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)
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==Examples==
 +
1.
 +
{| class="wikitable"
 +
|+ DATA1
 +
|-
 +
| 15
 +
| 27
 +
| 19
 +
| 32
 +
|}
  
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where,
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{| class="wikitable"
 +
|+ DATA2
 +
|-
 +
| 21
 +
| 12
 +
| 30
 +
| 11
 +
|}
  
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'''Array1 and Array2 '''- Input range should be one  blocks.
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=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.
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{| 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>
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{| class="wikitable"  
−
----
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|+ 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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----
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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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+
|}
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F-TEST TWO SAMPLE FOR VARIANCES
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{| class="wikitable"  
−
 
+
|+ DATA1
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</div></div>
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  |-  
−
----
+
| 45
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<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>
 
−
 
 
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It returns the result in new sheet(5Sapce).
 
−
 
 
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<nowiki>=FTESTANALYSIS(R1C1:R3C2, R1C2:R3C2, -1, TRUE)</nowiki>
 
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It returns the #ERROR(Alpha =-1).
 
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</div>
 
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----
 
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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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----
 
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<div id="4SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="justify">Remarks </div></div>
 
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----
 
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<div id="3SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="justify">Examples </div></div>
 
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----
 
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<div id="11SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="justify">Description </div></div>
 
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----
 
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<div id="2SpaceContent" class="zcontent" align="left">
 
−
 
 
−
{| id="TABLE3" class="SpreadSheet blue"
 
−
|- class="even"
 
−
| class=" " |
 
−
| Column1
 
−
| Column2
 
−
| class="  " | Column3
 
−
| Column4
 
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|- 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)


  • and 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:

and

.
  • The sample variances :

and

  • Then the Test Statistic = has an F-distribution with Failed to parse (syntax error): {\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 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.

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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