Difference between revisions of "Manuals/calci/FTEST"

Revision as of 03:25, 10 December 2013

FTEST(ar1,ar2)

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 = Failed to parse (syntax error): {\displaystyle \frac {Sx^2}{Sy^2}<math> has an F-distribution with <math>n−1} and Failed to parse (syntax error): {\displaystyle m − 1} degrees of freedom.
In FTEST(ar1,ar2) where $ar1$ is the data of first array, $ar2$ 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 $ar1$ or $ar2$ is less than 2 or the variance of the array value is zero, then this function will return the result as error.

1.DATA1 DATA2

 15                   21
  27                  12
  19                  30
 32                    11

FTEST(B4:B8,C4:C8)=0.81524906747183 2.DATA 1={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={25},DATA2={45,65} FTEST(B1,C2:C3)=NAN

@@ Line 11: / Line 11: @@
   <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>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.