PS296 Chapter 9: r and rS
The Pearson Product-Moment Correlation Coefficient (r)
- the absolute value of covXY is also a function of the standard deviations of X and Y
-to resolve this, we divide the covariance by the standard deviations and make the result our
estimate of correlation (known as scaling the covariance by the SDs bc we are basically
changing the scale on which it is measured)
Pearson product-moment correlation coefficient (r) is
r = covXY
sXsY
-max value of covXY turns out to be +-sXsY thus the limits on r are +- 1.00
-r is a measure of the degree to which the covariance approaches its maximum
An equivalent way of writing that is the computational formulae simplified by cancellation:
Correlations with Ranked Data (rS)
-Spearman's correlation coefficient for ranked data is denoted rs and is a correlation
coefficient on ranked data
Document Summary
The absolute value of covxy is also a function of the standard deviations of x and y. To resolve this, we divide the covariance by the standard deviations and make the result our estimate of correlation (known as scaling the covariance by the sds bc we are basically changing the scale on which it is measured) Pearson product-moment correlation coefficient (r) is r = covxy sxsy. Max value of covxy turns out to be +-sxsy thus the limits on r are +- 1. 00. R is a measure of the degree to which the covariance approaches its maximum. An equivalent way of writing that is the computational formulae simplified by cancellation: Spearman"s correlation coefficient for ranked data is denoted rs and is a correlation coefficient on ranked data. If the data are ranks of n objects, you can either add up all the ranks, or you can calculate: X = n (n + 1) / 2.
