Difference between revisions of "Manuals/calci/PEARSON"
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==Description== | ==Description== | ||
| − | *This function gives the Pearson | + | *This function gives the Pearson product-moment correlation coefficient. |
*It is denoted by PPMC, which shows the linear relationship between two variables. | *It is denoted by PPMC, which shows the linear relationship between two variables. | ||
*It is a measure of the strength of a linear association between two variables . | *It is a measure of the strength of a linear association between two variables . | ||
| Line 12: | Line 12: | ||
<math> r= \frac{ \Sigma(x-\bar{x})(y-\bar{y})}{\sqrt {\Sigma(x-\bar{x})^2(y-\bar{y})^2}}</math> | <math> r= \frac{ \Sigma(x-\bar{x})(y-\bar{y})}{\sqrt {\Sigma(x-\bar{x})^2(y-\bar{y})^2}}</math> | ||
| − | where <math> \bar{x} and \bar{y} </math> are Average of the two Samples x and y. | + | where <math> \bar{x}</math> and <math>\bar{y} </math> are Average of the two Samples <math>x </math> and <math>y </math>. |
| − | *In <math>PEARSON(ar1,ar2)</math> , the value of <math> ar1</math> and <math> ar2</math> must be either numbers or names, array,constants or references that contain numbers. | + | *In <math>PEARSON(ar1,ar2)</math>, the value of <math> ar1</math> and <math> ar2</math> must be either numbers or names, array,constants or references that contain numbers. |
*Suppose the array contains text,logicl values or empty cells, like that values are not considered. | *Suppose the array contains text,logicl values or empty cells, like that values are not considered. | ||
*This function will return the result as error when the number of values are different for <math> ar1 </math> and <math> ar2 </math>. | *This function will return the result as error when the number of values are different for <math> ar1 </math> and <math> ar2 </math>. | ||
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==References== | ==References== | ||
| + | [http://en.wikipedia.org/wiki/Pearson_product-moment_correlation_coefficient Pearson] | ||
Revision as of 02:00, 7 January 2014
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle ar1} is the array of independent values
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle ar2} is the array of dependent values.
Description
- This function gives the Pearson product-moment correlation coefficient.
- It is denoted by PPMC, which shows the linear relationship between two variables.
- It is a measure of the strength of a linear association between two variables .
- The two variables Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle X } and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Y } , giving a value between +1 and −1 inclusive.
- Here +1 indicates the perfect positive correlation, 0 indicates no correlation and -1 indicates the perfect negative correlation.
- The formula for PPMC,Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r } is defined by:
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r= \frac{ \Sigma(x-\bar{x})(y-\bar{y})}{\sqrt {\Sigma(x-\bar{x})^2(y-\bar{y})^2}}}
where Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \bar{x}} and are Average of the two Samples Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x } and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y } .
are Average of the two Samples Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x }
and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y }
.
- In Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle PEARSON(ar1,ar2)} , the value of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle ar1} and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle ar2} must be either numbers or names, array,constants or references that contain numbers.
- Suppose the array contains text,logicl values or empty cells, like that values are not considered.
- This function will return the result as error when the number of values are different for Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle ar1 } and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle ar2 } .
Examples
- 1.Array1 Array2
5 8 9 12 10 15 PEARSON(B1:B3,C1:C3)=0.968619605
- 2.Array1 Array2
17 10
0 11 19 7 25 13 PEARSON(D1:D4,E1:E4)=-0.759206026
- 3.Array1 Array2
1 4 2 5 3 PEARSON(A1:A3,B1:B2)=NAN