FTest
Any statistical test that uses Fdistribution can be called an Ftest. It is used when the sample size is small i.e. n < 30.
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 1Statistical Hypothesis Testing
 2Relationships
 3Correlation
 4Regression
 5Student’s TTest
 6ANOVA
 7Nonparametric Statistics
 8Other Ways to Analyse Data
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, a ttest for difference of means can be used.
However one assumption of the ttest is that the variance of the two populations is equal; in this case the two populations are the populations of heights for male and female students. Unless this assumption is true, the ttest for difference of means cannot be carried out.
The Ftest can be used to test the hypothesis that the population variances are equal.
Ftests for Different Purposes
There are different types of ttests for different purposes. Some of the more common types are outlined below.

Ftest for testing equality of variance is used to test the hypothesis of the equality of two population variances. The height example above requires the use of this test.

Ftest for testing equality of several means. The test for equality of several means is carried out by the technique called ANOVA.
For example, suppose that an experimenter wishes to test the efficacy of a drug at three levels: 100 mg, 250 mg and 500 mg. 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 Ftest.

Ftest 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 value indicates a linear relationship between Y and at least one of the Xs.
Assumptions
Irrespective of the type of Ftest used, one assumption has to be met: the populations from which the samples are drawn have to be normal. In the case of the Ftest for equality of variance, a second requirement has to be satisfied in that the larger of the sample variances has to be placed in the numerator of the test statistic.
Like ttest, Ftest is also a small sample test and may be considered for use if sample size is < 30.
Deciding
In attempting to reach decisions, we always begin by specifying the null hypothesis against a complementary hypothesis called the alternative hypothesis. The calculated value of the Ftest with its associated pvalue is used to infer whether one has to accept or reject the null hypothesis.
All statistics software packages provide these pvalues. If the associated pvalue is small i.e. (< 0.05) we say that the test is significant at 5% and we may reject the null hypothesis and accept the alternative one.
On the other hand if the associated pvalue of the test is > 0.05, we should accept the null hypothesis and reject the alternative. Evidence against the null hypothesis will be considered very strong if the pvalue is less than 0.01. In that case, we say that the test is significant at 1%.
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Explorable.com, Lyndsay T Wilson (Jul 5, 2010). FTest. Retrieved Jul 10, 2019 from Explorable.com: https://explorable.com/ftest
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