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# Correlation

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### Correlation

1. 1. Correlation Nabaz N. Jabbar Near East University 25 Oct 2011
2. 2. Definition of correlation• Correlational research determines to what degree a relationship exists between 2 variables (or more variables).
3. 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. 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. 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. 6. Three Sets of Data ShowingDifferent 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. 7. A positive correlation y x
8. 8. A negative correlation y x
9. 9. No correlationy x
10. 10. No correlationy x
11. 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 studies2. Prediction studies3. More complex correlational techniques
12. 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. 13. Prediction Using a Scatterplot
14. 14. More Complex Correlational Techniqueso Multiple Regressiono Coefficient of multiple correlation(R)o Coefficient of Determinationo Discriminant Function Analysiso Factor Analysiso Path Analysiso Structural Modeling
15. 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. 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. 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. 18. Path Analysis Diagram
19. 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. 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. 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. 22. Partial Correlation• A method of controlling the subject characteristics threat in correlational research by statistically holding one or more variables constant.
23. 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