TD_FTest performs an F-test, for which the test statistic follows an F-distribution under the Null hypothesis.
TD_FTest compares the variances of two independent populations. If the variances are significantly different, TD_FTest rejects the Null hypothesis, indicating that the variances may not come from the same underlying population.
Use TD_FTest to compare statistical models that have been fitted to a data set, to identify the model that best fits the population from which the data were sampled.
Assumptions
- Populations from which samples are drawn are normally distributed.
- Populations are independent of each other.
- Data is numeric.
Test Type
- One-tailed (lower and upper-tailed) or two-tailed (your choice)
- Two-sample
- Unpaired
Computational Method
The F-test is used to test the Null hypothesis σ2 = 
in various applications. For example, you might need to test the variability in the measurement of the thickness of a manufactured part in a factory. If the thickness is not equal to a certain thickness ( ) then you can conclude that the manufacturing process is uncontrolled. The types of hypothesis are as follows:
H0: σ2 =
versus
H1: σ2 > (upper-tailed)
or
H1: σ2 < (lower-tailed)
or
H1: σ2 ≠ (two-tailed)
Let x1, x2,....xn be a random sample. To test the above hypotheses, the test statistic is calculated as:
where 
The statistic χ2 follows an F distribution with n-1 degrees of freedom.
For the one-sided upper-tailed test σ2 > the Null hypothesis H0 is rejected if 
.
For the one-sided lower-tailed test σ2 < , the Null hypothesis H0 is rejected if 
.
For the two-sided alternative σ2≠ , the Null hypothesis H0 is rejected if
- One-tailed test: The test is used to determine if the variance of one population is either greater than (upper-tailed) or less than (lower-tailed) the variance of another population.
- Two-tailed test: The test is used to determine significant differences in variances of the two populations and tests the Null hypothesis (H0) against the alternative hypothesis (H1) to find out if the variances are not equal.
- Sample Means Formula:
- Sample Variance Formula:
- Sample Variance Formula for
and 
: 
and 
In the following calculation, assume that sample 1 has a larger variance than sample 2. If sample 2 has a larger variance than sample 1, switch the samples and apply the same formula.
H0: 
= 
versus
H1: >
or
<
The test statistic for the one-sided upper tailed test ( > ) is calculated as:
where: n1-1 and n2-1 are degrees of freedom corresponding to sample 1 and sample 2.
The Null hypothesis H0 is rejected if 
.
The test statistic for the one-sided lower-tailed test ( < ) is calculated as:
The Null hypothesis H0 is rejected if 
.
For the two-sided hypothesis test:
H0: =
versus
H1: ≠
The Null hypothesis H0 is rejected if:
The two-tailed test is based on the upper tail of the F-distribution.