Gaussian forced-choice sensitivity relation
= Gaussian forced-choice sensitivity relation
{title2=$P(\mathrm{correct})=\Phi(d'/\sqrt2)$}
Compare independent Gaussian samples $R_s,R_n$ with means $\mu_s,\mu_n$ and common <variance> $\sigma^2$. Choosing the larger is correct when $R_s-R_n>0$. The difference has mean $\mu_s-\mu_n$ and <variance> $2\sigma^2$, so standardization proves the displayed relation. Correlated samples, unequal variances or a different response rule need a different calculation.