Math Question

[SacDuc]

I suck at math so please pardon if I have my terminology all messed up.

Let's say you have an event that you believe is a 99:1 shot. How many independent trials would you have to run to be 95% sure that there is actually a 1% chance of this event happening?

Is there a formula where you could plug in odds of something happening (e.g. - 3:1 or 25%) the percentage of accuracy you need to confirm those odds to (presuming you only get perfect accuracy with an infinite number of trials) and get the number of trials you need to run.

Let me know if I need to clarify.

Thanks.

sac

[derby]

well, technically, you could run the same 99:1 trial 100 times and get the same result every time.

[il d00d]

I am not a math nerd, but remembering back to my statistic class probability always assumes an infinite number of "tries" -  if the probability of something happening is 10:1, in infinite amount of tries, this should be the actual outcome.  If you flipped a coin 10 times you might come up heads seven times, tails three, but the head to tail ratio would change the more you flipped the coin.  So, are you asking how many times, given a probability, you would have to try something to have the outcome come within 95% of the probability?  If so, I think that is a standard deviation problem, and I will be damned if I can remember how to do those.

[SacDuc]

well, technically, you could run the same 99:1 trial 100 times and get the same result every time.

Yes you could. But if you did run 100 trials of a 99:1 shot, how accurate are the results? That's the question.


sac

[Monster Dave]

Your question:

I suck at math so please pardon if I have my terminology all messed up.

Let's say you have an event that you believe is a 99:1 shot. How many independent trials would you have to run to be 95% sure that there is actually a 1% chance of this event happening?

Is there a formula where you could plug in odds of something happening (e.g. - 3:1 or 25%) the percentage of accuracy you need to confirm those odds to (presuming you only get perfect accuracy with an infinite number of trials) and get the number of trials you need to run.

Let me know if I need to clarify.

Thanks.

sac

What I read:

I suck at math so please pardon if I have my terminology all messed up.

Let's say you have an event that you believe is a 99:1 shot. How many blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah

blah blah blah blah blah blah blah

Thanks.










Explanation:

I saw "math" and the start of a word problem......


......my brain just shut down.  

[SacDuc]

I am not a math nerd, but remembering back to my statistic class probability always assumes an infinite number of "tries" -  if the probability of something happening is 10:1, in infinite amount of tries, this should be the actual outcome.  If you flipped a coin 10 times you might come up heads seven times, tails three, but the head to tail ratio would change the more you flipped the coin.  So, are you asking how many times, given a probability, you would have to try something to have the outcome come within 95% of the probability?  If so, I think that is a standard deviation problem, and I will be damned if I can remember how to do those.

This is exactly what I am asking. It is indeed a standard deviation problem. Which is something I know make the beast with two backs all about.

sac

[zooom]

THE ANSWER IS 42




nuff said...

[SacDuc]

THE ANSWER IS 42




nuff said...

Incorrect.


The answer is ... 4?

[akmnstr]

As you have written your question you really cannot come up with an answer.  However if you were to change it slightly and say you would like to 99% certain of the outcome + or - 1% (or any amount you choose) then you could do a trial, use the outcome of that trial to do a power analysis (it would take to long to explain) and then you would have an estimate with an upper and lower limit.  

On the other hand, you might need to take a stats class.  

[Rameses]

The 95% certainty that you're referring to is known as the confidence level.

You're talking about a data set with an infinite population, since there is no finite limit to how many times the test can be repeated.

In order to calculate your sample size, you need one more parameter.  Confidence interval.

Confidence interval is a margin of error on your 1% chance.  Because there isn't a finite data set, you can never be 95% sure that the chance of the expected result is 1%.  You can only be 95% sure that the expected result is between 0% and 2% (which would be a confidence interval of 2%).

I think I remembered all of that right.  It's been a long time.

[SacDuc]

As you have written your question you really cannot come up with an answer.  However if you were to change it slightly and say you would like to 99% certain of the outcome + or - 1% (or any amount you choose) then you could do a trial, use the outcome of that trial to do a power analysis (it would take to long to explain) and then you would have an estimate with an upper and lower limit.  

On the other hand, you might need to take a stats class.  

But I don't want to take a stats class. I build houses for a living. I have no practical use for this knowledge. This is just the shit I think about when I'm awake at 3am. And no, I wasn't high.

Is this a valid question:

I ran 100,000 trials and 90,000 came up x and 10,000 came up y. How sure can I be that the ratio of x to y is actually 9:1?

Show you work.


sac

[SacDuc]

The 95% certainty that you're referring to is known as the confidence level.

You're talking about a data set with an infinite population, since there is no finite limit to how many times the test can be repeated.

In order to calculate your sample size, you need one more parameter.  Confidence interval.

Confidence interval is a margin of error on your 1% chance.  Because there isn't a finite data set, you can never be 95% sure that the chance of the expected result is 1%.  You can only be 95% sure that the expected result is between 0% and 2% (which would be a confidence interval of 2%).

I think I remembered all of that right.  It's been a long time.

Okay. So how do you calculate how many trials it takes to get to a 95% confidence level?

sac

[akmnstr]

I forgot to mention.  Don't forget about Type 1 and Type 2 error.  










just messing with ya

[Monster Dave]

[akmnstr]

But I don't want to take a stats class. I build houses for a living. I have no practical use for this knowledge. This is just the shit I think about when I'm awake at 3am. And no, I wasn't high.

Is this a valid question:

I ran 100,000 trials and 90,000 came up x and 10,000 came up y. How sure can I be that the ratio of x to y is actually 9:1?

Show you work.



sac

From what you did you can be certain that the ratio of your sample is 9:1.  If you took 10,000 samples of 10 each you could then average them and calculate a confidence interval around that average and that could be used to describe the population that you are taking your samples from.