# 9.4.4. Chauvenet Criterion

Chauvenet criterion is a stronger statistical test that may be used to determine possible Outliers and decide whether or not a bad data point should be discarded. An outlier among residuals is one that is far greater than the rest and lies three or four standard deviations or further from the mean of all the residuals. An outlier indicates a data point which is not at all typical of the rest of the data. Then an outlier should be submitted to particularly careful examination.

Suppose to have a set of residuals: where is ith real value and is the value estimated in the Response Surface.

We can calculate the number of standard deviations by: modeFRONTIERTM identifies as outliers the points that have: where depends on the total number of designs (n).

Some of the values for used in modeFRONTIERTM are given in the following table.

Number of DesignsNumber of Designs
51.65 302.39
61.73 402.49
71.81 502.57
81.86 602.64
91.91 802.74
101.96 1002.81
122.04 1502.93
142.10 2003.02
162.15 3003.14
182.20 4003.23
202.24 5003.29
252.3310003.48

Note: The Chauvenet criterion can be repeatedly applied to clean up sets of data. This criterion must be applied with great care to avoid the throwing away of correctly designs with relevant, even surprising, information.