# Quantum and Survey Reporter t-Test of a Mean

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Where $\bar x$ is the observed mean, $e$ is the expected value, $s$ is the sample standard deviation and $n$ is the effective sample size,

$t = \sqrt{nd_{eff}}\frac{\bar x - e}{s}$

where $t \approx 2 \Pr(t_{n-1} \ge |t|)$ if $\bar x \ne e$ and NaN otherwise, and $d_{eff}$ is Extra deff.

Note that if wishing to replicate results from IBM SPSS Data Collection products (including Survey Reporter and Quantum) additional settings need to be modified (see How to Replicate Survey Reporter Significance Tests).