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 :

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

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 SY^2=\frac{1}{m-1} \sum_{i=1}^m (Yi-\bar Y)^2.  *Then the Test Statistic = <math>\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 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 ar1} is the data of first array, 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 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 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 ar1} or 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 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