Coefficient of Determination
- Correlation Coefficient Squared
- Percentage of the variability among scores on one variable
that can be attributed to differences in the scores on the other variable
One way researchers often express the strength of the relationship between two
variables is by squaring their correlation coefficient. Suppose a group of students was
administered a reading achievement test and a verbal IQ test. If the students' reading
achievement scores and verbal IQ-test scores had a correlation of 0.80, a researcher might
report the squared correlation as 0.80 times 0.80 = 0.64. This squared correlation
coefficient is called a COEFFICIENT OF DETERMINATION.
|The coefficient of determination is useful
because it gives the proportion of the variance (fluctuation) of one variable that is
predictable from the other variable.
So we might say that 0.64 (or 64%) of the variance of the students' reading
achievement scores is predictable from their verbal IQ-test scores. If two variables had a
correlation of plus or minus 1.00, the corresponding coefficient of determination would
equal +1.00. This would mean that 100% of the variance of one variable would be
predictable using the other variable, and vice versa...Conversely, suppose that two
variables had a correlation of zero. Then the coefficient of determination would equal
zero, suggesting that none of the variance of one variable was linearly predictable from
the other variable. (Jaeger, 1990, p.67)
Jaeger, R. M. (1990). Statistics: A spectator sport (2nd ed.). Newbury Park, CA:
Note: The author writes "predictable" not "caused"
Del Siegle, Ph.D.
Neag School of Education - University of Connecticut