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In statistical theory, Chauvenet's criterion (named for William Chauvenet〔Chauvenet, William. ''A Manual of Spherical and Practical Astronomy'' V. II. 1863. Reprint of 1891. 5th ed. Dover, N.Y.: 1960. pp. 474–566.〕) is a means of assessing whether one piece of experimental data — an outlier — from a set of observations, is likely to be spurious. ==Derivation== 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''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''max ≥ (ABS(''x'' − ''μ''))/''σ'' where * ''D''max = maximum allowable deviation, * ABS = absolute value, * ''x'' = value of suspected outlier, * ''μ'' = sample mean, * ''σ'' = sample standard deviation. In order to be considered as including all ''n'' observations in the sample, the probability band ( centered on the mean) must only account for ''n'' − ½ samples (if ''n'' = 3 then only 2.5 of the samples must be accounted for in the probability band). In reality we cannot have partial samples so ''n'' − ½ (2.5 for ''n'' = 3) is approximately ''n''. Anything less than ''n'' − ½ is approximately ''n'' − 1 (2 if ''n'' = 3) and is not valid because we want to find the probability band that contains ''n'' observations, not ''n'' − 1 samples. In short, we are looking for the probability, ''P'', that is equal to ''n'' − 1/2 out of ''n'' samples (Eq.2). Eq.2) ''P'' = (''n'' − ½)/''n'' which can be re-written as ''P'' = 1 − (1/2''n'') where * ''P'' = probability band centered on the sample mean, * ''n'' = sample size. The quantity 1/(2''n'') corresponds to the combined probability represented by the two tails of the normal distribution that fall outside of the probability band ''P''. In order to find the standard deviation level associated with P, only the probability of one of the tails of the normal distribution needs to be analyzed due to its symmetricity (Eq.3). Eq.3) ''P''''z'' = 1/(4''n'') where * ''P''''z'' = probability represented by one tail of the normal distribution, * ''n'' = sample size. Eq.1 is analogous to the Z-score equation (Eq.4). Eq.4) ''Z'' = (''x'' − ''μ'')/''σ'' where * ''Z'' = z-score, * ''x'' = sample value, * ''μ'' = 0 (mean of standard normal distribution), * ''σ'' = 1 (standard deviation of standard normal distribution). Based on Eq.4, to find the ''D''max (Eq.1) find the z-score corresponding to ''P''''z'' in a z-score table. ''D''max is equal to the z-score for ''P''''z''. Using this method ''D''max can be determined for any sample size. In Excel, ''D''max can be found with the following formula: =ABS(NORM.S.INV(1/(4''n''))). 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Chauvenet's criterion」の詳細全文を読む スポンサード リンク
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