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samplestat >> samplestat > Outlier-Tests > ST_nalimov

ST_nalimov

Nalimov outlier test

Calling Sequence

[outlierfree] = ST_nalimov(v, p)
[outlierfree, outlier] = ST_nalimov(v, p)

Parameters

v:

vector of numerical values

p:

statistical confidence level (%) as a string or the level of significance (alpha) as a decimal value, "95%", "99%", "99.9%" or 0.05, 0.01, 0.001 resp (see examples).

outlierfree:

vector of outlier-free data

outlier:

vector of outliers

Description

Performs Nalimov outlier test for small and larger sample sizes. It calculates for all values the test value "q". It compares these q-values with the appropriate qcrit value from a table.

\begin{eqnarray}
q = \left | \frac{1}{s}(x_i- \bar{x}) \right | \sqrt{\frac{n}{n-1}} \quad;\quad q>q_{crit}\;\Rightarrow \; x_i=\text{outlier} \\
x_i: \text{test value} \quad ; \quad \bar{x}: \text{arithmetic mean} \\
s: \text{sample standard deviation} \quad ; \quad n: \text{number of values}
\end{eqnarray}

q-values of the sample values which are greater than the qcrit value are outliers

Do use ST_nalimov ONLY with NORMAL distributed data and with more than 3 and less than 1000 values!

Do use ST_nalimov with care. It indicates outliers very strict and is controversially discussed in the scientific community. For a convervative outlier test substitute Nalimov with Dean-Dixon (ST_deandixon) small sample sizes (<30) and Pearson-Hartley (ST-pearsonhartley) for larger ones (>30).

Examples

data = [6 8 14 12 35 15];
of = ST_nalimov(data, "95%")      // outlier-free values
[of, o] = ST_nalimov(data, "95%") // outlier and outlier-free values
[of, o] = ST_nalimov(data, 0.05)  // outlier and outlier-free values

See also

Authors

Bibliography

R. Kaiser, G. Gottschalk; "Elementare Tests zur Beurteilung von Meßdaten", BI Hochschultaschenbücher, Bd. 774, Mannheim 1972.


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