Saturday, 12 November 2016

Standard deviation (σ or s)

«The standard deviation of a population is denoted by σ and the standard deviation of a sample, by s [1].» It is a measure of dispersion or absolute variability [2,3] in original units (unit of measurement equal to that of the mean). It is the positive square root of the variance (σ2 or s2 or Var[X]). It «is useful as a measure of variation within a given set of data» [4]. «A small value of the standard deviation indicates that most values are close to the sample mean. A large value of the standard deviation indicates many values are far from the sample mean. Other words which are used to convey the concept of the standard deviation are “spread” and “scale.”» It is «the “typical” spread of observations about the sample mean [2].» It «is a numerical value used to indicate how widely individuals in a group vary. If individual observations vary greatly from the group mean, the standard deviation is big; and vice versa [1].»
Bibliographic references:
[1] Stattrek.com. (2016). Statistics Dictionary. [online] Available at: http://stattrek.com/statistics/dictionary.aspx [Accessed 13 Nov. 2016].
[2] Supino, P. and Borer, J. (2012). Principles of research methodology. 1st ed. New York, NY: Springer.
[3] Doi, S. and Williams, G. (2013). Methods of clinical epidemiology. 1st ed. Berlin: Springer.
[4] Daniel, W. and Cross, C. (2013). Biostatistics: a foundation for analysis in the health sciences. 10th ed. Danvers, Massachusetts, USA: John Wiley & Sons, Inc.