t-test
compares the mean of two datasets and determines if they are similar enough
t-test
$$\frac{\hat{p}{1}-\hat{p}{2}}{\sqrt{ \frac{p_{1}(1-p_{1})}{n_{1}} +\frac{p_{2}(1-p_{2})}{n_{2}}}}$$
# null hypothesis
assumes that the mean of two populations is the same
# calculation
from Z-score
$$\frac{\text{difference between the samples}}{\sqrt{ \text{some measure of spread} }}$$
# Variance of $(\hat{p}{1}-\hat{p}{2})$
$$Var(\hat{p}{1}-\hat{p}{2})=Var(\hat{p}{1})+Var(\hat{p}{2})$$
$$Var\left(\sum^{n}{i=1}X{i}\right)=\sum^{n}{i=1}Var(X{i})$$
# Sudent’s t-test
# critical t statistic
$$t=\frac{\bar{x}{A}-\bar{x}{B}}{\sqrt{ \frac{s^{2}{A}}{n{A}}+\frac{s^{2}{B}}{n{B}} }}$$