Peirce's criterion is a rule based on likelihood for rejecting one or more suspected outliers from a set of observations whose errors are assumed to follow a normal distribution. Its rejection threshold is chosen jointly for a proposed number of rejected observations and depends on the total number of observations and the number of fitted model parameters. This permits several observations to be tested simultaneously, unlike the usual one-at-a-time use of Chauvenet's criterion. Because its threshold is determined for several proposed rejections together, Peirce's criterion is less susceptible to one extreme observation masking another than a one-at-a-time rule.
The criterion compares the likelihood of the full residual set with the likelihood after the proposed observations are treated as abnormal. If the resulting threshold rejects a different number of observations than was proposed, the calculation is repeated with the new number.
