Difference between revisions of "Manuals/calci/FTEST"

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<div style="font-size:30px">'''FTEST(ar1,ar2)'''</div><br/>
+
<div style="font-size:30px">'''FTEST(Array1,Array2)'''</div><br/>
−
*<math>ar1</math> and <math>ar2 </math> are array of data.
+
*<math>Array1</math> and <math>Array2 </math> are array of data.
 +
**FTEST(), returns the result of an F-test.
 +
 
 
==Description==
 
==Description==
 
*This function gives the result of F-test.  
 
*This function gives the result of F-test.  
 
*The F-test is designed to test if two population variances are equal.  
 
*The F-test is designed to test if two population variances are equal.  
 
*It does this by comparing the ratio of two variances.  
 
*It does this by comparing the ratio of two variances.  
−
*So, if the variances are equal, the ratio of the variances will be 1.Let X1, ..., Xn and Y1, ..., Ym be independent samples each have a normal distribution .  
+
*So, if the variances are equal, the ratio of the variances will be 1.
−
*It's sample means: X(bar)=1/n summation(i=1 to n)Xi and  Y(bar)=1/m summation(i=1 to m)Yi .  
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*Let X1,...Xn and Y1,...Ym be independent samples each have a Normal Distribution .  
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*The sample variances : Sx^2=1/n-1 summation(i=1 to n)(Xi-X(bar))^2.and SY^2=1/m-1 summation(i=1 to m)(Yi-Y(bar))^2.
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*It's sample means:  
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*Then the test statistic= Sx^2/Sy^2   has an F-distribution with n − 1 and m − 1 degrees of freedom.
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<math>\bar X=\frac{1}{n} \sum_{i=1}^n Xi</math>
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*In FTEST(ar1,ar2) where ar1 is the data of  first array,ar2 is the data of second array.  
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and   
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*The array may be any numbers, names, or refernces that contains numbers.  
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:<math>\bar Y =\frac {1}{m} \sum_{i=1}^m Yi</math> .  
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*Suppose the array contains any text, logical values or empty cells like that values are not considered.  
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*The sample variances :
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When the ar or ar2 is less than 2 or the variance of the array value is zero then this function will return the result as error.
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<math>SX^2=\frac{1}{n-1} \sum_{i=1}^n (Xi-\bar X)^2</math>
 +
and
 +
:<math>SY^2=\frac{1}{m-1} \sum_{i=1}^m (Yi-\bar Y)^2</math>
 +
*Then the Test Statistic = <math>\frac {Sx^2}{Sy^2}</math> has an F-distribution with 'n−1'  and 'm−1' degrees of freedom.
 +
*In FTEST(Array1,Array2) where <math>Array1</math> is the data of  first array, <math>Array2</math> is the data of second array.  
 +
*The array may be any numbers, names, or references that contains numbers.  
 +
*values are not considered if the array contains any text, logical values or empty cells.  
 +
When the <math>Array1</math> or <math>Array2</math> is less than 2 or the variance of the array value is zero, then this function will return the result as error.
 +
 
 +
==ZOS==
 +
*The syntax is to calculate FTEST in ZOS is <math>FTEST(Array1,Array2)</math>.
 +
**<math>Array1</math> and <math>Array2 </math> are array of data.
 +
*For e.g.,FTEST([15,29,30],[62,74,80])
 +
{{#ev:youtube|y_uVl6UbHtE|280|center|F-Test}}
 +
 
