Educational Research: Correlational Studies

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Educational Research Correlational
Studies
EDU 8603 Educational Research Richard M. Jacobs,
OSA, Ph.D.
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Research...

• The systematic application of a family of methods
  employed to provide trustworthy information about
  problems

an ongoing process based on many accumulated
understandings and explanations that, when taken
together lead to generalizations about problems
and the development of theories
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The basic steps of research...
Scientific and disciplined inquiry is an orderly
process, involving
? recognition and identification of a topic to
be studied (problem)
? description and execution of procedures to
collection information (method)
? objective data analysis
? statement of findings (results)
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Research methods...
Quantitative
collects and analyzes numerical data obtained
from formal instruments
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Quantitative methods...

• descriptive research (survey research)

• correlational research

• causal-comparative research (ex post facto
  research)

• experimental research

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• correlational research

determines whether and to what degree a
relationship exists between two or more
quantifiable variables
the degree of the relationship is expressed as a
coefficient of correlation
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the presence of a correlation does not indicate
a cause-effect relationship primarily because of
the possibility of multiple confounding factors
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A correlation study
a study providing a numerical estimate?the
correlation coefficient?about the relationship
between two or more variables
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Types of correlation studies

• relationship studies

attempt to gain insight into variables that are
related to more complex variables

• prediction studies

conducted to facilitate decisions about
individuals, to aid in various types of
selection, to test variables believed to be good
predictors of a criterion, or to determine
predictive validity of measuring instruments
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Conducting a correlational study
1. select the problem
2. select participants and instrument
3. design and procedure
4. data analysis and interpretation
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1. select the problem
the variables to be correlated should be
selected on the basis of some rationale
a shotgun or fishing approach is discouraged
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2. select participants and instrument
using an acceptable sampling methodology, a
minimum of 30 participants is acceptable
larger samples are used if validity and
reliability are important because error
measurement may mask the true relationship
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3. design and procedure
two or more scores are obtained for each member
of the sample, one score for each variable of
interest, and the paired scores are then
correlated
the result is expressed as a correlation
coefficient
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4. data analysis and interpretation
the two or more scores are obtained for each
member of the sample, one score for each variable
of interest, and the paired scores are then
correlated
the correlation coefficient indicates the degree
of relationship between the variables of interest
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Correlation coefficient
-1.00
1.00
0.00
strong positive
strong negative
no relationship
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A positive correlation
y
x
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A negative correlation
y
x
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No correlation
y
x
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No correlation
y
x
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• statistical significance

a statement that the relationship between the
variables, at a given level of probability (a,
alpha), are truly related
is dependent upon the sample size
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Conducting relationship studies
Follows the procedure for correlational studies
with two adaptations
1. data collection
2. data analysis and interpretation
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relationship studies
attempt to gain insight into variables that are
related to complex variables
indicate whether causal-comparative and
experimental studies may determine a causal
connection between the variables
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1. select the problem
the variables to be correlated should be
selected on the basis of some rationale
identify an appropriate population of
participants from which to sample
if needed, administer instrument to collect data
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2. data analysis and interpretation
the scores for one variable are correlated with
the scores for another variable and expressed in
the form of a correlation coefficient
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• The method for computing a correlation
  coefficient

depends upon the type of data represented by
each variable
types of data
nominal (dichotomous)
interval (continuous)
ordinal (rank)
ratio (continuous)
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• with continuous data

use the product moment correlation, Pearson r
(?, rho)

• with rank data

use the rank difference correlation, Spearman r
(?, rho)
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• with dichotomous data

use the phi correlation (?)

• with curvilinear data

use the eta correlation (?)
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Conducting prediction studies
Follows the procedure for correlational studies
with two adaptations
1. data collection
2. data analysis and interpretation
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predictive studies
when two variables are highly related, scores on
one variable can be used to predict scores on the
other variable
facilitate decisions about individuals or to aid
in various types of selection
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predictor variable
the variable used to predict
criterion variable
the variable predicted
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1. data collection
valid measuring instruments should be carefully
selected to represent the variables of interest
it is especially important that the measure used
as the criterion variable be valid
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2. data analysis and interpretation
single prediction studies use one predictor
multiple prediction studies use more than one
predictor
in both, a continuous predictor variable is used
to predict a continuous criterion variable
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• single prediction studies

