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Pearson's correlation coefficient is the covariance of the two variables divided by the product of their standard deviations. The form of the definition involves a "product moment", that is, the mean (the first moment about the origin) of the product of the mean-adjusted random variables; hence the modifier product-moment in the name.
The ability to demonstrate a correlation between a pair of bio-molecules was greatly enhanced by Erik Manders of the University of Amsterdam who introduced Pearson's correlation coefficient (PCC) to microscopists, [2] along with other coefficients of which the "overlap coefficients" M1 and M2 have proved to be the most popular and useful.
The Pearson product-moment correlation coefficient, also known as r, R, or Pearson's r, is a measure of the strength and direction of the linear relationship between two variables that is defined as the covariance of the variables divided by the product of their standard deviations. [4]
Yule's Y varies from −1 to +1. −1 reflects total negative correlation, +1 reflects perfect positive association while 0 reflects no association at all. These correspond to the values for the more common Pearson correlation. Yule's Y is also related to the similar Yule's Q, which can also be expressed in terms of the odds ratio.
As an example, weighted gene co-expression network analysis uses Pearson correlation to analyze linked gene expression and understand genetics at a systems level. [50] Another measure of correlation is linkage disequilibrium. Linkage disequilibrium describes the non-random association of genetic sequences among loci in a given chromosome. [51]
Human enzymes start to denature quickly at temperatures above 40 °C. Enzymes from thermophilic archaea found in the hot springs are stable up to 100 °C. [13] However, the idea of an "optimum" rate of an enzyme reaction is misleading, as the rate observed at any temperature is the product of two rates, the reaction rate and the denaturation rate.
If this is the case, a biserial correlation would be the more appropriate calculation. The point-biserial correlation is mathematically equivalent to the Pearson (product moment) correlation coefficient; that is, if we have one continuously measured variable X and a dichotomous variable Y, r XY = r pb. This can be shown by assigning two ...
Pearson was joined by Sir Francis Galton [5] and Walter Frank Raphael Weldon [1] in cautioning scientists to be wary of spurious correlation, especially in biology where it is common [6] to scale or normalize measurements by dividing them by a particular variable or total. The danger he saw was that conclusions would be drawn from correlations ...