Week 9 Flashcards
Relate a sufficient statistic to the NP lemma
It is trivial to prove that if the test statistic inequality holds, so to does the one above
Can you use a sufficient statistic for composite hypothesis testing
Yes if the suff stat has a monotone likelihood ratio
Def monotone likelihood ratio
Karlin Rubin theorem
finding c for LRT
Intuitive interpretation of LRT
Lecture 27
Tests of significance
Purpose of test of significance
To measure the strength of the evidence provided by experimental data AGAINST NULL
Test of significance requires
Discrepancy measure or test criterion D(x) >= 0
P dist of D under Null
Define significance level or p value
= 1 - F0(d)
= 1 - CDF under null hypothesis at discrepancy value d
= area under curve P( D | H0)
Interpretation of p value
Smaller the p value, the larger the evidence against null by observed x
Lack of evidence against null CANT be interpreted as evidence in favour of null
p values do not provide evidence in favour of hypothesis
Interpretation of discrepancy measure
D(•) ranks samples x according to their strength of evidence against null
If x’ contains stronger evidence against null than x’’ then D(x’) > D(x’’)
Observed discrepancy D = d is regarded as large if the P of getting a larger value is small
That is to say d is an outlier in the dist of D
Distribution of p value
Prove dist of p value
Choosing discrepancy test
Generally
