ST_trustarea

Arguments

v:: vector of numerical values
p:: statistical confidence level (%) as a string or the level of significance (α) as a decimal value, "95%", "99%", "99.9%" or 0.05, 0.01, 0.001 resp (see examples).
trustval:: trust area, range of dispersion of the mean.

Description

"ST_trustarea" determines the range of dispersion of the mean. It describes the quality of the mean and indicates the range of dispersion of the mean and not of the raw values as the stray area does. It defines the range around the mean may vary at a given significance level.

$\begin{eqnarray} T &=& s \cdot t \\ T_{\bar{x}} &=& T/ \sqrt{n} \end{eqnarray}$

T: stray area of values; s: sample standard deviation; t: student factor (dependent on statistical confidence level P% and degree of freedom f=n-1 with n: number of values)

E.g. if trustval = 1.4 at p = 95% and mean(v) = 10.0, the confidence interval for the population mean according to this formulation is approximately 10.0 +/- 1.4.

Examples

v = [6 8 14 12 5 15];
mean(v) // = 10.
ST_trustarea(v, "95%") // = 4.4514
ST_trustarea(v, 0.05)  // = 4.4514

Authors

Hani A. Ibrahim - hani.ibrahim@gmx.de

Bibliography

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

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