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 = Failed to parse (syntax error): {\displaystyle \frac {Sx^2}{Sy^2}<math> has an F-distribution with <math>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 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

See Also

• FDIST
• FINV

References

Correlation