researcher found that there was a +0.
correlation between the variable of height and
Mental Age among a random sample of 100
individuals.
From these data the researcher determines
that taller people are smarter than shorter
people.
What do you think?
Interpret this finding.
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Correlation vs. Causation
Even a perfect correlation does not necessarily
imply a causal connection between variables.
For example, in a recent CDE study, the number of
support staff in school districts was positively
correlated with poor attendance.
An educational research example:
Attention span is highly correlated with reading
comprehension test scores.
But both are also correlated with basic reading skill.
The correlation may be the result of a mutual
association with these other variables.
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Correlation vs. Causation
Attention Deficits
Reading Comprehension
Basic Reading Skill
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Correlation vs. Causation
A statistically significant relationship
(correlation) is a necessary, but not sufficient
condition when determining causation.
Must be able to document that the causal
variable occurred first and that all other
factors are accounted for.
Experiments are typically necessary to
determine causation.
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Types of Correlational Studies
Descriptive
Used to simply describe relationships.
Often a precursor to the experimental study. Variables suggested to be related would be the subject of further study. Also helps to identify variables that need to be controlled during an experiment. e.g., basic reading skill in a study of the effects of ADHD on reading comprehension. Hypotheses, if offered, are often non- directional.
Predictive
Hypotheses are directional
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The Correlational Research Process
1. Problem selection
Variables to be correlated should be selected based
on
a) A logical relationship b) Theoretical grounds c) Personal experience What are some examples of problems (or questions) that are consistent with these three bases for correlational research?
Correlational “treasure hunts” (AKA “the shotgun
approach”) are strongly discouraged.
What does r = .50, p = .05 mean? r = strength of the relationship ( actually it is r 2 or 25% of variance) p = significance of the relationship ( how unlikely a given r value will occur given NO relationship in the population, 5% chance of an r of .50 if there is no real relationship between variable in the population )
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2. Select/Obtain Participants
Sample from the population so as to maximize
generalizability.
What are examples of preferred sampling techniques?
At least 30 participants.
If you are dealing with a sample and the correlation between two variables is r = .05, p = .50, what would you say about the relationship? If you are dealing with a population and the correlation between two variables is r = .05, what would you say about the relationship?
The Correlational Research Process
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5. Conduct Data Analysis (continued)
Correlation’s significance vs. its strength.
Just because a correlation is significant does not mean it is high enough to reflect an important relationship.
Variance (the correlation coefficient squared)
“When two or more variables are correlated, each variable will have a range of scores. Each variable will have some variance; that is not everyone will get the same score. Common or shared variance indicates the extent to which variables vary in a systematic way” (pp. 314-315). r^2 is the amount of variance explained (or accounted for) by the correlation coefficient. Determine the amount of variance accounted for by the following r values: 1.0, .95, .75, .50,. http://www.calculator.org/jcalc98.html
The Correlational Research Process
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Relationship Studies
Often used to study complex variables before
beginning an experiment.
To identify variables (other than the independent
variable) that correlate with the dependent measure.
When relationships are identified these variables are
then controlled for.
For example, before studying how a given IV (like ADHD symptom severity) influences reading comprehension you would want to identify other variables (such as word reading, word attack, vocabulary, background knowledge) that also affect reading comprehension and then control for them. How would this be done?
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Relationship Studies
Why is it important to be selective when
identifying variables to be correlated?
What problems might arise if you used a “shotgun
approach” and obtained correlations among 100
randomly selected variables and you used a p
value of .05?
Chances are that 5 of the obtained coefficients will
not reflect a true relationship greater than zero.
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Prediction Studies
Regression Analysis
A method of analyzing the variability of a criterion
variable by examining information available on
one or more predictor variables.
When only one predictor variable is used, the
analysis is referred to as simple regression. When
more than one predictor is used, the analysis is
referred to as multiple regression
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Simple Regression
A college football coach wishes to use the
scores on one variable to predict the scores
on another variable.
He wishes to determine the best prediction
equation for the grade-point averages of
potential freshmen recruits.
SAT test scores for the current group of
recruits as well as their grade point averages
are available.
From the available SAT and GPA scores for
this year’s class, the prediction equation for
next year’s class can be calculated.
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Simple Regression
A teacher wishes to determine the effects of
hours of study (the predictor variable) on
vocabulary test performance (the criterion
variable).
When vocabulary test means associated with
different amounts of study differ from each
other and lie on a straight line, it is said that
there is a simple linear regression of
vocabulary test performance on hours of
study
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Types of Statistical Correlations
Partial Correlations
If you have three variables and you wish to know how highly two of them are related when the mutual relationships with the third variable are taken out (“partialed out”), use partial correlation.
Height r^ = .835 M.A.
(A spurious correlation?)
Age
After partialing out Age this correlation dropped to .219. This is an example of statistical control. What might be another variable to partial out? What might be another way to control for the Age?
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Types of Statistical Correlations
Multiple Correlations
If you have three variables and you wish to know how highly two of them, taken together, are related to the third, use multiple correlation. Reading Achievement (^) Phonological awarenessReading Speed +
In a typical multiple-correlation study, the first set of numbers represents measures of a criterion variable (e.g., reading achievement) and the other two sets of numbers are measures of predictors (e.g., reading speed and sound awareness). The multiple-correlation coefficient between the criterion variable and the two predictor variables will give an indication of the degree to which the two predictors, taken together, actually predict the criterion Questions: What is the difference between prediction and causation?
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Next Meeting:
Causal Comparative and Experimental
Research
Read Educational Research Chapters
Portfolio Element #8 Due:
Mini-proposal 3
Week after next, April 2
Portfolio Element #9 Due:
Mini-proposal 4
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Portfolio Activity # 8
Mini-proposal 3
Students will briefly describe a causal
comparative research project relevant to
one of their identified research topics.
Chapter 10 provide guidance necessary to
complete this mini-proposal.
