Correlation study

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Educational Research:
Correlational Studies
Compiled by: Dr.V.Singh
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
E-Content- Module 10- Research Methods and Statistics.
SXCE, Patna

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The basic steps of research...
Scientific and disciplined inquiry is an
orderly process, involving:
 description and execution of
procedures to collection information
(“method”)
 objective data analysis
 statement of findings (“results”)
 recognition and identification of a
topic to be studied (“problem”)
Research methods...
Quantitative…
…collects and analyzes numerical data
obtained from formal instruments
SXCE, Patna

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Quantitative methods...
 descriptive research (“survey research”)
 correlational research
 causal-comparative research
(“ex post facto research”)
 experimental research
 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
SXCE, Patna

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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
A correlation study…
…a study providing a numerical
estimatethe correlation
coefficientabout the relationship
between two or more variables
SXCE, Patna

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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 Compiled by: Dr.V.Singh
Conducting a correlational study…
1. select the problem
2. select participants and instrument
3. design and procedure
4. data analysis and interpretation
SXCE, Patna

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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
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
SXCE, Patna

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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
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
SXCE, Patna

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Correlation coefficient…
-1.00 +1.00
strong negative strong positive
0.00
no
relationship
A positive correlation…
y
x
SXCE, Patna

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A negative correlation…
y
x
No correlation…
y
x
SXCE, Patna

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No correlation…
y
x
 statistical significance…
…a statement that the relationship
between the variables, at a given
level of probability (α, alpha), are
truly related
…is dependent upon the sample size
SXCE, Patna

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Conducting relationship studies…
Follows the procedure for correlational
studies with two adaptations…
1. data collection
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
SXCE, Patna

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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
…the scores for one variable are
correlated with the scores for
another variable and expressed in
the form of a correlation coefficient
SXCE, Patna

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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)
ordinal (rank)
interval (continuous)
ratio (continuous)
 with continuous data…
…use the product moment correlation,
Pearson r (ρ, rho)
 with rank data…
…use the rank difference correlation,
Spearman r (ρ, rho)
SXCE, Patna

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 with dichotomous data…
…use the phi correlation (ψ)
 with curvilinear data…
…use the eta correlation (η)
Conducting prediction studies…
Follows the procedure for correlational
studies with two adaptations…
1. data collection
SXCE, Patna

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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
predictor variable…
…the variable used to predict
criterion variable…
…the variable predicted
SXCE, Patna

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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
…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
SXCE, Patna

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 single prediction studies…
Y = a + bX
Where Y = predictor criterion
X = an individual’s 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
 multiple prediction studies…
…use multiple predictors
Y = a + bX1 + bX2 + … + bXn
Where Y = predictor criterion
Xn = an individual’s 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
SXCE, Patna

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 discriminant function analysis
…similar to multiple regression
analysis but a continuous predictor
variable is used to predict a
categorical variable
 path analysis
…studies relationships and patterns
among a number of variables,
yielding a diagram showing the
direct or indirect relationships
SXCE, Patna

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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
 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
SXCE, Patna

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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 Compiled by: Dr.V.Singh
Mini-Quiz…
 True and false…
…a high degree of correlation between
two variables implies that one
causes the other
False
SXCE, Patna

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…the existence of a high negative
correlation permits prediction
True
the percentage of relationship
False
SXCE, Patna

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the amount of common variance
shared by the variables
True
…common, or shared, variance
indicates the extent to which
variables vary in a systematic way
True
SXCE, Patna

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…the more systematically two
variables vary, the lower the
False
…the amount common, or shared,
variance is much less than the
numerical value of the correlation
coefficient
True
SXCE, Patna

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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
…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
SXCE, Patna

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…a statistically significant correlation
coefficient establishes a cause-effect
relationship
False
…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
SXCE, Patna

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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
…an appropriate population is one for
which the data on each of the
identified variables can be collected
True
SXCE, Patna

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…an artificial dichotomy is one where
ordinal, interval, or ratio data are
artificially turned into nominal data
True
…most correlational techniques
assume that the relationship being
investigated is linear
True
SXCE, Patna

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…a correction for unreliability should
be used in prediction studies
False
…the greater the variability there is in
each set of scores being correlated,
the higher the correlation coefficient
is likely to be
True
SXCE, Patna

29
…in a prediction study, it is especially
important that the measure used as
the criterion be reliable
False
…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
SXCE, Patna

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…the mathematical expression of the
degree of relationship between
variables
…a research strategy in which the
researcher correlates all sorts of
variables to discover relationships
shotgun or fishing approach
 Fill in the blank…
SXCE, Patna

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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
…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
SXCE, Patna

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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
…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
SXCE, Patna

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…the fact that correlation coefficients
tend to be lowered if the measures
being correlated have low reliability
attenuation
…the variable used to predict
predictor
SXCE, Patna

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…the variable that is predicted
criterion
…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
SXCE, Patna

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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
…the equation used in a multiple
prediction study
multiple regression equation
SXCE, Patna

Correlation study

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