Manuals/calci/FTEST

FTEST(ar1,ar2)

• $ar1$ and $ar2$ 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:

${\bar {X}}={\frac {1}{n}}\sum _{i=1}^{n}Xi$ 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 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 $ar1$ 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.

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

• FDIST
• FINV

References

F Test