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A correlation coefficient can theoretically range from — 1 to +1 (Figure 22.11). A positive value indicates that there is a direct association between the variables (IFigure 22.11a); as one variable increases, the other variable also tends to increase. A positive correlation exists for human height and weight: tall people tend to weigh more. A negative correlation coefficient indicates that there is an inverse relation between the two variables (I Figure 22.11b); as one variable increases, the other tends to decrease (as is the case for egg number and hen weight).

The absolute value of the correlation coefficient (the size of the coefficient, ignoring its sign) provides information about the strength of association between the variables. A coefficient of — 1 or + 1 indicates a perfect correlation between the variables, meaning that a change in x is always accompanied by a proportional change in y. Correlation coefficients close to — 1 or close to + 1 indicate a strong association between the variables —a change in x is almost always associated with a proportional increase in y, as seen in 4 Figure 22.11c. On the other hand, a correlation coefficient closer to 0 indicates a weak correlation—a change in x is associated with a change in y but not always (I Figure 22.11d). A correlation of 0 indicates that there is no association between variables (I Figure 22.11e).

A correlation coefficient can be computed for two variables measured for the same individual, such as height (x) and weight (y). A correlation coefficient can also be computed for a single variable measured for pairs of individuals. For example, we can calculate for fish the correlation between the number of vertebrae of a parent (x) and the number of vertebrae of its offspring (y), as shown in I Figure 22.12. This approach is often used in quantitative genetics.

A correlation between two variables indicates only that the variables are associated; it does not imply a cause and effect relation. Correlation also does not mean that the values of two variables are the same; it means only that a change in one variable is associated with a proportional change in the other variable. For example, the x and y variables in the following list are almost perfectly correlated, with a correlation coefficient of .99.

Average:

x value

y value

0 0

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