statistics 2....immediate help required?

Let’s start from scratch.

I have here a bag of marbles. You are not permitted to look into the bag. I tell you it contains all white marbles. You reach in and pull one out. It is black. What do you know?? Well, you know I’m a liar. (With a name like “Tony” wot do youse expect?)

O.K., now that you’ve “caught me”, I tell you. “Well, actually, there is one black marble in the bag and 9 white ones.” You replace the marble you took out, reach in, and pull out a(nother?) black marble. What do you know? Well, it is unlikely you would pull out two black marbles in a row if the probability is 1/10 on each try. With two tries, you have a 1/100 chance of doing that. Is it possible? Sure. You then reach in and pull out another black marble. NOW you have a decision to make. Do you call me a liar or not??

If you call me a liar and there is in fact only one black marble in the bag, you have made an error (and hurt my feelings). On the other hand, if you say, “Well, it could be true” and it is NOT true, then you have also made an error. The first error is called a “Type I” or “alpha” error; the second is called a “Type II” or Beta error.

That, my dear, is the essence of “hypothesis testing”. We take a sample from some population and compute some statistic on it (e.g. mean). We make some hypothesis about what that number should look like based upon some theory or information. We then compute how likely (probability--root word probably) that result is if in fact our original supposition is correct. Typically, in most instances, we choose .05 as the “significance level” in that if the result we observe would happen less than 5 times in a hundred, we will conclude that our original hypothesis is incorrect (reject the “null” hypothesis).

There are MANY statistics we can compute and MANY ways to determine the probability in various cases.

You never "prove" something is true in statistics. You DISPROVE things. Once you have divided the space into two mutually exclusive sets (bet you thought you would never use that set theory again), and you can prove that "truth" is NOT contained in one of those spaces, you conclude that it MUST be in the other set. NOTE: The fact that it is in the other space is a logical statement, not a statistical one.

As such, we conclude that the results are reasonable given our original data. There is no reason to conclude that this sample statistic (mean) is other than chance variation. (not to say it IS, only that we cannot conclude it is NOT.)

always,

tony

A Type I error is when you reject a true null hypothesis.

A Type II error is when you accept a false null hypothesis.