Difference between revisions of "Manuals/calci/FTESTANALYSIS"

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(Created page with "<div id="6SpaceContent" class="zcontent" align="left"> '''FTESTANALYSIS'''(Array1, Array2, Alpha, NewTableFlag) where, '''Array1 and Array2 '''- Input range should...")
 
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<div id="6SpaceContent" class="zcontent" align="left">
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<div style="font-size:30px">'''FTEST(ar1,ar2)'''</div><br/>
 +
*<math>ar1</math> and <math>ar2 </math> are array of data.
 +
==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:
 +
<math>\bar X=\frac{1}{n} \sum_{i=1}^n Xi</math>
 +
and 
 +
:<math>\bar Y =\frac {1}{m} \sum_{i=1}^m Yi</math> .
 +
*The sample variances :
 +
<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 <math>n−1</math> and <math>m−1</math> degrees of freedom.
 +
*In FTEST(ar1,ar2) where <math>ar1</math> is the data of  first array, <math>ar2</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>ar1</math> or <math>ar2</math> 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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'''FTESTANALYSIS'''(Array1, Array2, Alpha, NewTableFlag)
+
==Examples==
 +
1.
 +
{| class="wikitable"
 +
|+ DATA1
 +
|-
 +
| 15
 +
| 27
 +
| 19
 +
| 32
 +
|}
  
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where,
+
{| class="wikitable"
 +
|+ DATA2
 +
|-
 +
| 21
 +
| 12
 +
| 30
 +
| 11
 +
|}
  
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'''Array1 and Array2 '''- Input range should be one  blocks.
+
=FTEST(B4:B8,C4:C8)=0.81524906747183
  
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'''Alpha''' - is a constant and value should be in between 0 and 1.
+
2.
 +
{| class="wikitable"
 +
|+ DATA1
 +
|-  
 +
| 5
 +
| 8
 +
| 12
 +
| 45
 +
| 23
 +
|}
  
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'''NewTableFlag''' - is the TRUE or FALSE.If set as TRUE,the result in new sheet.If NewTableFlag is omitted, it assumed to be FALSE.
+
{| class="wikitable"
 +
|+ DATA2
 +
|-  
 +
| 10
 +
| 20
 +
| 30
 +
| 40
 +
| 50
 +
|}
 +
=FTEST(A1:A5,C1:C5)=0.9583035732212274 
 +
3.
 +
{| class="wikitable"
 +
|+ DATA1
 +
|-
 +
| 14
 +
| 26
 +
| 37
 +
|}
  
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</div>
+
{| class="wikitable"  
−
----
+
|+ DATA2
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<div id="1SpaceContent" class="zcontent" align="left">F-Test Two Sample for Variances is also knowns as Fisher test. It compares the variances between two groups of data. Variance is a measure of how much the values are dispersed around the mean value.</div>
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|-  
−
----
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| 45
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<div id="7SpaceContent" class="zcontent" align="left">
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| 82
 +
| 21
 +
|17
 +
|}
 +
FTEST(B1:B3,C1:C4} = 0.26412211240525474
  
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If Alpha &lt; 0 or Alpha &gt;1, FTESTANALYSIS returns the #ERROR.
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4.
−
 
+
{| class="wikitable"  
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</div>
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|+ DATA1
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----
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|-  
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<div id="12SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="left">
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  | 14
−
 
+
|}
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F-TEST TWO SAMPLE FOR VARIANCES
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{| class="wikitable"  
−
 
+
|+ DATA1
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</div></div>
+
  |-  
−
----
+
| 45
−
<div id="8SpaceContent" class="zcontent" align="left">
+
| 65
−
 
 
−
Lets see an example in (Column3, Row1)
 
−
 
 
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<nowiki>=FTESTANALYSIS(R1C1:R6C1, R1C2:R6C2, 0.05, TRUE)</nowiki>
 
−
 
 
−
It returns the result in new sheet(5Sapce).
 
−
 
 
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<nowiki>=FTESTANALYSIS(R1C1:R3C2, R1C2:R3C2, -1, TRUE)</nowiki>
 
−
 
 
−
It returns the #ERROR(Alpha =-1).
 