Y a bX Where Y predictor criterion
X an individuals score on the
predictor variable a a constant
calculated from the scores of all participants
b the coefficient indicating the
contribution of the predictor to the criterion
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• multiple prediction studies

use multiple predictors
Y a bX1 bX2 bXn Where Y
predictor criterion Xn an
individuals score on the predictor variable
a a constant calculated from the
scores of all participants b the
coefficient indicating the contribution of the
predictor to the criterion
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• discriminant function analysis

similar to multiple regression analysis but a
continuous predictor variable is used to predict
a categorical variable
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• path analysis

studies relationships and patterns among a
number of variables, yielding a diagram showing
the direct or indirect relationships between the
variables
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• structural equation modeling

a sophisticated form of path analysis providing
greater theoretical validity and statistical
precision clarifying the direct or indirect
interrelationships among variables relative to a
given variable
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• canonical correlation

an extension of multiple regression analysis
that produces a correlation based on a group of
predictor variables and a group of criterion
variables
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• factor analysis (FANOVA)

a statistical method for making sense of a large
number of variables
approach group a larger number of variables
into a smaller number of clusters derive factors
by finding groups of variables that are highly
among each other, but lowly with other variables
use factors as variables
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Mini-Quiz

• True and false

a high degree of correlation between two
variables implies that one causes the other
False
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the existence of a high negative correlation
permits prediction
True
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the correlation coefficient indicates the
percentage of relationship between the variables
False
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the correlation coefficient indicates the amount
of common variance shared by the variables
True
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common, or shared, variance indicates the extent
to which variables vary in a systematic way
True
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the more systematically two variables vary, the
lower the correlation coefficient
False
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the amount common, or shared, variance is much
less than the numerical value of the correlation
coefficient
True
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for a given sample size, the value of the
correlation coefficient needed for significance
increases as the level of confidence increases
True
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the level of significance indicates the
probability that a given relationship is a true
one, regardless of whether it is a strong or weak
relationship
True
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a statistically significant correlation
coefficient establishes a cause-effect
relationship
False
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relationship studies that have not uncovered
useful relationships have at least identified
variables that can be excluded from future
studies, which is a necessary step in science
True
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the more correlation coefficients computed at
one time, the more likely it is that some wrong
conclusions about the existence of a relationship
will be reached
True
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an appropriate population is one for which the
data on each of the identified variables can be
collected
True
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an artificial dichotomy is one where ordinal,
interval, or ratio data are artificially turned
into nominal data
True
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most correlational techniques assume that the
relationship being investigated is linear
True
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a correction for unreliability should be used in
prediction studies
False
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the greater the variability there is in each set
of scores being correlated, the higher the
correlation coefficient is likely to be
True
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in a prediction study, it is especially
important that the measure used as the criterion
be reliable
False
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one reason for shrinkage is that an initial
predictor equation may be the result of chance
relationship that will not be found again with
another group of participants
True
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the mathematical expression of the degree of
relationship between variables
correlation coefficient
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• Fill in the blank

a research strategy in which the researcher
correlates all sorts of variables to discover
relationships
shotgun or fishing approach
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indicates that an obtained correlation
coefficient is really different from a
correlation of zero, or no relation, usually
stated at a given level of probability
statistical significance
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a type of study in which a researcher identifies
variables that are correlated with the dependent
variable and removes their influence so that they
will not be confused with that of the independent
variable
relationship study
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a chart on which the variables to be correlated
are placed which provides a visual representation
of their relationship
scatter plot
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a relationship between variables in which an
increase in one variable is associated with a
corresponding increase in another variable up to
a point, at which further increases in the first
variable result in corresponding decreases in the
other variable (or vice versa)
curvilinear
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the fact that correlation coefficients tend to
be lowered if the measures being correlated have
low reliability
attenuation
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the variable used to predict
predictor
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the variable that is predicted
criterion
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the tendency of a prediction equation to become
less accurate when used with a group other than
the one on which the equation was originally
developed
shrinkage
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the procedure by which a prediction equation is
validated with at least one other group and the
variables no longer found to be related to the
criterion measure are removed from the equation
cross-validation
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the equation used in a multiple prediction study
multiple regression equation
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This module has focused on...
correlational studies
which involve collecting data in order to
determine whether, and to what degree, a
relationship exists between two or more
quantifiable variables
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The next module will focus on...
causal-comparative studies
...which attempt to determine the cause, or
reasons for pre-existing differences in groups of
individuals