# Boards

## Is anyone on DiS a maths genius?

Then please help explain "ODDS RATIOS" to me.....I've googled like forever and am still no closer to understanding what the fuck they are about :(

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Then please help explain "ODDS RATIOS" to me.....I've googled like forever and am still no closer to understanding what the fuck they are about :(

## yeah, no idea what you're on about.

i know odds and i know ratios but i aint ever heard of odds ratios.

but seeing as other maths geeks will click on this, i need to know the different terms for the following situations:

a) when three balls are picked out of a possible twenty-six, the chance of predicting the balls is 1/26 x 1/25 x 1/24

b) but the chance of predicting the last three letters of a registration plate is 1/26 x 1/26 x 1/26.

so what are the terms for the calculation of each of those probabilities?

## the difference

is that in example (a), I presume that you are working with a closed finite set i.e. 26 numbered balls in a bag, and you are not replacing them. Therefore, when you take a ball out of the bag, you are not putting it back, and so the number of balls decreases, hence the calculation in (a)

in (b), the letters can be next to each other, and repetition can occur, therefore the number of letters is always the same, hence calculation that you have.

hope that makes sense.

## .

A is known as Conditional Probablity. B is presumably Unconditional.

## odds ratios

are basically statistics to help you determine how sensitive a number of sets are compared to a variable that affects them both. That way, you can compare the two (or more) sets in relation to each other, using the common variable as the medium.

wiki's got a really good example that prob makes more sense than I do:

Suppose that in a sample of 100 men, 90 have drunk wine in the previous week, while in a sample of 100 women only 20 have drunk wine in the same period. 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 odds ratio is thus 9/0.25, or 36, showing that men are much more likely to drink wine than women. Using the above formula for the calculation yields the same result:

The above example also shows how odds ratios are sometimes sensitive in stating relative positions: in this sample men are 90/20 = 4.5 times more likely to have drunk wine than women, but have 36 times the odds. The logarithm of the odds ratio, the difference of the logits of the probabilities, tempers this effect, and also makes the measure symmetric with respect to the ordering of groups. For example, using natural logarithms, an odds ratio of 36/1 maps to 3.584, and an odds ratio of 1/36 maps to ?3.584.

http://en.wikipedia.org/wiki/Odds_ratios