= Fisherian conditional inference
{c}
In a <parametric statistical model>, the <likelihood function> compares parameter values, while sampling distributions calibrate tests and <confidence intervals>. A <sufficient statistic> retains the parameter information. Conditioning on an observed <ancillary statistic> restricts that calibration to experiments with the same ancillary configuration, instead of averaging over configurations whose distribution is unrelated to the parameter. Since the ancillary's marginal law is parameter-free, conditional and unconditional likelihoods have the same parameter-dependent factor. With a <nuisance parameter>, a conditional law or <pivotal quantity> must remove it before inference for the parameter of interest can use a nuisance-free reference law.
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