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Reverted to revision 538433062 by Citation bot: Messed up the parsing all around..

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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 can be used as an intermediate step in the development of [[Pearson product-moment correlation coefficient|Pearson's correlation coefficient]].<ref name=KaderFranklin2008>{{cite journal|last=Kader|first=Gary, D.|coauthors=Christine A. Franklin|title=The Evolution of Pearson's Correlation Coefficient|journal=Mathematics Teacher|year=2008|month=November|volume=102|issue=4|pages=292–299}}</ref>

== Definition and properties ==
To calculate the QCR, the data are divided into [[Quadrant (plane geometry)|quadrants]] based on the mean of the <math>X</math> and <math>Y</math> variables. The formula for calculating the QCR is then:

: <math>q=\frac{n(\text{Quadrant I})+n(\text{Quadrant III})-n(\text{Quadrant II})-n(\text{Quadrant IV})}{N},</math>

where <math>\text{n(Quadrant)}</math> is the number of observations in that quadrant and <math>N</math> is the total number of observations.<ref name=Holmes2001>{{cite journal|last=Holmes|first=Peter|title=Correlation: From Picture to Formula|journal=Teaching Statistics|year=2001|month=Autumn|volume=23|issue=3}}</ref>

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 [[Correlation and dependence|perfect linear relationship]].

== Example ==
[[File:QCR for Wind Speed and Pressure from Category 5 Hurricanes (1924-2007) (jitter applied).png|thumb|Data from 35 [[Saffir–Simpson_Hurricane_Scale#Category_5|Category 5 Hurricanes]] showing the relationship between wind speed (''X'') and pressure (''Y''). The blue and green lines represent the means of the ''X'' and ''Y'' values, respectively. The Quadrants have been labeled. The points have been jittered to reduce overlap of observations.]]
The scatterplot shows the maximum wind speed (''X'') and minimum pressure (''Y'') for 35 [[List_of_Category_5_Atlantic_hurricanes#Category_5_Atlantic_hurricanes|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 <math>\frac{(6+5)-(13+11)}{35}=-0.43</math>, 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 ==
* [[Guidelines for Assessment and Instruction in Statistics Education]]
* [[Absolute deviation#Mean absolute deviation|Mean absolute deviation]] (MAD) – A statistic used as a precursor to [[standard deviation]].

== References ==
{{Reflist}}

{{statistics-stub}}

[[Category:Statistical ratios]]
[[Category:Covariance and correlation]]
[[Category:Statistical dependence]]

Pairwise error probability - Revision history

en>Mrt3366: Reverted to revision 538433062 by Citation bot: Messed up the parsing all around..