This toolbox provides elementary tests for the evaluation of univariate
measuring data which were generated by natural scientists and engineers in the
first place. These data have to be normal distributed.
SampleSTAT is focused on small sample sizes but offers routines for bigger
distributions (>30 values), too. It offers functions for calculates the range
of dispersion of the values and the mean regarding a given statistical
confidence level. Furthermore it provides tests on outliers and a method for
testing the data for normality.
FUNCTIONS - Measures of Variation:
Gives you more information of your data as the standard deviation (S.D.) can do
with just 68% confidence. These tests provide confidence level of 95%, 99% and
99.9% and calculate the range of dispersion not only for values but for the
mean, too. It extends the internal functions: mean, stdev, median.
- ST_strayarea:
Calculates the stray area (range of dispersion of the values).
Determines the range in which the values are expected to fall
within the specified statistical confidence level.
- ST_trustarea:
Calculates the trust area (range of dispersion of the mean or
S.D. of the mean). Determines the range in which the mean stray
within the specified statistical confidence level.
- ST_studentfactor:
Determines the student factor for an amount of numbers, service
function for ST_staryarea and ST_trustarea
FUNCTIONS - Tests on Outliers
It is not always easy to distinguish whether a value is a valid part of a sample
distribution or not. These outlier tests provides quick hints.
- ST_grubbs:
Grubbs outlier Test. Ideal for small and medium sample sizes
<50.
- ST_esd:
Generalized Extreme Studentized Deviate (ESD) outlier test. For
sample sizes >=25.
- ST_nalimov:
Nalimov test for small to big sample sizes (3-1002). Very
common in chemistry and quality control in Eastern Europe and
Germany.
- ST_deandixon:
Dean-Dixon outlier test for small sample sizes (<30). Grubbs is
more common.
- ST_pearsonhartley:
Pearson-Hartley outlier test for bigger sample sizes (>30). ESD
is more common.
- ST_outlier:
Basic and often used tests for medium to large sample sizes,
based on S.D. (standard deviation) or IQR (inter-quartile
range). Last (IQR) is robust against skewed (non-normally
distributed) data.
FUNCTIONS - Distribution Tests
All routines above rely on a normal distributed data. To test for normality a
powerful test is provided.
- ST_shapirowilk:
Shapiro-Wilk test for normality is powerful even for small
sample sizes.
- ST_ivplot:
Individual value plot to examine and compare the distributions
of sample data. In a scatter plot, a point is plotted for the
actual value of each observation in a group. The spread of the
distribution can be slearly seen.
-----------------------------------------------------------------
CHANGELOG:
2.1.0 - Grubbs outlier test (classic and iterated) added
- Generalized Extreme Studentized Deviate (ESD) outlier
test according to Rosner added
- Individual Value Plot ST_ivplot completed & extended
- Multiple dataset capability
- Same or similar values are plotted beside each
others
- Tolerance threshold for similar values
- Setting markers and colors
- Shapiro-Wilk test extended (test statistic output
added)
- Checks for NaN and INF in the input data
- More demos added
- All documentation updated
- Bug fixes
- Preserve orientation of imput vectors in the output in
ST_nalimov and ST_personhartley
- ST_shapirowilk typos fixed
- ST_nalimov table typo fixed (had no impact on results)
- ST_deandixon table mapping fixed (severe bug)
2.0.2 - Help-Bugfix
2.0.1 - Bug and compatibility fixes related to Scilab 6
2.0.0 - Outlier tests (Dean-Dixon, Pearson-Hartley, Nalimov)
and a basic test added
- Distribution tests (Shapiro-Wilk, Skewness) added
- Individual Value Plot added (EXPERIMENTAL)
-----------------------------------------------------------------
DEPENDENCIES:
apifun >= 0.4.0
-----------------------------------------------------------------
LITERATURE:
- R. Kaiser, G. Gottschalk; "Elementare Tests zur
Beurteilung von Meßdaten", BI Hochschultaschenbücher, Bd. 774,
Mannheim 1972.
- Lohringer, H., "Grundlagen der Statistik", Oct, 10th, 2012,
http://www.statistics4u.info/
- Shapiro, Wilk: "An Analysis of Variance Test for Normality",
Biometrika, Vol. 52, No. 3/4. (Dec., 1965), pp. 591-611.
- Grubbs, F. E. (1950). Sample criteria for testing outlying
observations. Annals of Mathematical Statistics, 21(1), 27-58.
- Grubbs, F. E. (1969). Procedures for detecting outlying
observations in samples. Technometrics, 11(1), 1-21.
- NIST/SEMATECH e-Handbook of Statistical Methods.
- Rosner, B. (1983). Percentage Points for a Generalized ESD
Many-Outlier Procedure. Technometrics, 25(2), 165-172.
