# Help to understand false positive ratio

From wikipedia:

In statistics, when performing multiple comparisons, the term false positive ratio, also known as the false alarm ratio, usually refers to the probability of falsely rejecting the null hypothesis for a particular test.

What's the meaning of falsely rejecting the null hypothesis for a particular test? Can you give me an example of the application of this?

EDIT: I'm not sure why one would want to use this concept.

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When we are making statistical decisions, we like to use hypothesis testing with which to base those on.

The hypothesis being tested is often called the null hypothesis and the other possibility is called the alternate hypothesis.

One of four things can happen

$\bullet$ Accept null

$\bullet$ Reject null (or accept alternate)

$\bullet$ Accept alternate

$\bullet$ Reject alternate (or accept null)

When we reject a hypothesis when it should be accepted, we say that is a Type I error.

When we accept a hypothesis when it should be rejected, we say that is a Type II error.

In either case, the wrong decision or error in judgement has occured.

Your tests should be designed to minimize errors of decision.

Example:

If you toss a coin a certain number of times, you expect a 50% chance for heads and for tails.

How can we tell if the coin is actually fair?

Let $p = \frac{1}{2}$ that we get a head.

So, lets decide on a hypothesis, and let it be that $p = \frac{1}{2}$, so this is the null hypothesis.

The other, alternate hypothesis, is that the coin is not fair, that is, $p \ne \frac{1}{2}$.

The null or alternate hypothesis must be true, since we only have two choices.

The question, which do you accept, the null and say it is false or reject the null and say the coin is unfair?

We decide to flip the coin n times, and get close to $\frac{n}{2}$, so we should accept it is fair. If it is very far from n/2, we should reject that it is fair.

How far from n/2 should we get before we say the coin is unfair? We want to make the right decision about the null hypothesis.

There are two ways to be right, accept the hypothesis when it is true, or reject it when it is false.

However, that also means there are two ways to be wrong.

Hopefully, you get the idea and have enough to seek out other examples.

Regards

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+1 for a full documentary answer. Thanks for your edit to my answer. – Babak S. Feb 1 '13 at 14:47
@BabakSorouh: Thanks and Regards! – Amzoti Feb 1 '13 at 15:34
@amWhy: Thank you for the support my friend! – Amzoti May 5 '13 at 0:41
Good for you for effort! – amWhy May 5 '13 at 0:50

This is the way hypothesis testing works in classical statistics. Suppose e.g. you want to test whether factor $X$ affects $Y$. So you conduct an experiment, in which you gather data and compute the value of a certain statistic $S$. The null hypothesis is that $X$ has no effect, the alternative hypothesis is that it has an effect. If you find a value of $S$ greater than a certain predetermined threshold $s$, you will reject the null hypothesis and thus conclude that $X$ does affect $Y$. If $S$ is less than $s$, you don't reject the null hypothesis: you can't ever say that there is no effect, just that you haven't found significant evidence for it.

Now you can never be completely sure: even if $X$ has no effect, there is a possibility that $S$ will turn out to be greater than $s$, and thus you will falsely reject the null hypothesis.
If your experiment is well-designed, the probability of that will be small.

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