Hypothesis testing

[mangogogo ()]

Arbuthnot(1710) observed that there were systematically more male than female

                births in any years

Edgeworth(1885) consider a test of difference of two means (normal)

                                           ^    ^       ^  2   ^   2
                (a)Edgeworth's proposal:(|μ_1-μ_2|)/(σ_1  + σ_2 )^(1/2)

Karl Person(1900) Introdution to the chi-square test

                (a)chi-square test uses an asymptotuc distribution

                (b)This is the first use of p-value

                (c)The distribution for the test is free of assuming f_0

Gossett(1908) Introduce t-statistics to test the hypothesis H_0
(pen-name:student)

                (a)First finite same theorey for hypothesis testing

                (b)First pivotal quantity was developed

                (c)He devived the t-distribution

                   (Fisher success)

Fisher(1915)    (a)He introduced the null hypothesis
                                                         _
                (b)He formally  introduced the notation (X-μ_0)/s/√n  ~t(n-1)

                (c)He introduced the terminology "test statistic"

                (d)Most test statistics currently used were introduced by him

Neyman-pearson(1933)
(kral-pearson's sun)
                Optimal properties

                (a)If in the sample hypothesis,MP-test always exists

                (b)If in the one side hypothesis,UMP test exists unless

                   monotonic likelihood in a statistic exist.

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