Since I’m ending up typing a lot of these in LaTeX lately, I’d figured I post them out there for reference. There’s a great LaTeX formula builder that I’ve been using here, definitely check it out if you need to do this kind of thing often.

Standard error of the difference between means

`$ sigma_{M_{1}-M_{2}} = sqrt{frac{sigma_{1}^{2}}{n_{1}}+frac{sigma_{2}^{2}}{n_{2}}}=sqrt{frac{sigma^2}{n}+frac{sigma^2}{n}}=sqrt{frac{2sigma^2}{n}} $`

**Standard Error**

`$ sigma_{M} = frac{sigma}{sqrt(N)} $`

**Binomial Probabilities**

`$ P(x)= frac{N!}{x!(N-x)!} pi^{x}(1-pi)^{N-x} $`

**Standard Error of the Estimate**

`$ sigma_{est} = sqrtfrac{sum (Y-Y')^2}{N} $`

**Pearson’s R**

`$ r = frac{Nsum{XY}-(sum{X}sum{Y})}{sqrt{ [N sum{x^2}-(sum{x})^2 ][N sum{y^2}-(sum{y})^2 }]} $`