chapter 3 correlation. association between scores on two variables –e.g., age and coordination...
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Chapter 3
Correlation
Correlation
Association between scores on two variables– e.g., age and coordination skills in children,
price and quality
Graphing CorrelationsThe Scatter Diagram
Steps for making a scatter diagram1. 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
Graphing CorrelationsThe Scatter Diagram
For example:Hours Slept Happy Mood
7 4 9 5 8 3 9 7 8 4 6 1 8 3 7 2
10 6 8 5
Graphing Correlations The Scatter Diagram
Patterns of Correlation
Linear correlation Curvilinear correlation No correlation Positive correlation Negative correlation
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
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
Correlation and Causality
Three possible directions of causality:
1. X Y
2. X Y
3. Z
X Y
Correlation and Causality
Correlational research design– Correlation as a statistical procedure– Correlation as a kind of research design
Issues in Interpreting the Correlation Coefficient
Statistical significance Proportionate reduction in error
– r2
– Used to compare correlations
Restriction in range Unreliability of measurement
Correlation in Research Articles
Scatter diagrams occasionally shown Correlation matrix