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Chapter 22
Correlation Coefficients
22
Correlation Coefficients
The Meaning of Correlation
Correlation and Data Types
Pearson’s r
Spearman rho
Other Coefficients of Note
Coefficient of Determination r2
The concept of correlation was introduced in Chapters 1 and 5. Our focus since
Chapter 16 has been basic statistical procedures that measure differences between groups -- one-sample, two-sample, and k-sample tests.
Now we turn our attention to basic statistical procedures that measure the degree of association between variables.
Dr. Wesley Black studied the relationship between rankings of selected learning objectives in a youth discipleship taxonomy between full-time church staff youth ministers and seminary students*…show more content…*

The third scatterplot shows a moderately positive correlation. Notice how most of the data points do not fall on the line. It is a moderate correlation, however, because the points fall in a tight pattern around the line. Notice the pattern is linear -- that is, a pattern suggesting a line. The fourth scatterplot shows no correlation. Scores on one variable have no systematic association with scores on the other. The scatterplot presents no linear pattern among the points. Beyond the graphical representation of association, we can mathematically compute the degree of association between two variables. The numerical result of such a computation is called a correlation coefficient. The value of these coefficients usually range from -1.00 to +1.00. A positive coefficient indicates that two variables systematically vary in the same direction: as one variable increases, the other variable tends to increase. The closer the coefficient is to +1.00, the stronger the positive association. A negative coefficient indicates that two variables systematically vary in opposite directions: as one variable increases, the other variable tends to decrease. The closer the coefficient is to -1.00, the stronger the negative association. A coefficient close to zero indicates that no systematic co-varying exists between the variables. There are several important correlation procedures. They differ according to the data types of the variables. 22-2 © 4th ed.

The third scatterplot shows a moderately positive correlation. Notice how most of the data points do not fall on the line. It is a moderate correlation, however, because the points fall in a tight pattern around the line. Notice the pattern is linear -- that is, a pattern suggesting a line. The fourth scatterplot shows no correlation. Scores on one variable have no systematic association with scores on the other. The scatterplot presents no linear pattern among the points. Beyond the graphical representation of association, we can mathematically compute the degree of association between two variables. The numerical result of such a computation is called a correlation coefficient. The value of these coefficients usually range from -1.00 to +1.00. A positive coefficient indicates that two variables systematically vary in the same direction: as one variable increases, the other variable tends to increase. The closer the coefficient is to +1.00, the stronger the positive association. A negative coefficient indicates that two variables systematically vary in opposite directions: as one variable increases, the other variable tends to decrease. The closer the coefficient is to -1.00, the stronger the negative association. A coefficient close to zero indicates that no systematic co-varying exists between the variables. There are several important correlation procedures. They differ according to the data types of the variables. 22-2 © 4th ed.

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