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20 Feb 2017: Tests of homogeneity, and connections to confidence intervals 10.1. Tests of homogeneity. ... Lecture 10. Tests of homogeneity, and connections to confidence intervals 2 (1–56).

20 Feb 2017: Tests of homogeneity, and connections to confidence intervals 10.1. Tests of homogeneity. ... Lecture 10. Tests of homogeneity, and connections to confidence intervals 2 (1–9).

20 Feb 2017: Pearson’s Chi-squared tests. Example 9.1 continued using R:. chisq.test(n,p=ptilde). data: n. ... Goodness-of-fit of a fully-specified null distribution. Likelihood ratio tests. Pearson's Chi-squared tests.

20 Feb 2017: Pearson’s Chi-squared tests. Pearson’s Chi-squared tests. Notice that (?) and (?) are of the same form. ... Pearson’s Chi-squared tests. Example 9.1 continued using R:. chisq.test(n,p=ptilde). data: n.

21 Feb 2017: Find the form of the likelihoodratio test of H0 : θ = 1 against H1 : θ = 1.21. ... Isthe test uniformly most powerful for testing H0 : θ = θ0 against H1 : θ > θ0?

10 Mar 2017: Included Barnard, Lindley, Plackett, Armitage etc. • Barnard developed the Sequential probability ratio test’. • ... Sequential probability ratio test (SPRT). • Most powerful sequential test between two hypotheses H0 and H1. •

28 Feb 2017: Suppose test n H0i with independent test statistics. Prob(at least one will reject an H0i| H0i true) = 1 – Prob(reject none). = ... So a simple method is to multiply the observed significance level by the number of tests.

20 Feb 2017: The ’generalised likelihood ratio test’. The next theorem allows us to use likelihood ratio tests even when we cannotfind the exact relevant null distribution. ... Generalised likelihood ratio tests. The 'generalised likelihood ratio test'.

6 Feb 2017: It says that the most powerful test (ie the one with the smallest Type II errorprobability), among tests with size smaller than or equal to α, is the size αlikelihood ratio ... This is called a z-test. Lecture 7. Simple Hypotheses 9 (1–1).

20 Feb 2017: W (θ) W(θ) for all θ Θ1. UMP tests may not exist. ... The ’generalised likelihood ratio test’. The next theorem allows us to use likelihood ratio tests even when we cannotfind the exact relevant null distribution.