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