Statistics How To

Statistics Definitions > You may want to read this article first: What is a Bin? What is a Midpoint or Class Mark? The class midpoint (or class mark) is a specific point in the center of the bins (categories) in a frequency distribution table; It’s also the center of a bar in a histogram. A … Read more

Probability Distributions > What is Infinite Variance? Variance is a measure of how spread out a distribution is. Distributions with infinite variance have fat upper tails that decrease at an extremely slow rate. Intuitively, this means that the distribution will take a very, very long time to disappear; in theory, it never disappears; We say … Read more

Probability Distributions > What is a Fat Tail Distribution? The term “fat tail” distribution has more than one definition, depending on where you read about it. Part of the problem is that there’s no universal definition for the term tail in the first place (does it begin at 2 standard deviations from the mean? A … Read more

Sampling > Acceptance-Rejection sampling Acceptance-Rejection sampling is a way to simulate random samples from an unknown (or difficult to sample from) distribution (called the target distribution) by using random samples from a similar, more convenient probability distribution. A random subset of the generated samples are rejected; the rest are accepted. The goal is for the … Read more

Statistics Definitions > Parametrization This article is about defining probability distributions using parameters. If you’re trying to find out about population parameters (covered in elementary statistics), see: What is a Parameter in Statistics? What is Parametrization? Simply put, parametrization (or parameterization) is where you change certain aspects a probability distribution by tweaking its parameters. Many … Read more

Normal Distributions > In statistics, the Q function Q(x) usually refers to the normal distribution function Φ(x). For other meanings, see Other Uses. The Normal Distribution Q Function Φ(x) The Q function is just one minus the cumulative distribution function (CDF) for the standardized normal distribution. In other words, it gives you the right tail … Read more

SEM > An index of fit is a catch-all term for a variety of methods to tell you how well observed data fits a particular probability distribution. An index of fit is typically normalized (i.e. units of measurement are removed), and the values will usually be between 0 and 1. What these values mean depends … Read more

Central Limit Theorem > The Galton board (also called a Quincunx) is a physical model of the binomial distribution which beautifully illustrates the central limit theorem; When you add independent random variables, their sum tends toward a normal distribution. In particular, it demonstrates that the binomial distribution is approximately a normal distribution. Invented by Sir … Read more

Matrices > An idempotent matrix is one which, when multiplied by itself, doesn’t change. If a matrix A is idempotent, A2 = A. Examples of Idempotent Matrix The simplest examples of n x n idempotent matrices are the identity matrix In, and the null matrix (where every entry on the matrix is 0). Nontrivial examples … Read more

Graph Theory > Binary Trees are graphs or tree data structures where each node (shown as circles in the graph to the left) has up to a possible two branches (‘children’). These are called the left branch and right branch, or, sometimes, the left child and right child. Although they are relatively simple structures, binary … Read more