paranoid android: stats 101: std error question

[paranoid android]

As I delve deeper into blackjack, I now realize there would have been value in opening my stats 101 book in college.

I'm trying to comprehend what standard error is. If through simulation of a game of chance, I compute an edge of X% with a standard error of Y, does that indicate that the true edge (if I were to simulate infinitely) has a 68% chance of being X% +- Y and a 95% chance of being X% +- 2Y?

Or am I off base here? Thanks.

[Cacarulo]

> As I delve deeper into blackjack, I now
> realize there would have been value in
> opening my stats 101 book in college.

> I'm trying to comprehend what standard error
> is. If through simulation of a game of
> chance, I compute an edge of X% with a
> standard error of Y, does that indicate that
> the true edge (if I were to simulate
> infinitely) has a 68% chance of being X% +-
> Y and a 95% chance of being X% +- 2Y?

Yes, and 99% chance of being X% +- 3Y.

> Or am I off base here? Thanks.

Nope.

Sincerely,
Cac

[ES]

> Yes, and 99% chance of being X% +- 3Y.

> Nope.

> Sincerely,
> Cac

Doesn't the above refer to Standard DEVIATION, as opposed to Standard ERROR? When is Std. Dev. appropriate; when is Std. Err. appropriate? Std. Err. = Std. Dev./Sqrt(n), where n is the size of the sample.

[Cacarulo]

[paranoid android]

Standard deviation is a measure of the variability of what we are sampling. Standard error is the confidence we have in the results of our sample. The standard error is in fact a standard deviation. Rather than being a measure of the variability of what we are sampling, standard error is the standard deviation of the result produced by our sampling (if we were to perform an infinite number of samples using the same parameters - e.g. same number of rounds). That's why we can say we are 95% certain that our measurement is accurate within +- 2 standard errors of our result, similar to what we do with standard deviations.

This is according to my understanding. Bear in mind I'm still trying to get a grasp on these concepts myself, so take this for what it's worth.

> Doesn't the above refer to Standard
> DEVIATION, as opposed to Standard ERROR?
> When is Std. Dev. appropriate; when is Std.
> Err. appropriate? Std. Err. = Std.
> Dev./Sqrt(n), where n is the size of the
> sample.

[Don Schlesinger]

Everything you've written is 100% correct -- with standard error of zero! :-)

Don