1 Black sea bass (Centropristis striata), whose range is the eastern coast of the United States. 2  Genus Caesioperca. 3  Butterfly perch (Caesioperca lepidoptera), found in the eastern Indian Ocean, and southwest Pacific Ocean including southern Australia and New Zealand. Black sea bass (Centropristis striata), whose range is the eastern coast of the United States. 2  Genus Caesioperca. 3  Butterfly perch (Caesioperca lepidoptera), found in the eastern Indian Ocean, and southwest Pacific Ocean including southern Australia and New Zealand.
The F ratio is drawn from a distribution. If we assume the null hypothesis is true we get one distribution, and if we assume that it is false with various assumptions about effect size, sample size, and so forth we get another distribution. We then do a study and get an F value. When the null hypothesis is false, it is still possible to get an F ratio less than one. The larger the population effect size is (in combination with sample size), the more the F distribution will move to the right, and the less likely we will be to get a value less than one.
It does this by comparing the ratio of two variances. So, if the variances are equal, the ratio of the variances will be 1. All hypothesis testing is done under the assumption the null hypothesis is true. If the null hypothesis is true, then the F test-statistic given above can be simplified (dramatically). This ratio of sample variances will be test statistic used. If the null hypothesis is false, then we will reject the null hypothesis that the ratio was equal to 1 and our assumption that they were equal. There are several different F-tables. Each one has a different level of significance.