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# Correlational Studies * Dr. A. Asgari

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### Correlational Studies * Dr. A. Asgari

1. 1. CORRELATIONAL RESEARCH Dr. Azadeh Asgari Research Methodology
2. 2. Correlational Studies <ul><li>PURPOSE – To establish there is relationship, and strength of relationship between two or more quantitative variables based on a coefficient value </li></ul><ul><li>PURPOSE – To ascertain there exist a relationship or to use relationships to predict </li></ul>
3. 3. Correlational Studies <ul><ul><li>EXAMPLE: </li></ul></ul><ul><ul><ul><li>Relationship between achievement in English and achievement in Mathematics </li></ul></ul></ul><ul><li>Variables that have strong relationships vs variable that is the cause and it affects another variable </li></ul><ul><ul><li>EXAMPLE: </li></ul></ul><ul><ul><li>Relationship between self concept and achievement) </li></ul></ul>
4. 4. Coefficient of Determination <ul><li>Assesses the proportion of variability in one variable that can be determined or explained by A second variable. </li></ul><ul><li>E.G.: </li></ul><ul><ul><li>r = .7 </li></ul></ul><ul><ul><li>r 2 = .49 = 49% </li></ul></ul><ul><ul><li>i.e. 49% of the variability in Y can be determined or explained by X </li></ul></ul><ul><ul><li>E.g. parents' education level explains 49% of students satisfaction </li></ul></ul>
5. 5. Examples of Correlational Studies <ul><li>Relationships between grades obtained through criterion reference for several subjects </li></ul><ul><li>A study to predict success at the graduate level based on inter-correlational patterns of variables at the undergraduate level </li></ul>
6. 6. SCATTERGRAM OF ‘r’ Y HIGH X HIGH LOW LOW PERFECT POSITIVE CORRELATION (+1.00)
7. 7. SCATTERGRAM OF ‘r’ Y PERFECT NEGATIVE CORRELATION ( - 1.00) HIGH X HIGH LOW LOW
8. 8. SCATTERGRAM OF ‘r’ Y HIGH POSITIVE CORRELATION ( .83) HIGH X HIGH LOW LOW
9. 9. SCATTERGRAM OF ‘r’ Y SUBSTANTIAL NEGATIVE CORRELATION ( - .76) HIGH X HIGH LOW LOW
10. 10. SCATTERGRAM OF ‘r’ Y MODERATE POSITIVE CORRELATION (.57) HIGH X HIGH LOW LOW
11. 11. SCATTERGRAM OF ‘r’ Y ZERO CORRELATION (0.00) HIGH X HIGH LOW LOW
12. 12. Coefficient of Correlation (Bivariate) <ul><li>Pearson’s product moment coefficient of correlation </li></ul><ul><li>Point biserial correlation </li></ul><ul><li>Biserial correlation </li></ul><ul><li>Phi ( φ ) coefficient </li></ul><ul><li>Contingency coefficient </li></ul><ul><li>Spearman’s rho coefficient of correlation </li></ul>
13. 13. Multivariate Correlation <ul><li>MULTIPLE REGRESSION </li></ul><ul><li>DISCRIMINANT ANALYSIS </li></ul><ul><li>CANONICAL CORRELATION </li></ul><ul><li>PATH ANALYSIS </li></ul>