• The normal, or Gaussian, distribution is one of the most familiar in statistics, endeared to statisticians by its simplicity and by virtue of the Central Limit Theorem (which states that a sample mean will follow an approximately normal distribution, if sample size is large enough, even if the data themselves are not normally distributed). (gsu.edu)
  • Test statistics that follow a chi-squared distribution arise from an assumption of independent normally distributed data, which is valid in many cases due to the central limit theorem . (wikipedia.org)
  • For these hypothesis tests, as the sample size, n, increases, the sampling distribution of the test statistic approaches the normal distribution (central limit theorem). (wikipedia.org)
  • In the early nineteenth century Pierre-Simon Laplace (1749 - 1827), when working on the central limit theorem , showed that the distribution of sample means tends to be normally distributed: The larger the number of samples, the closer is the fit to normality - a result that holds regardless of whatever the population distribution might be. (encyclopedia.com)
  • For example, it is used for testing: equality of variances of two independent normal distributions, equality of means in the one-way ANOVA setting, overall significance of a normal linear regression model, and so on. (scirp.org)
  • Understand the theoretical framework of linear regression models: standard model assumptions, Least Squares estimators for the model parameters and their properties, inference techniques for the model parameters. (york.ac.uk)
  • As a result, the distribution mean is identical to the two alternative measures of central tendency , namely, the mode (the most frequent value of X ) and the median (the middle value of X ). Second, the mathematical function provides the basis for specifying the number of observations that should fall within select portions of the curve. (encyclopedia.com)
  • In the first decade of the nineteenth century the mathematicians Adrien-Marie Legendre (1752 - 1833) and Carl Friedrich Gauss (1777 - 1855) worked out the precise mathematical formula, and Gauss demonstrated that this curve provided a close fit to the empirical distribution of observational errors. (encyclopedia.com)
  • However, the normal distribution also appeared in other mathematical contexts. (encyclopedia.com)