Refreshing Statistics
Robert J. Moffat, Roy W. Henk · 2020
This chapter aims to refresh basic statistics concepts and illustrates the most fundamental data distributions. It also aims to construct a simple model to explain results using free open-source software. The Normal Distribution or Gaussian Distribution is useful because it typifies results for an infinite number of repeated trials. The distribution of a small sample size rarely matches any theoretical distribution, whether normal, uniform, or other. However, when a set of several small samples is taken from the same population, the distribution of the means fits the t-distribution. A quick, easy, and accurate way to analyze statistics is available via the free open-source R language. Since the R function for linear modeling performs a least-squares fit, the Standard Error for each term and for the Residual are orthogonal (that is, independent) to each other and add together similar to the Pythagorean Theorem.