Correlation

Nabaz N. Jabbar Near East University

25 Oct 2011

Definition of correlation

• Correlational research determines

to what degree a relationship

exists between 2 variables (or

more variables).

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.

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.

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).

Three Sets of Data Showing Different Directions and Degrees of

Correlation

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

(A) (B) (C) r = +1.00 r = -1.00 r = 0

A positive correlation

x

y

A negative correlation

x

y

No correlation

x

y

No correlation

x

y

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 studies2. Prediction studies3. More complex correlational techniques

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.

Prediction Using a Scatterplot

More Complex Correlational Techniques

o Multiple Regressiono Coefficient of multiple correlation(R)o Coefficient of Determinationo Discriminant Function Analysiso Factor Analysiso Path Analysiso Structural Modeling

More Complex Correlational Techniques

• Multiple RegressionTechnique 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

More Complex Correlational Techniques

• Coefficient of DeterminationIndicates the percentage of the variability

among the criterion scores that can be attributed to differences in the scores on the predictor variable.

• Discriminant Function AnalysisRather than using multiple regression, this

technique is used when the criterion value is categorical.

More Complex Correlational Techniques

• Factor AnalysisAllows the researcher to determine whether many

variables can be described by a few factors.• Path AnalysisUsed to test the likelihood of a causal connection

among three or more variables.• Structural ModelingSophisticated method for exploring and possibly

confirming causation among several variables.

Path Analysis Diagram

Correlation coefficient

• A decimal number between .00 and +1.00 or –1.00 that indicates the degree to which two quantitative variables are related.

0.00 +1.00-1.00

no relationshipstrong positivestrong negative

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

Threats to Internal Validityin 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

Partial Correlation

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

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