−
 
 
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</div>
 
−
----
 
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<div id="10SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="justify">Syntax </div><div class="ZEditBox"><center></center></div></div>
 
−
----
 
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<div id="4SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="justify">Remarks </div></div>
 
−
----
 
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<div id="3SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="justify">Examples </div></div>
 
−
----
 
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<div id="11SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="justify">Description </div></div>
 
−
----
 
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<div id="2SpaceContent" class="zcontent" align="left">
 
−
 
 
−
{| id="TABLE3" class="SpreadSheet blue"
 
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|- class="even"
 
−
| class=" " |
 
−
| Column1
 
−
| Column2
 
−
| class="  " | Column3
 
−
| Column4
 
−
|- class="odd"
 
−
| class=" " | Row1
 
−
| 8
 
−
| 3
 
−
| class="sshl_f" | 5Space
 
−
| class="sshl_f" | 5
 
−
|- class="even"
 
−
| class=" " | Row2
 
−
| 7
 
−
| 8
 
−
| class="  " | 9
 
−
| class="sshl_f" | 128
 
−
|- class="odd"
 
−
| Row3
 
−
| 12
 
−
| 9
 
−
| 14
 
−
| class="sshl_f    " | 15
 
−
|- class="even"
 
−
| Row4
 
−
| class=" " | 17
 
−
| class=" " | 18
 
−
| class="sshl_f" | 10000
 
−
| class=" " | 20
 
−
|- class="odd"
 
−
| class=" " | Row5
 
−
| class=" " | 44
 
−
| class=" " | 35
 
−
| class="sshl_f" | #ERROR
 
−
| 168
 
−
|- class="even"
 
−
| Row6
 
−
| class=" " | 6
 
−
| class=" " | 2
 
−
| class="      SelectTD1 ChangeBGColor SelectTD1" |
 
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<div id="2Space_Handle" class="zhandles" title="Click and Drag to resize CALCI Column/Row/Cell. It is EZ!"></div><div id="2Space_Copy" class="zhandles" title="Click and Drag over to AutoFill other cells."></div><div id="2Space_Drag" class="zhandles" title="Click and Drag to Move/Copy Area.">[[Image:copy-cube.gif]]  </div>1.619775
 
−
| 0.525322
 
 
|}
 
|}
 +
=FTEST(B1,C2:C3)=NAN
  
−
<div align="left">[[Image:calci1.gif]]</div></div>
+
==See Also==
−
----
+
*[[Manuals/calci/FDIST  | FDIST ]]
−
<div id="5SpaceContent" class="zcontent" align="left">
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*[[Manuals/calci/FINV  | FINV ]]
−
 
 
−
{| class="SpreadSheet blue"
 
−
|+ <br />F-Test Two-Sample for Variances
 
−
|- class="even"
 
−
!
 
−
! Variable1
 
−
! Variable2
 
−
|- class="odd"
 
−
| Mean
 
−
| 15.666666666666666
 
−
| 12.5
 
−
|- class="even"
 
−
| Variance
 
−
| 209.0666666666667
 
−
| 153.9
 
−
|- class="odd"
 
−
| Observations
 
−
| 6
 
−
| 6
 
−
|- class="even"
 
−
| Degree Of Freedom
 
−
| 5
 
−
| 5
 
−
|- class="odd"
 
−
| F Value
 
−
| 1.3584578730777563
 
−
|- class="even"
 
−
| P(F&lt;=f) one-tail
 
−
| 0.37247330494764646
 
−
|- class="odd"
 
−
| F Critical one-tail
 
−
| NaN
 
−
|}
 
  
−
</div>
+
==References==
−
----
+
[http://en.wikipedia.org/wiki/F-test  F Test]

Revision as of 05:21, 17 December 2013

FTEST(ar1,ar2)


  • 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 } are array of data.

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:

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=\frac{1}{n} \sum_{i=1}^n Xi} 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 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 n−1} 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 m−1} degrees of freedom.
  • In FTEST(ar1,ar2) 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 ar1} 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 ar2} 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 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} 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 ar2} is less than 2 or the variance of the array value is zero, then this function will return the result as error.

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

See Also

References

F Test

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