The material I am working with:
http://personal.vu.nl/a.f.de.vos/primer/primer.pdf
The example that I am working on can be found on page 2, see picture at bottom of post. It is stated that "Prior odds of 99:1 ...change by the result to posterior odds 99:13.7, a 12% probability." Later it says the posterior odds are 13.7:1, so 6.7% still rather different."
What am I missing here?
Could this not be described as decimal too:
.073 * .99 = .07227
In other words 7.2%, a number different than stated in the paper
EDIT: still having trouble with final part of the problem
now solving (1-x)/x = 0.072993, we arrive at x = 93.2%
and
so (1-x)/x = 7.226 or x = 1/8.226 = 12.16% probability
are throwing me off
if the prior odds ratio is 99:1 (with a corresponding pre-felt probability of (1-x)/x = 99 ... x = 1% chance that the aunt has the ability)... multiplication by the likelihood results in posterior odds ratio of 99:13.7 = 7.226
odds are ratios of probabilities that add to unity
so (1-x)/x = 7.226 or x = 1/8.226 = 12.16% probability that p = 0.75 vs the alternative hypothesis of p=0.5 with a probability of 88.8% of the aunt not having the ability
if, instead the prior odds ratio was 1:1 (a priorly believed probability of 50%), after multiplying by the likelihood, you'd end up with a posterior odds ratio of 1/13.7 or 0.072993
now solving (1-x)/x = 0.072993, we arrive at x = 93.2% probability that p = 0.75 vs the alternative hypothesis that p = 0.5
note that 100%-93.2% = 6.7%
so in the first case a prior probability of 1% that the aunt has the ability is increased to 12.2% by the data likelihood
in the second case, the prior probability of 50% that the aunt has the ability is increased to 93.2%