Introduction to Genetic Analysis 672

Introduction to Genetic Analysis 672 - 44200_20_p643-678...

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The usual measure of the precision of a relation be- tween two variables x and y is the correlation coefFcient ( r xy ) . It is calculated in part from the product of the de- viation of each observation of x from the mean of the x values and the deviation of each observation of y from the mean of the y values—a quantity called the covari- ance of x and y (cov xy ): A formula that is exactly algebraically equivalent but that makes computation easier is: By using this formula, we can calculate the covariance between the right ( x ) and the left ( y ) leg counts in Table 20-3. The correlation, r xy , is deFned as: In the formula for correlation, the products of the deviations are divided by the product of the standard deviations of x and y ( s x and s y ) . This normalization by the standard deviations has the effect of making r xy a di- mensionless number that is independent of the units in which x and y are measured. So deFned, r xy will vary from 2 1, which signiFes a perfectly linear negative rela- tion between x and y, to
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This note was uploaded on 01/10/2011 for the course BIOL BIOL taught by Professor Johnson during the Spring '08 term at Aberystwyth University.

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