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F-TEST
F-test can be defined as the statistical test in which the test statistic has an F-distribution under the null hypothesis and it is most often used when a Model selection has been fitted to a data set. This is to categorize the model that best fits the population from which the data were sampled and it arises mainly when the models have been fitted to the data using least squares
It arises by considering a decomposition of the variance in a collection of data in terms of the sum of squares and the test statistic in this test is the ratio of two scaled sums of squares reflecting different sources of variability.
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The sum of squares is computed so that the statistic tends to be greater. This situation arises when the null hypothesis is not true and in order for the statistic to follow the F-distribution under the null hypothesis, the sums of squares are considered to be independent. Apart from that, it must follow a scaled Chi-squared distribution and the latter condition is guaranteed if the data values are independent. It is having a normal distribution with a common variance.
It is the one-way analysis of variance used to assess whether the expected value of a quantitative variable within several pre-defined groups differs from each other and an example; is suppose that a medical trial compares four treatments.
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The ANOVA F-test is used to assess whether any of the treatments are on average superior or inferior to the others versus the null hypothesis. Then all four treatments result in the same mean responses. This is an example of an "omnibus" test which means that a single test is performed to detect any of several possible differences.
The advantage of the ANOVA F-test is that it is not required to pre-specify which treatments are to be compared. It is not required to correct for making multiple comparisons. One of the disadvantages of is that if the null hypothesis is rejected, the treatments required are unknown and can be said to be significantly different from the others.
If the test is carried out at level α it is impossible to state that the treatment pair with the greatest mean difference is significantly different at level α.
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