Objective Function and Generic Function (4)
―Mathematical Methods for Functionality Evaluation (2) Statistics and Probablity, R.A.Fisher & Mathematical Statistics―
2005 Volume 13 Issue 1 Pages 7-16
Details
2005 Volume 13 Issue 1 Pages 7-16
The F test was derived by R.A.Fisher. It was not, by any means, derived as a variance ratio test, but as a likelihood ratio test. An explanation of the shortest way of deriving the F test from the likelihood ratio is the purpose of this section. The author considers that the F value as the ratio of variance, since that R.A.Fisher does not take the standpoint of this section. Variance ratio is the concept that holds more broadly. The probability Pr that a phenomenon which occurs r times with probability p when tried n times independently is determined by the theory of probability as a binomial distribution,
pr=(n) pr(1-p)n-r (r=0, 1, ・・・, n)
(r)
That is
Premise regarding Phenomenon
How much degree the phenomenon occur?
But in statistics, we ask: What is the true value of p, after observing an actual result, that is
Observed r time after n trial
How much degree the phenomenon occur?
