The quadrant count ratio (QCR) 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.[1]
To calculate the QCR, the data are divided into quadrants based on the mean of the
X
Y
| q= | n(QuadrantI)+n(QuadrantIII)-n(QuadrantII)-n(QuadrantIV) |
| N |
,
where
n(Quadrant)
N
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.
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
| (6+5)-(13+11) | |
| 35 |
=-0.37