1. Research Designs
Correlational
By Mike Rippy

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.

24. Multivariate correlational
Statistics
 These are used when examining the
interrelationship of three or more
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