In other words, 77% of the "spread" (variance) of the height data is shared with the "spread" of the age data. age was 0.88, indicating that age and height share 77% of their variance in common. By the time r 2 has fallen to 0.5, r 2 = 0.25, so the variables have only one-fourth of their variance in common.įor our simulated height data, the correlation coefficient for height vs. The variables now have just less than half of their variance in common. When r = 0.7, that might seem like a fairly strong correlation, but r 2 has fallen to 0.49. When r = 0.9, r 2 = 0.81, and the variables have 81% of their variance in common. Interpreting the Correlation Coefficienct Using r 2 rĪs you can see from the table, r 2 decreases much more rapidly than r. (Note: for the corresponding values of r between 0 and −1, r 2 will be the same, since squaring a negative number results in a positive number.) Let's see what this means by calculating r 2 over the range from 0 to +1.
This gives you the percent variance in common between the two variables (Rummel, 1976). How close to +1 or −1 does the correlation coefficient need to be in order for us to consider the correlation to be "strong"? A good method for deciding this is to calculate the square of the correlation coefficient ( r 2) and then multiply by 100. If the correlation coefficient is positive, the variables are positively correlated (when one variable increases, the other increases also). If the correlation coefficient is negative, the variables are inversely correlated (when one variable increases, the other decreases). What do the values of the correlation coefficient mean? Well, the closer the correlation coefficient is to either +1 or −1, the more strongly the two variables are correlated. The correlation coefficient ranges between −1 and +1. It is a scale-independent measure of how two measures co-vary (change together). The statistic that describes this relationship between two variables is the correlation coefficient, r (or, more formally, the "Pearson product-moment correlation coefficient"). Scatter plot of height versus birth month, color-coded by grade level. The grouping of bands show a stronger correlation between grade level and height than birth month and height.įigure 4.
The data points (with shapes denoting grade level) are grouped together in bands across the graph. An example scatterplot of boys' height and birth month has data points spread across the entirety of the graph.
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