目的機能と基本機能 (4)

―機能性の評価の数理(2), 統計と確率, R.A.Fisherの尤度と数理統計―

抄録

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 P_r 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,

　　　p_r=(n) p^r(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?