SOSstat - Descriptive statistics
Descriptive statistics
At the end of an experiment, a series of testing or sampling, a set of raw data is available that is desirable to provide a synthetic representation. The purpose of descriptive statistics is indeed to provide tools to make a summary of this data set. Tools can be cut into two families: the graphical summaries and digital summaries.
SOSstat offers many descriptive statistics functions in its analysis modules.
Graphical summaries
There are many graphic tools, but some are essential such as:
- The histogram that provides an approximation of the distribution of data
- The Boxplot cuts the sample into 4 parts having the same number of individuals (quartiles). This representation, very synthetic, is used to compare graphically several samples at the same time.
Numerical summary
The digital summary is to calculate parameters representative of the specific characteristics of the population. It essentially identifies three groups of parameters : Centering, dispersion and shape parameters.
SOSstat can easily calculate the parameters of a large number of samples.
Centering parameters or position
The most widely used centering parameters are :
The arithmetic mean :
It represents the center of gravity of the sample (it expresses the value that would have each member of the sample if they were all identical without changing the overall size of the sample)
The median :
Value that allows you to share an ordered numeric series into two parts of the same number of elements. For an odd sample, the median is defined by the relation
and for a even sample by
Dispersion or scale parameters
The most used dispersion parameters are :
Range :
distance between the min and max value of a sample
Variance :
Measuring the concentration of data around the average.
Standard deviation :
Root of variance
Shape parameters
Forms parameters are usually called Skewness for symmetry and Kurtosis for flattening, but under that name can hide different forms of calculation.
Bibliography
DROESBEKE, J. Éléments de Statistique , Éditions Ellipses, 2015, ISBN-13: 978-2340009080 GoogleBooks
SAPORTA, G. Probabilités, analyse des données et statistique, Technip, 2011- 622 pages, ISBN-13: 978-2710809807 GoogleBooks