Statistics How To

Regression Analysis > Regularized least squares is a way of solving least squares regression problems with an extra constraint on the solution. The constraint is called regularization. Regularization limits the size of coefficients in the least squares method in a simple way: it adds a penalty term to the error. While doing a standard least … Read more

Statistics Definitions > Discretization is taking continuous functions or variables and transforming them into discrete functions or variables, respectively. It’s a first step in many types of analysis, because discrete functions and data are much easier to analyze than their continuous counterparts. The Theory Behind Discretization We can visualize the process of discretizing as: Analyzing … Read more

Sampling > Latin Hypercube Sampling (LHS) is a way of generating random samples of parameter values. It is widely used in Monte Carlo simulation, because it can drastically reduce the number of runs necessary to achieve a reasonably accurate result. LHS is based on the Latin square design, which has a single sample in each … Read more

Regression Analysis > Influential data consists of data points that influence (skew) an analysis in a major way. They are outliers that have enough clout to significantly change a regression line or statistical coefficients; removing them leads an analysis to a different conclusion. Properties of Influential Data An influential data point has two key properties: … Read more

Statistics Definitions > Content analysis is a research method for pulling scientific, objective, systematic and generalizable quantitative (numerical) data out of textual, language-based media. How to Define Content Analysis It’s fairly simple to define content analysis: it is what happens if you take a political speech and run it through the ‘search’ function in Microsoft … Read more

Probability Distributions > A long tail distribution has tails that taper off gradually rather than drop off sharply. They are a subset of heavy-tailed distributions. It’s easy to visualize the idea of a long tailed function, and slightly harder to make it concrete. If we want to be rigorous, though, there is a exact mathematical … Read more

Confounding Variables > Nonnormative influences are influences which don’t influence every member of a set in the same way. The term normative refers to something that affects everyone in a culture at the same time, so nonnormative implies it affects everyone differently (or not at all). In psychology, they’re the things that change an individual’s … Read more

Confounding Variables > Normative age graded influences are influences that affect an individual in a predictable or semi-predictable way according to age. The word normative here means that they are ‘the norm’ for a large number of people in a semi-predictable way. This doesn’t mean they must happen to everyone at exactly the same time, … Read more

Probability Distributions The Lévy Distribution is a probability distribution that is both continuous—for non-negative random variables—and stable. To be stable means that if you sum up random variables x and y in a distribution, their sum (i.e. x + y) is a random variable from that same distribution. Another important property of the Lévy distribution … Read more

Markov Chain Monte Carlo > Gibbs Sampling What is Gibbs Sampling? Gibbs sampling (also called alternating conditional sampling) is a Markov Chain Monte Carlo algorithm for high-dimensional data such as image processing and micro arrays. It is called Monte Carlo because it draws samples from specified probability distributions; the Markov chain comes from the fact … Read more