Difference between revisions of "Manuals/calci/FTEST"

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(Created page with "<div id="6SpaceContent" class="zcontent" align="left"> '''FTEST''' ('''arr1''',''' arr2''') Where '''arr1'''   is the first array or range of data and a'''rr2''' is t...")
 
 
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<div id="6SpaceContent" class="zcontent" align="left">
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<div style="font-size:30px">'''FTEST(Array1,Array2)'''</div><br/>
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*<math>Array1</math> and <math>Array2 </math> are array of data.
 +
**FTEST(), returns the result of an F-test.
  
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'''FTEST''' ('''arr1''',''' arr2''')
+
==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 '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.
  
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Where '''arr1'''   is the first array or range of data and a'''rr2''' is the second array or range of data.
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==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}}
  
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</div>
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==Examples==
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----
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1.
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<div id="1SpaceContent" class="zcontent" align="left">
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{| class="wikitable"  
 +
|+ DATA1
 +
|-
 +
| 15
 +
| 27
 +
| 19
 +
| 32
 +
|}
  
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F-test calculates the two-tailed probability that the variances in arr1 and arr2 are not significantly different.
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{| class="wikitable"
 +
|+ DATA2
 +
|-  
 +
| 21
 +
| 12
 +
| 30
 +
| 11
 +
|}
  
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</div>
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=FTEST(B4:B8,C4:C8)=0.81524906747183
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----
 
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<div id="7SpaceContent" class="zcontent" align="left">
 
  
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·          The arguments must either be numbers or names, arrays, or references that contain numbers.
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2.
 +
{| class="wikitable"
 +
|+ DATA1
 +
|-
 +
| 5
 +
| 8
 +
| 12
 +
| 45
 +
| 23
 +
|}
  
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·          When the number of data points in arr1 or arr2 is less than 2, or if the variance of arr1 or arr2 is zero FTEST displays NaN.
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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="12SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="left">FTEST</div></div>
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|-  
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----
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| 45
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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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| 82
−
----
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| 21
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<div id="4SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="justify">Remarks </div></div>
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|17
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----
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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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FTEST(B1:B3,C1:C4} = 0.26412211240525474
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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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<div id="2SpaceContent" class="zcontent" align="left">
 
  
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{| id="TABLE3" class="SpreadSheet blue"
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4.
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|- class="even"
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{| class="wikitable"  
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| class="  " |
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  |+ DATA1
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<div id="2Space_Copy" title="Click and Drag over to AutoFill other cells."></div>
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  |-  
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| class=" " | Column1
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  | 14
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| class="     " | Column2
 
−
| class=" " | Column3
 
−
| class=" " | Column4
 
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|- class="odd"
 
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| class=" " | Row1
 
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| class="sshl_f " | 5
 
−
| class="sshl_f " | 17
 
−
| class="sshl_f" |
 
−
| class="sshl_f" |
 
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|- class="even"
 
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| class=" " | Row2
 
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| class="sshl_f" | 10
 
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| class="sshl_f" | 28
 
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| class="sshl_f" |
 
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| class="sshl_f" |
 
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|- class="odd"
 
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| Row3
 
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| class="sshl_f" | 4
 
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| class="sshl_f" | 35
 
−
| class="sshl_f" |
 
−
| class="sshl_f" |
 
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|- class="even"
 
−
| Row4
 
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| class="sshl_f" | 8
 
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| class="sshl_f" | 48
 
−
| class="sshl_f" |
 
−
| class="sshl_f" |
 
−
|- class="odd"
 
−
| class=" " | Row5
 
−
| class=" " | 19
 
−
| class="sshl_f " | 40
 
−
| class="sshl_f" |
 
−
| class="sshl_f" |
 
−
|- class="even"
 
−
| class="sshl_f" | Row6
 
−
| class="sshl_f" | 0.21573734399999997
 
−
| class="sshl_f" |
 
−
| class="sshl_f" |
 
−
|
 
−
|- class="odd"
 
−
| class="sshl_f" | Row7
 
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| class="sshl_f        " |
 
−
| class="SelectTD" |
 
−
| class="sshl_f" |
 
−
| class="sshl_f" |
 
 
|}
 
|}
 +
{| class="wikitable"
 +
|+ DATA1
 +
|-
 +
| 45
 +
| 65
 +
|}
 +
=FTEST(B1,C2:C3)=NAN
 +
 +
==Related Videos==
 +
 +
{{#ev:youtube|tscL1fzjSTY|280|center|F-Test}}
 +
 +
==See Also==
 +
*[[Manuals/calci/FDIST  | FDIST ]]
 +
*[[Manuals/calci/FINV  | FINV ]]
 +
 +
==References==
 +
[http://en.wikipedia.org/wiki/F-test  F Test]
  
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<div align="left">[[Image:calci1.gif]]</div></div>
 
−
----
 
−
<div id="8SpaceContent" class="zcontent" align="left"><font size="3"><font face="Times New Roman">''' <font size="3"><font face="Times New Roman">AVEDEV (N1, N2...)</font></font> <font size="3"><font face="Times New Roman">Where N1, N 2 ...   are positive integers.</font></font> '''</font></font></div>
 
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----
 
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<div id="5SpaceContent" class="zcontent" align="left">
 
  
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i.e =FTEST (C1R1:C1R5, C2R1:C2R5) is 0.2157
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*[[Z_API_Functions | List of Main Z Functions]]
  
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</div>
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*[[ Z3 |  Z3 home ]]
−
----
 

Latest revision as of 17:07, 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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