Quadrant count ratio


The quadrant count ratio is a measure of the association between two quantitative variables. The QCR is not commonly used in the practice of statistics; rather, it is a useful tool in statistics education because it can be used as an intermediate step in the development of Pearson's correlation coefficient.

Definition and properties

To calculate the QCR, the data are divided into quadrants based on the mean of the and variables. The formula for calculating the QCR is then:
where is the number of observations in that quadrant and 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. 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 and minimum pressure for 35 Category 5 Hurricanes. The mean wind speed is 170 mph, and the mean pressure is 921.31 hPa. 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, 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..