# Z-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, ${\displaystyle n}$ is the sample size, and ${\displaystyle d_{eff}}$ is Extra deff:
${\displaystyle z={\sqrt {n/d_{eff}}}{\frac {{\bar {x}}-e}{s}}}$
where ${\displaystyle p=2(1-\Phi (|z|))}$ if ${\displaystyle {\bar {x}}\neq e}$ and NaN otherwise.