1.5 lecture05

1.5 lecture05 - Odds Ratio STAT 1301 Probability &...

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1 STAT 1301 Lecture 5 Odds Ratio The odds ratio of an event A is defined by . ) ( 1 ) ( ) ( ) ( A P A P A P A P c The odds ratio of an event A tells how much more likely it is that the event A occurs than it does not occur. If the odds is equal to r , then it is common to say that the odds are “ r to 1” in favor of the hypothesis. Odds Ratio Consider now an hypothesis H that is true with probability P(H) and suppose that new evidence E is introduced. Then the conditional probabilities, given the evidence E, that H is true and that H is not true are given by The new odds ratio after the evidence E has been introduced is . ) ( ) ( ) | ( ) | ( , ) ( ) ( ) | ( ) | ( E P H P H E P E H P E P H P H E P E H P c c c . ) | ( ) | ( ) ( ) ( ) | ( ) | ( c c c H E P H E P H P H P E H P E H P Example Two coins, A and B, show heads with respective probabilities ¼ and ¾. Suppose that one of these coins is randomly selected
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This note was uploaded on 05/04/2011 for the course STAT 1301 taught by Professor Smslee during the Spring '08 term at HKU.

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1.5 lecture05 - Odds Ratio STAT 1301 Probability &...

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