Chauvenet's criterion

In statistical theory, Chauvenet's criterion (named for William Chauvenet) is a means of assessing whether one piece of experimental data — an outlier — from a set of observations, is likely to be spurious. In statistical theory, Chauvenet's criterion (named for William Chauvenet) is a means of assessing whether one piece of experimental data — an outlier — from a set of observations, is likely to be spurious. The idea behind Chauvenet's criterion is to find a probability band, centered on the mean of a normal distribution, that should reasonably contain all n samples of a data set. By doing this, any data points from the n samples that lie outside this probability band can be considered to be outliers, removed from the data set, and a new mean and standard deviation based on the remaining values and new sample size can be calculated. This identification of the outliers will be achieved by finding the number of standard deviations that correspond to the bounds of the probability band around the mean ( D m a x {displaystyle D_{mathrm {max} }} ) and comparing that value to the absolute value of the difference between the suspected outliers and the mean divided by the sample standard deviation (Eq.1). Eq.1) D m a x ≥ | x − x ¯ | s x {displaystyle D_{mathrm {max} }geq {frac {|x-{ar {x}}|}{s_{x}}}}