Statistics How To

Statistics Definitions > What is a Poisson Trial? A Poisson trial is a collection of Bernoulli trials with unequal probabilities. In other words, one Poisson trial is exactly the same as one Bernoulli trial. However, when you have many of them with different probabilities, they are called Poisson trials [1]. A binomial trial is an … Read more

Statistics Definitions > Contents: Circular Statistics Circular Scatter Plot Circular Statistics Circular statistics (or directional statistics) occurs around a circle. It involves data with no true zero and has no beginning or end on the number line; Designation of high or low values is arbitrary. For example [1]: Hours in a day, Months of the … Read more

Probability Distributions > The gamma-normal distribution (also called the Gaussian normal distribution, GN distribution or normal-gamma distribution) is a bivariate compound probability distribution for the sum of a gamma random variable and a normal/Gaussian random variable. It is the conjugate prior (from Bayesian statistics) of a normal distribution with unknown mean and precision [1]. “Conjugate” … Read more

Statistics Definitions > Confidence limits are a pair of numbers used to describe an estimate or other characteristic of a population. They are the upper and lower boundaries of confidence intervals [1]. Anywhere you calculate a confidence interval (e.g., effect sizes, noncentrality parameters, risk ratios), you will have associated confidence limits. It represents limits between … Read more

Statistics Definitions > What is a Noncentrality Parameter? A noncentrality parameter (NCP) is a way to distinguish noncentral distributions, which have nonzero means, from their “central” counterparts which have zero means. In other words, if a population mean is μ0, then the NCP represents the normalized difference between μ0 and μ. If no NCP is … Read more

Statistics Definitions > What is a Tail Bound? The tails of a random variable X are those parts of the probability mass function far from the mean [1]. Sometimes we want to create tail bounds (or tail inequalities) on the PMF, or bound the probability that the random variable deviates a long way from the … Read more

Statistics Definitions > In statistics, a subsample is a sample of a sample. In other words, a sample is part of a population and a subsample is a part of a sample. For example, let’s say you had a population of one million people, and you used simple random sampling to get a sample of … Read more

Multivariate Analysis > Homogeneity of Covariance Testing for homogeneity of covariance matrices (also called the assumption of homoscedasticity) is one assumption that must be met in multivariate analysis. Homogeneity of covariance is where multiple groups in an experimental design or statistical test have equal covariance matrices. It is the multivariate counterpart of homogeneity of variance … Read more

Clustering > Hierarchical Clustering What is Hierarchical Clustering? Hierarchical clustering is where you build a cluster tree (a dendrogram) to represent data, where each group (or “node”) links to two or more successor groups. The groups are nested and organized as a tree, which ideally ends up as a meaningful classification scheme. Each node in … Read more

Statistics Definitions > What is an Asymptotic Test? In hypothesis testing, you generally have two choices: an exact test or an asymptotic test. You can think of an asymptotic test as an approximation and an exact test as “the exact result.” For example, the chi-square test is an asymptotic test; the exact version is the … Read more