Difference between revisions of "Manuals/calci/FTEST"

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<div style="font-size:30px">'''FTEST(ar1,ar2)'''</div><br/>
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<div style="font-size:30px">'''FTEST(Array1,Array2)'''</div><br/>
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*<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 .  
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*So, if the variances are equal, the ratio of the variances will be 1.
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*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>
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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==
  
−
1.DATA1          DATA2
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{{#ev:youtube|tscL1fzjSTY|280|center|F-Test}}
−
  15                  21
 
−
  27                  12
 
−
  19                  30
 
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  32                    11
 
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FTEST(B4:B8,C4:C8)=0.81524906747183
 
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2.DATA 1={5,8,12,45,23};  DATA2={10,20,30,40,50}
 
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FTEST(A1:A5,C1:C5)=0.9583035732212274 
 
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3. DATA1={14,26,37};DATA2={45,82,21,17}
 
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FTEST(B1:B3,C1:C4}=0.26412211240525474
 
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4.DATA1={25},DATA2={45,65}
 
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FTEST(B1,C2:C3)=NAN
 
  
 
==See Also==
 
==See Also==
Line 32: Line 113:
 
*[[Manuals/calci/FINV  | FINV ]]
 
*[[Manuals/calci/FINV  | FINV ]]
  
 +
==References==
 +
[http://en.wikipedia.org/wiki/F-test  F Test]
  
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==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)


  • 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 Array1} 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 Array2 } 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

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 Y =\frac {1}{m} \sum_{i=1}^m Yi} .
  • The sample variances :
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 SX^2=\frac{1}{n-1} \sum_{i=1}^n (Xi-\bar X)^2}

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 SY^2=\frac{1}{m-1} \sum_{i=1}^m (Yi-\bar Y)^2}
  • Then the Test Statistic = 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 \frac {Sx^2}{Sy^2}} has an F-distribution with 'n−1' and 'm−1' degrees of freedom.
  • In FTEST(Array1,Array2) 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 Array1} is the data of first array, 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 Array2} 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 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 Array2} 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 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 FTEST(Array1,Array2)} .
    • 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 Array1} 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 Array2 } 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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