Difference between revisions of "Manuals/calci/FTEST"

Revision as of 14:48, 26 February 2018

FTEST(array1,array2)

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

.

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

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.

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

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

@@ Line 16: / Line 16: @@
 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.
+*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.