Statistics How To

Probability and Statistics > Normal Distributions > Area to the Right of a z score How to find the Area to the Right of a z score There are a few ways to find the area to the right of a z-score where z is less than the mean. With any word problem like this, … Read more

Normal distribution curve index > Area between two z scores How to Find the Area Between Two Z Scores on One Side of the Mean If you want to find the area between two z scores, the technique will differ slightly depending on whether you have two scores on one side of the mean or … Read more

Probability and Statistics > Normal Distributions > Two Tailed Normal Curve Two Tailed Normal Curve: How to find the area A two tailed normal curve is one where there’s an area in each of the two tails. In order to find the area for a two tailed normal curve, you have to read a z-table. … Read more

Probability Distributions > The hyperexponential distribution (also called a mixed exponential or parallel m-phase exponential distribution) is created by a probabilistic mixture of exponential distributions. It is a generalization of the Erlang distribution and a special case of the phase-type distribution (made by a convolution or mixture of exponential distributions) [1]. It’s called hyperexponential because … Read more

Probability > A probability measure gives probabilities to a sets of experimental outcomes (events). It is a function on a collection of events that assigns a probability of 0 and 1 to every event, meeting certain conditions. The role of a probability measure is to quantify the likelihood of each outcome from each event in … Read more

Probability Distributions > A univariate distribution is the probability distribution of a single random variable. For example, the energy formula (x – 10)2/2 is a univariate distribution because only one variable (x) is given in the formula. In contrast, bivariate distributions have two variables and multivariate distributions have two or more. Types of Univariate Distribution … Read more

Statistics Definitions > The midrank is a tied observation’s average rank. An observation’s rank is its position in an order list, from smallest to largest. A midrank is one way to deal with tied ranks in nonparametric tests that based on ranks, like the Wilcoxon rank-sum test. You can extend a test to allow for … Read more

Hypothesis Testing > The Brunner Munzel test (also called the Generalized Wilcoxon Test) is a non parametric statistical test for stochastic equality of two samples. Stochastic equality is a similarity measure between two populations, which means that the populations have roughly the same frequency of greater values. The BM test isn’t widely available in statistical … Read more

Statistics Definitions > Quantum statistical mechanics is the study of probability potential of subatomic particles and bulk properties. Subatomic particles don’t obey the classical counting rules and anyons take the bizarre world of quantum theory a step further–disobeying the “usual” rules for subatomic particles including fractional charges. Quantum statistics governs the way things work in … Read more

Statistics Definitions > A canonical statistic (sometimes called a natural statistic) is a way to specify a particular exponential distribution. All exponential families of distributions over x have the general form (Creager, 2018) p(x| η) = h(x) g(η) exp{ηT u(x)} Where: u(x) is the canonical (natural) statistic, which is a function of x, η is … Read more