Any statistical test that uses F-distribution can be called a F-test. It is used when the sample size is small i.e. n < 30.
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For example suppose one is interested to test if there is any significant difference between the mean height of male and female students in a particular college. In such a situation, t-test for difference of means can be applied.
However one assumption of t-test is that the variance of the two populations is equal- here two populations are the population of heights of male and female students. Unless this assumption is true, the t-test for difference of means cannot be carried out.
F-test's for Different Purposes
There are different types of t-tests each for different purpose. Some of the popular types are outlined below.
- F-test for testing equality of variance is used to test the hypothesis of equality of two population variances. The example considered above requires the application of this test.
- F-test for testing equality of several means. Test for equality of several means is carried out by the technique named ANOVA.
For example suppose that the efficacy of a drug is sought to be tested at three levels say 100mg, 250mg and 500mg. A test is conducted among fifteen human subjects taken at random- with five subjects being administered each level of the drug.
To test if there are significant differences among the three levels of the drug in terms of efficacy, the ANOVA technique has to be applied. The test used for this purpose is the F-test.
- F-test for testing significance of regression is used to test the significance of the regression model. The appropriateness of the multiple regression model as a whole can be tested by this test. A significant F indicates a linear relationship between Y and at least one of the X's.
Irrespective of the type of F-test used, one assumption has to be met. The populations from which the samples are drawn have to be normal. In the case of F-test for equality of variance, a second assumption has to be satisfied in that the larger of the sample variances has to be placed in the numerator of the test statistic.
Like t-test, F-test is also a small sample test and may be considered for use if sample size is < 30.
In attempting to reach decisions, we always begin by specifying the null hypothesis against a complementary hypothesis called alternative hypothesis. The calculated value of the F-test with its associated p-value is used to infer whether one has to accept or reject a null hypothesis.
All software's provide these p-values. If the associated p-value is small i.e. (<0.05) we say that the test is significant at 5% and one may reject the null hypothesis and accept the alternative one.
On the other hand if associated p-value of the test is >0.05, one may accept the null hypothesis and reject the alternative. Evidence against the null hypothesis will be considered very strong if p-value is less than 0.01. In that case, we say that the test is significant at 1%.