Statistics class today : Am I correct or is my teacher?

A

Algo_Design_Kid

Unless I got way too high in the parking lot before class I do not see how this makes any sense. Here is how it went down.

She takes a small box of blue and white crystals, they were split evenly. She shook them up etc.

So she hands 5 people a "random" ( even though it wasn't ) sample of crystals. There was a total of about 50.

Here is a close example of how it turned out.

Person 1 - 9 Total - 3 Blue

Person 2 - 10 Total - 0 Blue

Person 3 - 5 Total - 2 Blue

Person 4 - 2 Total - 1 Blue

Person 5 - 3 Total - 3 Blue


Anyway, she is going over what type(s) of bias were present. Some person raises their hand and says it is biased because some people GOT MORE than the other when she was handing them out.

I thought in my mind immediately that was strange. The teacher was like yepp.. then went on.. I didnt say anything.

So when she was done talking I raised my hand and asked why would it matter the amount each person got as long as you handed out the same amount of crystals and hypothetically it really was random?

She was like, you will learn why in chapter 5 and hurried along. I was going to say "Are you sure about that?" - but didn't - just because I could have really been too high at the time, but on the other hand it obviously wasn't worth it.

So really the question is, or better put my point, is that it shouldn't matter who got what because in the end the fractions should total up to the same amount from the total sample.

Did I fail here big time ( wouldn't surprise me ) or is my teacher really that dumb? State school of course.
 
I don't know, I'm still working my way through my Probability book. But I'd guess, Sample Size bias, or something named like that. I'd imagine it as, take it to an extreme case: suppose one person got a sample size of 46 of the 50 crystals, then the remaining 4 people got 1 crystal each. Then their estimates of the proportions would differ quite a bit. It's something like you need a sufficiently large sample to represent the true population sample.
I've found this in my own research -- sometimes, the probabilities will be 0%, 20%, 40%, 60%, 80%, or 100%, and I think, "why is it never 30%"? The answer is one result per day, grouped by week, so the fractions are multiples of 1/5. In this case, I would need larger groups, or combine several weeks together, so it would be a multiple of a smaller fraction.

(To qualify my post, I don't know and and this is just a guess. I don't even have a class, I just try to read and do the questions in the text on my own.)
 
She had a bias as to how she handed them out ( come to find out after the results ). She did this on purpose, but this shouldn't matter at all.

But my point is that it doesn't matter to whom she handed them, the total amount would still be the same.

For example, if someone got 5/5 blue, we could give 5 people 1 blue each and it would be the same exact thing.

Doesn't this make sense?
 
Quote from Mike805:

Have you been exposed to the central limit theorm yet?
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No, but I don't think this is any more advanced than adding and subtracting fractions, wouldn't you agree?
 
Quote from zedDoubleNaught:

I don't know, I'm still working my way through my Probability book. But I'd guess, Sample Size bias, or something named like that. I'd imagine it as, take it to an extreme case: suppose one person got a sample size of 46 of the 50 crystals, then the remaining 4 people got 1 crystal each. Then their estimates of the proportions would differ quite a bit. It's something like you need a sufficiently large sample to represent the true population sample.
I've found this in my own research -- sometimes, the probabilities will be 0%, 20%, 40%, 60%, 80%, or 100%, and I think, "why is it never 30%"? The answer is one result per day, grouped by week, so the fractions are multiples of 1/5. In this case, I would need larger groups, or combine several weeks together, so it would be a multiple of a smaller fraction.

(To qualify my post, I don't know and and this is just a guess. I don't even have a class, I just try to read and do the questions in the text on my own.)
More...

The proportions wouldn't matter though ( IMO ) because in the end it would all add up. I agree others had different proportions ( this is obvious ). But in the end they all add up to the same thing so how could the sample size make this have a "biased" result?
 
Quote from Algo_Design_Kid:

No, but I don't think this is any more advanced than adding and subtracting fractions, wouldn't you agree?
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The way your initial post was written, I immediately thought of a binary case of the CLT.

The CLT is one of those ideas that is useful to understand now since its is 1 of maybe 3 fundamental (and important) things you're going to learn in a basic stats class. If you learn anything from this class, learn the CLT.

Take a look at this neat calculator, it might shed some light on the example:

http://elonen.iki.fi/articles/centrallimit/index.en.html
 
Quote from Mike805:

The way your initial post was written, I immediately thought of a binary case of the CLT.

The CLT is one of those ideas that is useful to understand now since its is 1 of maybe 3 fundamental (and important) things you're going to learn in a basic stats class. If you learn anything from this class, learn the CLT.

Take a look at this neat calculator, it might shed some light on the example:

http://elonen.iki.fi/articles/centrallimit/index.en.html
More...

OK, I will take a look at this.

Maybe I explained this poorly in the beginning.

Nothing really matters, IMO, in this example except eventually how many of these crystals were handed out. No matter if she divided all these up between 2 or 100 people, in the end it doesn't matter who received how many because in the end the exact amount would remain the same.

In this example we weren't looking for how many permutations could occur etc. -> just a straight up first day example. My point was that there could be no such thing as "sample size bias" because it doesn't matter to whom the crystals were given - only how many.
 
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