Test of Chauvenet

The test of Chauvenet makes it possible to determine if a data (resulting from a measurement) is aberrant compared to the other values.

That is to say $n$ measurements: $x\_1$, $x\_2$ $\backslash \; ldots$ $x\_n$

Having,

• for Average value : $\backslash \; bar\; \{X\}$
• for standard deviation: $\backslash sigma\_x$

And the suspect value: $x\_s$

The Probability of having a value which deviates of more than green $\backslash \; x\_s-\; \backslash \; bar\; \{X\}\; \backslash \; vert$ of the average:

$P\; (\backslash \; green\; X\; \backslash \; bar\; \{X\}\; \backslash \; green\; \backslash \; geq\; \backslash \; green\; x\_s-\; \backslash \; bar\; \{X\}\; \backslash \; green)$

With for base, a law of distribution (Gaussian distribution).

The number of measurement awaited:

$n\_A\; =\; N\; \backslash \; cdot\; P\; (\backslash \; green\; X\; \backslash \; bar\; \{X\}\; \backslash \; green\; \backslash \; geq\; \backslash \; green\; x\_s-\; \backslash \; bar\; \{X\}\; \backslash \; green)$

If the number is lower than 0,5 , it is possible to regard $x\_s$ as an aberrant value (and to eliminate it).

It will be necessary all the same to take care not to eliminate too much from value with this test.

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