Statistics How To

Descriptive Statistics > Quadratic Mean / Root Mean Square What is the Quadratic Mean / Root Mean Square? The quadratic mean (also called the root mean square*) is a type of average. It measures the absolute magnitude of a set of numbers, and is calculated by: Squaring each number, Finding the mean of these squares, … Read more

Regression Analysis > Quartic regression fits a quartic function (a polynomial function with degree 4) to a set of data. Quartic functions have the form: f(x) = ax4 + bx3 + cx2 + dx + e. For example: f(x) = -.1072×4 + 13.2×3 – 380.1×2 – 154.2x + 998 The quartic function takes on a … Read more

Statistics Definitions > Shannon entropy (or just entropy) is a measure of uncertainty (or variability) associated with random variables. It was originally developed to weigh the evenness and richness of animal and plant species (Shannon, 1948). It’s use has expanded to many other areas including: Information theory, which considers stochastic processes as sources of information, … Read more

Statistics Definitions > Natural Numbers and Whole Numbers Contents (Click to skip to that section) Natural Number Whole Numbers Why Is a Natural Number a Whole Number? Whole Numbers Example Closed Sets and Wholes Properties of Whole numbers What is a Natural Number? Natural numbers are numbers that we use to count.  They are whole, … Read more

Statistics Definitions > What is Independence of Irrelevant Alternatives? Independence of Irrelevant Alternatives (IIA) is a condition that states that the relative likelihood of choosing from A from B won’t change if a third choice is placed into the mix. To put that another way: Let’s say an election was held between two candidates A, … Read more

Regression Analysis > Additive Model and Multiplicative Model in Regression The additive model and multiplicative model are generalizations of the “usual” linear regression model (Hastie & Tibshirani, 1990). The additive model is the arithmetic sum of the predictor variables‘ individual effects. For a two factor experiment (X, Y), the additive model can be represented by: … Read more

Statistics Definitions > A covariance stationary (sometimes just called stationary) process is unchanged through time shifts. Specifically, the first two moments (mean and variance) don’t change with respect to time. These types of process provide “appropriate and flexible” models (Pourahmadi, 2001). The concept is important in time series, where correlation coefficients between two series only … Read more

ANOVA > ANOVA vs Regression If you’re working on data analysis, there are many tools available to provide insights to your data. These tools include ANOVA and regression analysis. At first glance, the two methods may look similar—so similar in fact, that you wouldn’t be the first to completely confuse the two. ANOVA vs Regression: … Read more

Probability distributions > The Yule-Simon distribution (or Yule distribution) is a highly skewed discrete probability distribution named after George Udny Yule and Herbert A. Simon—winner of the 1978 Nobel Prize in economics. Yule (1925) wrote about the distribution first, applying it to distributions of biological genera by number of species. Simon (1955) rediscovered the “Yule” … Read more

Reliability and Validity > Alternate Forms Reliability Alternate forms reliability is a measure of reliability between two different forms of the same test. Two equivalent (but different) tests are administered, scores are correlated, and a reliability coefficient is calculated. A test would be deemed reliable if differences in one test’s observed scores correlate with differences … Read more