In Bayes' Theorem, the Likelihood Ratio is how likely your hypothesis is in relation to all other hypotheses posited, and also shows how strongly the evidence favors, or disfavors, your hypothesis. This is simply dividing P(E|H) by P(E|~H). Let's say we're presented with the following scenario:Two people have left traces of their own blood at the scene of a crime. A suspect, Oliver, is tested and found to have type O blood. The blood groups of the two traces are found to be of type O (a common type in the local population, having frequency 60%) and of type AB (a rare type, with frequency 1%). Do these data (the blood types found at the scene) give evidence in favour of the proposition that Oliver was one of the two people whose blood was found at the scene?So in this scenario, if Oliver accounts for the O type blood, then one unknown person accounts for the the AB. This gives us the P(E|H) = 1% or 0.01. You may say, at this point, that it fits the hypothesis of Oliver being there, since if Oliver was there, and he left blood, then at least one of the samples of blood would be type O.On the other hand, if Oliver is not guilty, ~H, then this gives us P(E|~H). Or that two unknown people left blood at the scene. What is the probability of finding the evidence at hand if Oliver is not guilty? This means we have two people at random who at each random selection has to account for either the 1% or the 60%. This becomes 2 * 0.01 * .6, which is 1.2% or 0.012.[table]As you can see from this chart, a Likelihood Ratio that is lower than 1 means that it slightly supports the hypothesis that Oliver isnotguilty! Or in other words, there's a higher probability of finding the evidence that we have if Oliver were indeed not at the scene of the crime and two other random people committed the murder. Going back to the simpler form of Bayes Theorem, P(E|H) would be the 0.01 and that is denominated by P(E). P(E) in this case would be the probability of finding the evidence at hand period, which is 2 * 0.01 * .6, which is 1.2% or 0.012. Again, P(E|H) < P(E). So even though the evidenceintuitivelyfits the hypothesis that Oliver is guilty, it is more likely, due to the math implicit in the evidence, that Oliver is not guilty.

*other*religion. Equally so from a Muslim point of view, a Zoroastrian point of view, a Mithraist point of view, and on. This means that our P(E | H), the probability of having a religious experience

*given*the truth of some religion, is insanely low, because the vast majority of people who have had religious experiences were not Christians (or Muslims, or Hindus, etc).

*against*the hypothesis of the truth value of some religion, even though it might be intuitive to think the opposite.

*even lower*.