Difference between revisions of "Manuals/calci/FTEST"

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:

${\bar {X}}={\frac {1}{n}}\sum _{i=1}^{n}Xi$ and

{\bar {Y}}={\frac {1}{m}}\sum _{i=1}^{m}Yi

.

The sample variances :

 $SX^{2}={\frac {1}{n-1}}\sum _{i=1}^{n}(Xi-{\bar {X}})^{2}$

and

SY^{2}={\frac {1}{m-1}}\sum _{i=1}^{m}(Yi-{\bar {Y}})^{2}

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

References

F Test

List of Main Z Functions

Z3 home

@@ Line 1: / Line 1: @@
-<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==
 *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 .
+*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 .
+*Let X1,...Xn and Y1,...Ym be independent samples each have a Normal Distribution .
-*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.
+*It's sample means:
-*Then the test statistic= Sx^2/Sy^2   has an F-distribution with n − 1 and m − 1 degrees of freedom.
+<math>\bar X=\frac{1}{n} \sum_{i=1}^n Xi</math>
-*In FTEST(ar1,ar2) where ar1 is the data of  first array,ar2 is the data of second array.
+and
-*The array may be any numbers, names, or refernces that contains numbers.
+:<math>\bar Y =\frac {1}{m} \sum_{i=1}^m Yi</math> .
-*Suppose the array contains any text, logical values or empty cells like that values are not considered.
+*The sample variances :
-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.
+ <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==
+.
+{| class="wikitable"
+ |+ DATA1
+ |-
+ | 15
+ | 27
+ | 19
+ | 32
+|}
+{| class="wikitable"
+ |+ DATA2
+ |-
+ | 21
+ | 12
+ | 30
+ | 11
+|}
+ =FTEST(B4:B8,C4:C8)=0.81524906747183
+.
+{| class="wikitable"
+ |+ DATA1
+ |-
+ | 5
+ | 8
+ | 12
+ | 45
+ | 23
+|}
+{| class="wikitable"
+ |+ DATA2
+ |-
+ | 10
+ | 20
+ | 30
+ | 40
+ | 50
+|}
+ =FTEST(A1:A5,C1:C5)=0.9583035732212274
+.
+{| class="wikitable"
+ |+ DATA1
+ |-
+ | 14
+ | 26
+ | 37
+|}
+{| class="wikitable"
+ |+ DATA2
+ |-
+ | 45
+ | 82
+ | 21
+ |17
+|}
+ FTEST(B1:B3,C1:C4} = 0.26412211240525474
+.
+{| class="wikitable"
+ |+ DATA1
+ |-
+ | 14
+|}
+{| class="wikitable"
+ |+ DATA1
+ |-
+ | 45
+ | 65
+|}
+ =FTEST(B1,C2:C3)=NAN
+==Related Videos==
-.DATA1          DATA2
+{{#ev:youtube|tscL1fzjSTY|280|center|F-Test}}
-                   21
-                  12
-                  30
-                    11
-FTEST(B4:B8,C4:C8)=0.81524906747183
-.DATA 1={5,8,12,45,23};  DATA2={10,20,30,40,50}
- FTEST(A1:A5,C1:C5)=0.9583035732212274
-. DATA1={14,26,37};DATA2={45,82,21,17}
-FTEST(B1:B3,C1:C4}=0.26412211240525474
-.DATA1={25},DATA2={45,65}
-FTEST(B1,C2:C3)=NAN
 ==See Also==
@@ Line 32: / Line 113: @@
 *[[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 ]]

Difference between revisions of "Manuals/calci/FTEST"

Latest revision as of 17:07, 7 August 2018

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