Quadrant count ratio

Definition and properties

To calculate the QCR, the data are divided into quadrants based on the mean of the X and Y variables. The formula for calculating the QCR is then:

: q=\frac{[n(\text{Quadrant I})+n(\text{Quadrant III})]-[n(\text{Quadrant II})+n(\text{Quadrant IV})]}{N},

where \text{n(Quadrant)} is the number of observations in that quadrant and N is the total number of observations.

The QCR is always between −1 and 1. Values near −1, 0, and 1 indicate strong negative association, no association, and strong positive association (as in Pearson's correlation coefficient). However, unlike Pearson's correlation coefficient the QCR may be −1 or 1 without the data exhibiting a perfect linear relationship.

Example

The scatterplot shows the maximum wind speed (X) and minimum pressure (Y) for 35 Category 5 Hurricanes. The mean wind speed is 170 mph (indicated by the blue line), and the mean pressure is 921.31 hPa (indicated by the green line). There are 6 observations in Quadrant I, 13 observations in Quadrant II, 5 observations in Quadrant III, and 11 observations in Quadrant IV. Thus, the QCR for these data is \frac{(6+5)-(13+11)}{35}=-0.37, indicating a moderate negative relationship between wind speed and pressure for these hurricanes. The value of Pearson's correlation coefficient for these data is −0.63, also indicating a moderate negative relationship..

References

References

1. Kader, Gary, D.. (November 2008). "The Evolution of Pearson's Correlation Coefficient". Mathematics Teacher.
2. Holmes, Peter. (Autumn 2001). "Correlation: From Picture to Formula". Teaching Statistics.