Correlation is a statistical technique used to determine the degree of relationship between two variables. Correlational research aims to identify and describe relationships but does not imply causation. Positive correlation indicates high scores on one variable are associated with high scores on the other, while negative correlation means high scores on one variable are associated with low scores on the other. Correlational research can be used for explanatory or predictive purposes. More complex techniques like multiple regression allow prediction using combinations of variables. Threats to internal validity like subject characteristics must be controlled.

1. Correlation
Nabaz N. Jabbar
Near East University
25 Oct 2011

2. Definition of correlation
• Correlational research determines
to what degree a relationship
exists between 2 variables (or
more variables).

3. The nature of correlational research
• Associational research: When the
relationships among two or more
variables are studied without any
attempt to influence them. (The
same as correlation and causal
comparative research).
• Experimental research: Differs from
correlational research in that
there’s manipulation of variables.

4. The nature of correlational research
• Correlational research is also
sometimes referred to as a form of
descriptive research because it
describes an existing relationship
between variables.

5. The nature of correlational research
• Positive correlation means that
high scores on one variable (X) tend
to be associated with high scores
on the other variable (Y).
• Negative Correlation means that
high scores on one variable (X) are
associated with low scores on the
other variable (Y).

6. Three Sets of Data Showing
Different Directions and Degrees of
Correlation
(A) (B) (C)
r = +1.00 r = -1.00 r=0
X Y X Y X Y
5 5 5 1 2 1
4 4 4 2 5 4
3 3 3 3 3 3
2 2 2 4 1 5
1 1 1 5 4 2

7. A positive correlation
y
x

8. A negative correlation
y
x

9. No correlation
y
x

10. No correlation
y
x

11. Purposes of Correlational Research
• Correlational studies are carried out to
explain important human behavior or to
predict likely outcomes. (identify
relationships among variables).
1. Explanatory studies
2. Prediction studies
3. More complex correlational techniques

12. Explanatory studies
• To identify relationships among variables.
Prediction studies
• If a relationship of sufficient magnitude exists
between two variables, it becomes possible to
predict score on one variable when score on
related variable is known.
1. Predictor variable: The variable that is used
to make the prediction.
2. Criterion variable: The variable about which
the prediction is made.

13. Prediction Using a Scatterplot

14. More Complex Correlational
Techniques
o Multiple Regression
o Coefficient of multiple correlation(R)
o Coefficient of Determination
o Discriminant Function Analysis
o Factor Analysis
o Path Analysis
o Structural Modeling

15. More Complex Correlational
Techniques
• Multiple Regression
Technique that enables researchers to
determine a correlation between a criterion
variable and the best combination of two or
more predictor variables.
• Coefficient of multiple correlation(R)
Indicates the strength of the correlation
between the combination of the predictor
variables and the criterion variable

16. More Complex Correlational
Techniques
• Coefficient of Determination
Indicates the percentage of the variability
among the criterion scores that can be
attributed to differences in the scores on the
predictor variable.
• Discriminant Function Analysis
Rather than using multiple regression, this
technique is used when the criterion value is
categorical.

17. More Complex Correlational
Techniques
• Factor Analysis
 Allows the researcher to determine whether many
variables can be described by a few factors.
• Path Analysis
 Used to test the likelihood of a causal connection
among three or more variables.
• Structural Modeling
 Sophisticated method for exploring and possibly
confirming causation among several variables.

18. Path Analysis Diagram

19. Correlation coefficient
• A decimal number between .00 and +1.00 or
–1.00 that indicates the degree to which two
quantitative variables are related.
-1.00 0.00 +1.00
strong negative strong positive
no relationship

20. Basic Steps in Correlational
Research
 Problem selection
 Choosing a sample
 Selecting or choosing proper instruments
 Determining design and procedures
 Collecting and analyzing data
 Interpreting results

21. Threats to Internal Validity
in Correlational Research
• Subject characteristics
• Mortality
• Location Instrument decay
• Instrumentation Data collector bias
• Testing Data collector characteristics
• The following must be controlled to reduce
threats to internal validity

22. Partial Correlation
• A method of controlling
the subject
characteristics threat in
correlational research
by statistically holding
one or more variables
constant.

23. References
• Cohen, L., & Manion, L. (1985). Research methods
in education. Sydney.
• Fraenkel, J., R., & Wallen, N., E., (1990). How to
design and evaluate research in education. New
York.
• http:// www. mcgraw-hill.com
• http://www. gandrewpage.com
• http://www. capilanou.ca