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Chapter 3

Chapter 3. Correlation. Correlation. Association between scores on two variables e.g., age and coordination skills in children, price and quality. Graphing Correlations The Scatter Diagram. Steps for making a scatter diagram 1. Draw axes and assign variables to them

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Chapter 3

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  1. Chapter 3 Correlation

  2. Correlation • Association between scores on two variables • e.g., age and coordination skills in children, price and quality

  3. Graphing CorrelationsThe Scatter Diagram • Steps for making a scatter diagram 1. Draw axes and assign variables to them 2. Determine range of values for each variable and mark on axes 3. Mark a dot for each person’s pair of scores

  4. Graphing CorrelationsThe Scatter Diagram • For example:

  5. Graphing Correlations The Scatter Diagram

  6. Patterns of Correlation • Linear correlation • Curvilinear correlation • No correlation • Positive correlation • Negative correlation

  7. Degree of Linear CorrelationThe Correlation Coefficient • Figure correlation using Z scores • Cross-product of Z scores • Multiply score on one variable by score on the other variable • Correlation coefficient • Average of the cross-products of Z scores

  8. Degree of Linear CorrelationThe Correlation Coefficient • Formula for the correlation coefficient: • Positive perfect correlation: r = +1 • No correlation: r = 0 • Negative perfect correlation: r = –1

  9. Correlation and Causality • Three possible directions of causality: 1. X Y 2. X Y 3. Z X Y

  10. Correlation and Causality • Correlational research design • Correlation as a statistical procedure • Correlation as a kind of research design

  11. Issues in Interpreting the Correlation Coefficient • Statistical significance • Proportionate reduction in error • r2 • Used to compare correlations • Restriction in range • Unreliability of measurement

  12. Correlation in Research Articles • Scatter diagrams occasionally shown • Correlation matrix

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