2. Correlational Research
Designs
Correlational studies may be used to
A. Show relationships between two
variables there by showing a cause and
effect relationship
B. show predictions of a future event or
outcome from a variable
3. Types of Correlation studies
1. Observational Research e.g. class
attendance and grades
2.Survey Research e.g. living together
and divorce rate
3. Archival Research e.g.violence and
economics
4. Advantages of the
correlational method
1. It allows the researcher to analyze
the relationship among a large number
of variables
2. Correlation coefficients can provide
for the degree and direction of
relationships
5. Planning a Relationship Study
Purpose to identify the cause and effects of
important phenomena
Method
1. Define the problem
2. Review existing literature
3. Select participants who can have
measurable variables-reasonably
homogeneous
4. Collect data-test, questionnaires,
interviews, &etc.
5. Analysis of data
6. What do correlations
measure?
Correlations measure the association, or co-
variation of two or more dependent variables.
Example: Why are some students
aggressive?
Hypothesis: Aggression is learned from
modeling
Test: Look for associations between
aggressive behavior and…
7. Interpreting Correlations
Scattergram- a pictorial representation
of correlations between two variables
Use of a scattergram
An x and y axes are produced
perpendicular to each other
Results of correlates are plotted
The relationship of these plots are
interpreted
8. Interpreting Correlations
continued
The amount of correlation is expressed as r=
The r scores can range from –1 to 1
If r= 1 there is said to be perfect correlation
with the other variable
An r score of 0 shows no relationship
If r= -1 there is a lack of relationship between
the two variables
Anything between 1 and –1 shows a varying
degrees of relationships
9. Interpreting Correlations
Continued
The expression r squared = the percent of
variation accounted for between the relations
between two variables like x and y this is
called the explained variance
Example: correlation between G.P.A. scores
and A.C.T. if r=.6 then r squared =.36 so the
per cent of accuracy is 36% in predicting
A.C.T. scores from the person G.P.A.
A complete interpretation would include
attempts to explain nonsignificant results
10. Other measures of interest in
Correlational Studies
R is multiple correlation (0 to 1)
(b) is regression weight which is a
multiplier added to a predictor variable
to maximize predictive value
B is beta weight which is used in a
multiple regression equation to
establish the equation in a standard
score form
11. Correlation and Causality
If there is no association between two
variables, then there is no causal connection
Correlation does not always prove causation
a third variable may have the causal relation
example: Women surveyed during pregnancy
that smoked correlated with arrest of their
sons 34 years later. Is a third variable the
cause. Other variables- socioeconomic
status, age, father’s or mother’s criminal
history, Parent’s psychiatric problems
12. Use of causal-comparative
approach
However, when comparing two
variables sometimes inference may be
made that one causes the other.
Only an experiment can provide a
definitive conclusion of a cause and
effect relationship.
13. Limitations of Relationship
Studies
Researcher tend to break down
complex patterns into two simple
components.
Researcher identify complex
components that interest them but
could probably be achieved in many
different ways.
14. Ways to fix problems of
correlational Design
Add more variables to the model
Replicate design
Convert question to the experimental
design
15. Prediction Studies
A variable whose value is being used to
predict is known as the predictor
variable
A variable whose value is being
predicted is the criterion variable.
The aim of prediction studies is to
forecast academic and vocational
success.
16. Types of Information provided
in a prediction study
The extent to which a criterion pattern
can be predicted
Data for developing a theory for
determining criterion patterns
Evidence about predicting the validity of
a test
17. Basic Design of Prediction
Studies
The problem-reflect the type of information
you are trying to predict
Selection of research participants- draw from
population most pertinent to your study
Data collection-predictor variables must be
measured before criterion patterns occur
Data Analysis- correlate each predictor
variable with the criterion
18. Definitions useful in Prediction
Studies
Bivariate correlational statistics- express the
magnitude of relationships between two
variables
Multiple regression- uses scores on two or
more predictor variables to predict
performance of criterion variables. The
purpose is to determine which variables can
be combined to form the best prediction of
each criterion variable.
19. Multiple Regression Facts
Too large of a sample may cause faulty
data to occur
15 to 54 people should be sampled per
variable used.
20. Statistical Factors in
Prediction Research
Prediction research in useful for
practical purposes
Definitions- selection ratio- proportion of
the available candidates that must be
selected
Base rate- percentage of candidates
who would be selected without a
selection process
21. Statistical Factors in
Prediction Research cont.
Taylor-Russell Tables- a combination of three
factors; predictive validity, selection ratio, and
base rate (If these three factors are present
the researcher should be able to predict the
proportion of candidates that will be
successful)
Shrinkage- The tendency for predictive
validity to decrease when research is
repeated
22. Techniques used to analyze
Bivariates
Product-Moment Correlation- Used
when both variables are expressed as
continuous scores
Correlation Ratio- Used to detect
nonlinear relationships
23. Part and Partial Correlation
This is an application employed to rule
out the influence of one or more
variables upon the criterion in order to
clarify the role of the other variables.
25. Correlation Coefficient
It measures the magnitude of the relationship
between a criterion variable and some
combination of predictor variables
Correlation coefficient of determination
equals R squared. This expresses the
amount of variance that can be explained by
a predictor variable of a combination of
predictor variables
26. Correlation Coefficient
Determinates cont.
R can range from 0.00 to 1.00. The
larger R is the better the prediction of
the criterion variable.
There is more statistical significance if
the R squared value is significantly
different from zero.
27. Canonical Correlations
Is when there is a combination of
several predictor variables used to
predict a combination of several
criterion variables
28. Path Analysis
Isa method of measuring the validity of
theories about causal relationships
between two for more variables that
have been studied in a correlational
research design
29. Steps of Path Anaylsis
Formulate a hypothesis that causally link the
variables of interest
Select or develop measures of the variables
that are specified by the hypothesis
Compute statistics that show the strength of
relationship between each pair of variables
that are causally linked in the hypothesis
Interpret to determine if they support the
theory
30. Correlation Matrix
Isan arrangement of row ad columns
that make it easy to see how measured
variables in a set correlate with other
variables in the set
31. Structural Equation Modeling
Is a method of multivariate analysis that
test causal relationships between
variables and supplies more reliable
and valid measures than path analysis
It is also called LISREL which stands for
Analysis of Linear Structural
Relationships
32. Differential Analysis
This is subgroup analysis in relationship
studies
This application is used when the
researcher believes that correlated
variables might be influenced by a
particular factor. Then subjects from the
sample are selected who have this
characteristic
33. Moderator Variables in a
prediction Study
There are times when a certain test is
more valid in predicting a subgroups
behavior. The variable that is used in
this instance is called a moderator
variable