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.
Under the null hypothesis, it has approximately a chi-square distribution whose number of degrees of freedom are. If the test statistic is improbably large according to that chi-square distribution, then one rejects the null hypothesis of independence. A related issue is a test of homogeneity.