# Quantum and Survey Reporter t-Test of a Mean

Where $\displaystyle{ \bar x }$ is the observed mean, $\displaystyle{ e }$ is the expected value, $\displaystyle{ s }$ is the sample standard deviation and $\displaystyle{ n }$ is the effective sample size,
$\displaystyle{ t = \sqrt{nd_{eff}}\frac{\bar x - e}{s} }$
where $\displaystyle{ t \approx 2 \Pr(t_{n-1} \ge |t|) }$ if $\displaystyle{ \bar x \ne e }$ and NaN otherwise, and $\displaystyle{ d_{eff} }$ is Extra deff.