Determining Sample Sizes

[magomago]

So I've been reading up on how to calculate sample sizes. I believe I understand it (Type I Error, Type II error, understand what each means and how you need to balance being accurate with what is cost effective based on previous data and indications, bla bla) save for one point:

The NIST handbook lists the sample size for a TWO sided test as :

http://www.itl.nist.gov/div898/handbook/prc/section2/prc222.htm

For a TWO sided test
N = [ Z(alpha/2) + Z(Beta)] ^2 * (ratio)^2

where ratio = std deviation
where alpha/2 = Assuming H0 is True, the probability of rejecting H0 (typically the tail end of the distrobution)
where Beta = Assuming H0 is False, the probability of accepting H0, when Ha is actually true (if HA is true, the distrobution that falls below the critical threshold value that alpha/2 is set at)


But these two sides actually, for a two sided test, have the equation multiplied by 2

http://vanbelle.org/chapters\webchapter2.pdf
http://www.jerrydallal.com/LHSP/sizenotes.htm

I've combed over both of these, as well as searched online (this has a good explanation of the error descriptions if you understand alpha levels and ocnfidence intervals http://www.statsdirect.com/help/basics/pval.htm) and it seems it comes down to the std error

on the .pdf on the second link, it looks like the std error = stdev *Sq(2/n). If you set both curve equal at the critical level, and use the std error = stdev * sq(2/n), you will get a factor of two in the equation
Elsewhere, I find the std error = stdev / sq(n)


so which is it? can anyone clear this up for me? thanks

 

[magomago]

so I figured out the answer a few weeks back and its just about the details:

when dealing with a single population mean, its sigma/sqrt(n) because bariance is sigma squared

the other (with the two) falls from the math when comparing TWO population means...