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6.7 earson!sproduct"moment correlation

coefficient

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earson!s product"moment correlation coefficient

#hen the relationship $et%een t%o &aria$les needs to $e studied' a

(ood %a) of representin( the data (raphicall) is to use a scatterdia(ram. #ith a scatter dia(ram' a series of points is plotted. *he x +

and y +coordinates of each point are ta,en from the &alues of the

&aria$les.

*he data and scatter dia(ram $elo% sho% the hei(ht of )oun( children

-cm plotted a(ainst their mass -,(.

Height Mass Height Mass

/ /. 6 11.1

0 7.0 7 16.

3.0 3 20.3

6 .2 36 16.2

2 10.1 36 1.0

3 6.2 101 13.

6/ 3.3 10 1.3

6 16.0 103 12.0

71 1. 117 13.

7/ 3.3 121 1./

 

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earson!s product"moment correlation coefficient

 

4rom the (raph it is

clear that there is arelationship $et%een the

t%o &aria$les. 5enerall)'

as hei(ht increases so

does mass. 

*his can $eemphasied $)

plottin( a line of $est

fit. *his should pass

throu(h the point

%hich represents the

mean &alues of the

hei(ht and mass.

( ) y x,

*o see ho% stron( a correlation there is $et%een the t%o &aria$les'

earson!s product"moment correlation coefficient can $e calculated.

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earson!s product"moment correlation coefficient

*he &alue of earson!s product"moment coefficient -r (i&es an

indication of the le&el of correlation $et%een t%o &aria$les. It has a

&alue in the ran(e "1 r   1.

 x s

 y s

*he &alue of r  is calculated usin( the formula

%here is the standard de&iation of x, is the

standard de&iation of y and is the co&arianceof x  and y 

 xy s

 xy

 x y

 s

r 

 s s

=

 8 &alue of r  near "1 implies a stron( ne(ati&e correlation $et%een

the t%o &aria$les.

 8 &alue of r  near 91 implies a stron( positi&e correlation $et%een thet%o &aria$les.

 8 &alue of r  near 0 implies there is little or no correlation $et%een the

t%o &aria$les.

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earson!s product"moment correlation coefficient

4or the data (i&en earlier' the results can $e entered in a5D: calculator and the &alue of r calculated.

r  ; 0.767

*his &alue of r  sho%s that there is a moderate positi&ecorrelation $et%een a child!s hei(ht and mass.