Difference between revisions of "Manuals/calci/PEARSON"

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<div style="font-size:30px">'''PEARSON (ar1,ar2)'''</div><br/>
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<div style="font-size:30px">'''PEARSON (Array1,Array2)'''</div><br/>
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*<math>ar1</math> is the array of independent values  
+
*<math>Array1</math> is the array of independent values  
−
*<math>ar2</math> is the array of dependent values.
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*<math>Array2</math> is the array of dependent values.
 +
**PEARSON(),returns the Pearson product moment correlation coefficient.
  
 
==Description==
 
==Description==
−
*This function gives the Pearson product-moment correlation coefficient.
+
*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 .
 
*The two variables  <math> X </math>  and <math> Y </math>, giving a value between +1 and −1 inclusive.  
 
*The two variables  <math> X </math>  and <math> Y </math>, giving a value between +1 and −1 inclusive.  
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*Here +1 indicates the perfect positive correlation, 0 indicates no correlation and -1 indicates the perfect negative correlation.
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*Here  
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*The formula for PPMC,<math> r </math> is defined by:
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+1 indicates the perfect positive correlation,
 +
  0 indicates no correlation  
 +
-1 indicates the perfect negative correlation.
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*The formula for PPMC, <math> r </math> is defined by:
 
<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}</math>  and  <math>\bar{y} </math>  are Average of the two Samples  <math>x </math> and  <math>y </math>.
 
where <math> \bar{x}</math>  and  <math>\bar{y} </math>  are Average of the two Samples  <math>x </math> and  <math>y </math>.
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*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.  
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*In  <math>PEARSON(Array1,Array2)</math>, the value of <math>Array1</math> and <math>Array2</math> must be either numbers or names, array,constants or references that contain numbers.  
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*Suppose the array contains text,logicl values or empty cells, like that values are not considered.
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*Suppose the array contains text, logicl values or empty cells, like that values are not considered.
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*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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*This function will return the result as error when the number of values are different for <math> Array1 </math> and <math> Array2 </math>.
  
 
==Examples==
 
==Examples==
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*1.Array1          Array2
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{| class="wikitable"
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5                        8
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|+Spreadsheet
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9                        12
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|-
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10                      15
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! !! A !! B !! C
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PEARSON(B1:B3,C1:C3)=0.968619605
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|-
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*2.Array1            Array2
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! 1
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17                    10
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| 5 || 9 || 10  
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0                        11
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|-
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19                        7
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! 2
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25                      13
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| 8 || 12 || 15
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PEARSON(D1:D4,E1:E4)=-0.759206026
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|}
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*3.Array1            Array2
 
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1                        4
 
−
2                       5
 
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3
 
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PEARSON(A1:A3,B1:B2)=NAN
 
  
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=PEARSON(A1:C1,A2:C2) = 0.968619605
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2.
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{| class="wikitable"
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|+Spreadsheet
 +
|-
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! !! A !! B !! C !!D
 +
|-
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! 1
 +
| 17 || 0 || 19 ||25
 +
|-
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! 2
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| 10 || 11 || 7 ||13
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|}
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=PEARSON(A1:D1,A2:D2) = 0.034204238054579846
 +
 +
3.
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{| class="wikitable"
 +
|+Spreadsheet
 +
|-
 +
! !! A !! B !! C
 +
|-
 +
! 1
 +
| 1 || 2 || 3
 +
|-
 +
! 2
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| 4 || 5 ||
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|}
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=PEARSON(A1:C1,A2:B2) = NAN
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 +
==Related Videos==
 +
 +
{{#ev:youtube|JO-Gc5bEG70|280|center|PEARSON}}
  
 
==See Also==
 
==See Also==
Line 42: Line 75:
 
==References==
 
==References==
 
[http://en.wikipedia.org/wiki/Pearson_product-moment_correlation_coefficient Pearson]
 
[http://en.wikipedia.org/wiki/Pearson_product-moment_correlation_coefficient Pearson]
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 +
 +
 +
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*[[Z_API_Functions | List of Main Z Functions]]
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*[[ Z3 |  Z3 home ]]

Latest revision as of 16:01, 8 August 2018

PEARSON (Array1,Array2)


  • is the array of independent values
  • is the array of dependent values.
    • PEARSON(),returns the Pearson product moment correlation coefficient.

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 and , giving a value between +1 and −1 inclusive.
  • Here
+1 indicates the perfect positive correlation,
 0 indicates no correlation 
-1 indicates the perfect negative correlation.
  • The formula for PPMC, is defined by:

where and are Average of the two Samples and .

  • In , the value of and 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 and .

Examples

Spreadsheet
A B C
1 5 9 10
2 8 12 15 
=PEARSON(A1:C1,A2:C2) = 0.968619605

2.

Spreadsheet
A B C D
1 17 0 19 25
2 10 11 7 13 
=PEARSON(A1:D1,A2:D2) = 0.034204238054579846

3.

Spreadsheet
A B C
1 1 2 3
2 4 5 
=PEARSON(A1:C1,A2:B2) = NAN

Related Videos

PEARSON

See Also

References

Pearson



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