 
==Examples==
 
==Examples==
 +
1.
 +
{| class="wikitable"
 +
|+ DATA1
 +
|-
 +
| 15
 +
| 27
 +
| 19
 +
| 32
 +
|}
 +
 +
{| class="wikitable"
 +
|+ DATA2
 +
|-
 +
| 21
 +
| 12
 +
| 30
 +
| 11
 +
|}
 +
 +
=FTEST(B4:B8,C4:C8)=0.81524906747183
 +
 +
2.
 +
{| class="wikitable"
 +
|+ DATA1
 +
|-
 +
| 5
 +
| 8
 +
| 12
 +
| 45
 +
| 23
 +
|}
 +
 +
{| class="wikitable"
 +
|+ DATA2
 +
|-
 +
| 10
 +
| 20
 +
| 30
 +
| 40
 +
| 50
 +
|}
 +
=FTEST(A1:A5,C1:C5)=0.9583035732212274 
 +
3.
 +
{| class="wikitable"
 +
|+ DATA1
 +
|-
 +
| 14
 +
| 26
 +
| 37
 +
|}
 +
 +
{| class="wikitable"
 +
|+ DATA2
 +
|-
 +
| 45
 +
| 82
 +
| 21
 +
|17
 +
|}
 +
FTEST(B1:B3,C1:C4} = 0.26412211240525474
 +
 +
4.
 +
{| class="wikitable"
 +
|+ DATA1
 +
|-
 +
| 14
 +
|}
 +
{| class="wikitable"
 +
|+ DATA1
 +
|-
 +
| 45
 +
| 65
 +
|}
 +
=FTEST(B1,C2:C3)=NAN
 +
 +
==Related Videos==
  
−
#Find the correlation coefficients for X and Y values are given below :X={1,2,3,4,5};  Y={11,22,34,43,56}
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{{#ev:youtube|tscL1fzjSTY|280|center|F-Test}}
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=CORREL(A4:A8,B4:B8)=0.99890610723867
 
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#The following table gives the math scores and times taken to run 100 m for 10 friends:SCORE(X)={52,25,35,90,76,40}; TIME TAKEN(Y)={11.3,12.9,11.9,10.2,11.1,12.5}
 
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=CORREL(A5:A10,B5:B10)= -0.93626409417769
 
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#Find the correlation coefficients for X and Y values are given below :X={-4,11,34,87};Y={9,2,59,24}  
 
−
=CORREL(A1:A4,B1:B4)=0.353184665607273
 
  
 
==See Also==
 
==See Also==
Line 26: Line 113:
 
*[[Manuals/calci/FINV  | FINV ]]
 
*[[Manuals/calci/FINV  | FINV ]]
  
 +
==References==
 +
[http://en.wikipedia.org/wiki/F-test  F Test]
  
−
==References==
+
 
−
[http://en.wikipedia.org/wiki/Pearson_product-moment_correlation_coefficient| Correlation]
+
*[[Z_API_Functions | List of Main Z Functions]]
 +
 
 +
*[[ Z3 |   Z3 home ]]

Latest revision as of 16:07, 7 August 2018

FTEST(Array1,Array2)


  • and are array of data.
    • FTEST(), returns the result of an F-test.

Description

  • This function gives the result of F-test.
  • The F-test is designed to test if two population variances are equal.
  • It does this by comparing the ratio of two variances.
  • So, if the variances are equal, the ratio of the variances will be 1.
  • Let X1,...Xn and Y1,...Ym be independent samples each have a Normal Distribution .
  • It's sample means:

and

.
  • The sample variances :

and

  • Then the Test Statistic = has an F-distribution with 'n−1' and 'm−1' degrees of freedom.
  • In FTEST(Array1,Array2) where is the data of first array, is the data of second array.
  • The array may be any numbers, names, or references that contains numbers.
  • values are not considered if the array contains any text, logical values or empty cells.

When the or is less than 2 or the variance of the array value is zero, then this function will return the result as error.

ZOS

  • The syntax is to calculate FTEST in ZOS is .
    • and are array of data.
  • For e.g.,FTEST([15,29,30],[62,74,80])
F-Test

Examples

1.

DATA1
15 27 19 32
DATA2
21 12 30 11 
=FTEST(B4:B8,C4:C8)=0.81524906747183

2.

DATA1
5 8 12 45 23
DATA2
10 20 30 40 50 
=FTEST(A1:A5,C1:C5)=0.9583035732212274

3.

DATA1
14 26 37
DATA2
45 82 21 17 
FTEST(B1:B3,C1:C4} = 0.26412211240525474

4.

DATA1
14
DATA1
45 65 
=FTEST(B1,C2:C3)=NAN

Related Videos

F-Test

See Also

References

F Test


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