# F test – Procedure & Examples

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The f test is a statistical test used to check for the equality of variance of two samples. It uses the F distribution to calculate the critical value.

We also use the F test in ANOVA and ANCOVA procedures to test for equality of means for three or more populations.

An example of a situation where the F test may be applied is as follows:

Suppose there are two manufacturers who produce bulbs of the same average lifetime. We wish to know whether the variances in the lifetimes of bulbs for the two manufacturing processes are equal or not.

To test this we shall formulate our null hypothesis as H0: σ12 vs the alternative hypothesis H1: σ1≠σ2. Here to test whether the variances are equal we shall use the F test.

### Procedure to carry out two sample F test for equality of variance:

1. Formulate the null hypothesis as σ12. In comparison, the alternative hypothesis will be H1: σ1≠σ2 for a two-sided test. The alternative hypothesis will be H1: σ1>σ2 or H1: σ1<σ2 for one-sided test.
2. Calculate the value of the F statistic using the formula, F= S12/S22 where S1 and S2 are the standard deviations for the two samples.
3. Compare the F statistic with the critical F table value at a given level of significance. If the value of the F statistic is greater than the critical value, then reject the null hypothesis otherwise accept the null hypothesis.

#### Assumptions when applying the F test:

1. The samples are independent.
2. The distribution is normal.

### Difference between the T test and the F test:

The main difference between the T-test and the F test is that the T-test is used to check for equality of means for one or two samples whereas the F test is used to test for equality of variances of two samples and also in ANOVA to test for equality of means in three or more populations.