Not able to play this movie? Please report it to us.We can remove problematic link immediately.F-ratio
For instance, at a 90 percent confidence level the null hypothesis is that the ratio of the average means is the same for the groups. The F-ratio, such as the one in Table 2, is then calculated as
where and are the averages for the two groups, and is the ratio of the averages.
Although the F-ratio does not depend on the actual size of the groups, the precision of its estimate does depend on the size of the groups. With two small samples, a significant difference may be apparent even if the ratio of the means is close to the null hypothesis.
It also assumes that the data follows a standard normal distribution, which is unlikely. In such cases, Fisher's Transformation should be used instead.
In equal-variance cases
F-ratios are used in significance tests for case-control studies. In these tests, a null hypothesis is that the (case vs control) ratio of the number of cases, for example, is the same as the (control vs case) ratio of the number of controls. If the null hypothesis is true, the controls should be chosen at random. If the null hypothesis is false, however, there are biases and inflations of false positives, where it is claimed that the treatment is effective.
Assume that there are two experimental groups, one a treatment group and the other a control group. It is assumed that the treatments are randomly assigned to the groups.
The number of subjects in the treatment group is, and in the treatment group is. We assume that the samples are approximately drawn from the same population and the same experiment is repeated over and over again in both groups.
Thus, where is the number of cases in the control group, and is the number of controls.
Then the one-sample F-test is given by
where is the number of cases in the study.
We assume that the variance of the number of cases in each of the groups is the same, that is, the variance of and the variance of are equal.
From the F-test we conclude that if where is the ratio of the two variances, then the null hypothesis is 0b46394aab