Examples of odds in the following topics:
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- An odds ratio is the ratio of two odds.
- In order to compute the odds ratio, one follows three steps:
- Divide the first odds by the second odds to obtain the odds ratio.
- The odds of a man drinking wine are $90$ to $10$ (or $9:1$) while the odds of a woman drinking wine are only $20$ to $80$ (or $1:4=0.25:1$).
- The log odds ratio shown here is based on the odds for the event occurring in group $B$ relative to the odds for the event occurring in group $A$.
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- Look in the sports section of a newspaper or on the Internet for some sports data (baseball averages, basketball scores, golf tournament scores, football odds, swimming times, etc.).
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- A third commonly used measure is the "odds ratio. " For our example, the odds of being healthy on the Mediterranean diet are 90:10 = 9:1; the odds on the AHA diet are 79:21 = 3.76:1.
- The ratio of these two odds is 9/3.76 = 2.39.
- Therefore, the odds of being healthy on the Mediterranean diet is 2.39 times the odds of being healthy on the AHA diet.
- Note that the odds ratio is the ratio of the odds and not the ratio of the probabilities.
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- The basic fallacy results from misunderstanding conditional probability, and neglecting the prior odds of a defendant being guilty before that evidence was introduced.
- However, if the DNA evidence is the sole evidence against the accused, and the accused was picked out of a large database of DNA profiles, then the odds of the match being made at random may be reduced.
- The odds in this scenario do not relate to the odds of being guilty; they relate to the odds of being picked at random.
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- Bayes' rule relates the odds of event $A_1$ to event $A_2$, before (prior to) and after (posterior to) conditioning on another event $B$.
- The odds on $A_1$ to event $A_2$ is simply the ratio of the probabilities of the two events.
- More specifically, given events $A_1$, $A_2$ and $B$, Bayes' rule states that the conditional odds of $A_1:A_2$ given $B$ are equal to the marginal odds $A_1:A_2$ multiplied by the Bayes factor or likelihood ratio.
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- This is called the "relative risk reduction. " The article does not provide information necessary to compute the absolute risk reduction, the odds ratio, or the number needed to treat.
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- Whenever you weigh the odds of whether or not to do your homework or to study for an exam, you are using probability.
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- The median is unique and equal to $m = round(np)$ in cases where either $p \leq 1 \ln 2$ or $p \geq \ln 2$ or $|m np| \leq \min{(p, 1 p)}$ (except for the case when $p = \frac{1}{2}$ and n is odd).
- When$p = \frac{1}{2}$ and n is odd, any number m in the interval $\frac{1}{2} \cdot (n 1) \leq m \leq \frac{1}{2} \cdot (n + 1)$ is a median of the binomial distribution.