Classical Measurement Theory

Abstract

The term descriptive statistics refers to all techniques used to obtain information based on the description of data from a population. The calculation of figures and parameters and the generation of graphics and tables are just some of the methods and techniques used in descriptive statistics. Inferential statistics, sometimes referred to as inductive statistics, did not develop until much later. It uses samples to make conclusions, or inferences, about a population. Many of the methods of inferential statistics go back to discoveries made by such thinkers as Jacob Bernoulli (1654–1705), Abraham de Moivre (1667–1754), Thomas Bayes (1702–1761), Pierre-Simon Laplace (1749–1827), Carl Friedrich Gaus (1777–1855), Pafnuty Lvovich Chebyshev (1821–1894), Francis Galton (1822–1911), Ronald A. Fisher (1890–1962), and William Sealy Gosset (1876–1937). Thanks to their work, we no longer have to count and measure each individual within a population, but can instead conduct a smaller, more manageable survey. This comes in handy when a full survey would be too expensive or take too long, or when collecting the data damages the elements under investigation (as with various kinds of material testing, such as wine tasting). But inferential statistics has a price: because the data are collected from a sample, not from a total population, our conclusions about the data carry a certain degree of uncertainty. But inferential statistics can also define the “price” of this uncertainty using margins of error. Classical measurement theory gives us the tools to calculate statistical error.