= Gaussian psychometric function
{title2=$P(\mathrm{yes}\mid x)=\Phi((\mu(x)-c)/\sigma)$}
Let internal evidence be $R=\mu(x)+\varepsilon$ with zero-mean <Gaussian noise> of <standard deviation> $\sigma$, and respond yes when $R>c$. Taking a distribution tail gives $1-\Phi((c-\mu)/\sigma)$, which equals the displayed expression by symmetry. Its derivative is $\phi((\mu-c)/\sigma)\mu'(x)/\sigma$. Thus sensory gain, variability and criterion all influence the observed relation, and a sigmoid in one stimulus coordinate need not remain symmetric in another.
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