Documentation/Calc Functions/FTEST
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Function name:
FTEST
Category:
Statistical Analysis
Summary:
Calculates the result of a two-tailed F-test to determine whether the variances of two sample sets are significantly different.
A returned value that is greater than some predetermined significance threshold (often taken to be 0.05 or 5% for example) indicates that the null hypothesis, that there is no difference between the variances of the two populations, should not be rejected. A smaller value than the significance threshold supports the alternative hypothesis that the variances of the two populations are not equal.
Syntax:
FTEST(Data 1; Data 2)
Returns:
Returns a real number in the range [0, 1], which is the result of the F-test expressed as a two-tailed probability.
Arguments:
Data 1 is an array of real numbers that is one of the sample data sets. This argument can take the form of an explicit cell range, the name of a named range, the name of a database range, or an inline constant array. Data 1 must contain at least two numbers.
Data 2 is an array of real numbers that is the other sample data set. This argument can take the form of an explicit cell range, the name of a named range, the name of a database range, or an inline constant array. Data 2 must contain at least two numbers. Data 2 need not have the same dimensions as Data 1.
- If either Data 1 or Data 2 is not a multi-cell array, then FTEST reports a #VALUE! error.
- FTEST ignores any referenced cell that contains text or is empty.
- If either Data 1 or Data 2 contains less than two numeric values, then FTEST reports a #VALUE! error.
- If either Data 1 or Data 2 has a variance of 0, then FTEST reports a #VALUE! error.
Additional details:
- Calc's FTEST and F.TEST functions perform identical calculations. The requirements for FTEST are specified in ODF 1.2; F.TEST is provided for interoperability with Microsoft Excel.
- FTEST calculates an F-statistic ([math]\displaystyle{ F\_stat }[/math]) from the supplied data arrays using the formula:
- [math]\displaystyle{ F\_stat~=~\frac{s_{larger}^2}{s_{smaller}^2} }[/math]
- where [math]\displaystyle{ s_{larger}^2 }[/math] and [math]\displaystyle{ s_{smaller}^2 }[/math] represent the sample variances of the two data sets, arranged so that the larger is the numerator and the smaller is the denominator.
- FTEST then returns the value:
- [math]\displaystyle{ \text{FTEST}~=~2\:\times\:\text{FDIST}(F\_stat;\:C_{larger}-1;\:C_{smaller}-1) }[/math]
- where [math]\displaystyle{ C_{larger} }[/math] is the count of numbers in the array with the larger variance and [math]\displaystyle{ C_{smaller} }[/math] is the count of numbers in the array with the smaller variance.
- For more information about F-tests, visit Wikipedia's F-test page.
Examples:
The data in the following table is utilized in the first example below.
A | B | |
---|---|---|
1 | 200 | 123 |
2 | 123 | 181 |
3 | 138 | 169 |
4 | 103 | 143 |
5 | 186 | 179 |
6 | 179 | 165 |
Formula | Description | Returns |
---|---|---|
=FTEST(A1:A6; B1:B6) where cells A1:B6 contain the data shown in the table above. | Here the function indicates a 26% probability that the variances of these two samples are not significantly different. Assuming a significance threshold of 0.05 or 5%, this result does not provide justification for rejecting the null hypothesis that there is no difference between the variances of the two populations. Note that the formulas =F.TEST(A1:A6; B1:B6) and =FTEST(B1:B6; A1:A6) return the same result. |
0.25968413745016 |
=FTEST({9;8;6;8}; {5;6;7}) | Here the function indicates an 82% probability that the variances of these two samples are not significantly different. Note that the two inline arrays passed as arguments have different dimensions. | 0.819367454566714 |
=FTEST({10;6;2;10;4}; {87;12;43;18;82}) | Here the function returns a very small probability of less than 1% and this undermines the null hypothesis and indicates that the two data sets may be taken from populations that have different variances. | 0.000637904251872183 |
Related LibreOffice functions:
ODF standard:
Related (or similar) Excel functions:
FTEST