Quadrant count ratio
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]
Definition and properties
[edit]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.[2]
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
[edit]![](http://upload.wikimedia.org/wikipedia/commons/thumb/7/71/QCR_for_Wind_Speed_and_Pressure_from_Category_5_Hurricanes_%281924-2007%29_%28jitter_applied%29.png/220px-QCR_for_Wind_Speed_and_Pressure_from_Category_5_Hurricanes_%281924-2007%29_%28jitter_applied%29.png)
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 , 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..
See also
[edit]- Guidelines for Assessment and Instruction in Statistics Education
- Mean absolute deviation (MAD) – A statistic used as a precursor to standard deviation.
References
[edit]- ^ Kader, Gary, D.; Christine A. Franklin (November 2008). "The Evolution of Pearson's Correlation Coefficient". Mathematics Teacher. 102 (4): 292–299. doi:10.5951/MT.102.4.0292.
{{cite journal}}
: CS1 maint: multiple names: authors list (link) - ^ Holmes, Peter (Autumn 2001). "Correlation: From Picture to Formula". Teaching Statistics. 23 (3): 67–71. doi:10.1111/1467-9639.00058. S2CID 123667316.