Quadrant Count Ratio and Pearson’s R in Education (GAISE)

Reading through the 2007 GAISE report, I’ve found some very cool teaching ideas and knowledge I didn’t know.  My first observation was that the report was bland and teaching elementary concepts, but as I progressed through the report I picked up on ideas to help incorporate in my own middle school and college classroom.  The report used some methods that I have used in my classes with the MAD to help students understand variation, but later used a Quadrant Count Ratio(QCR) to help students understand strength of a relationship.  This quadrant count directly relates to the covariance between two data sets, which is of course used in Pearson’s R.  I like the idea of using this to help students understand how Pearson’s R is either positive or negative relative to the relationship of the trend line.  I don’t see a page devoted to the QCR on wiki, but it does have some statistical usefulness (Holmes 2001).  If you have not heard of this method for relationship, it relates to what you see in many textbooks for an explation of the covariance between two random variables.  The scatter plot is divided into 4 quadrants based off of the mean for both variables.  The number of data points in quadrants that represent values that are both above the mean and both below the mean are added together and subtracted by the number of points in the 1st and 3rd quadrnants, then divided by the total observations to produce a number between -1 and 1.  The larger the number, the strong the relationship is positively.  It’s seem to be a mix between a parametric and non-parametric estimate on strength of a relationship.  It’s weakness lies in the fact that the values may lie anywhere within a quadrant and not particularly related to the linear relationship of the pairs of points.  It would be interesting to see how this relationship holds in extreme cases and any effectiveness of using the median instead of the mean to create quadrants.

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