Correlation Coefficients > The Matthews correlation coefficient (MCC), invented by Brian Matthews in 1975, is a tool for model evaluation. It measures the differences between actual values and predicted values and is equivalent to the chi-square statistic for a 2…
Uncountable Set
Probability > An uncountable set is a set that isn’t countable. It’s a bit more complicated than simply deciding whether a set contains a countable number of items (or not). T While you can’t imagine counting an infinite set, it’s…
True Error
Statistics Definitions > In general, the true error is the difference between the true value of a quantity and the observed measurement (Muth, 2006). In hypothesis testing, the true error is the error rate of a hypothesis over a whole…
Intersection of Events: Definition & Examples
Probability > An Intersection is a collection of elements (like people, places, or things) that belong to two or more sets. The intersection is like a container with the elements as the contents. The container itself says nothing about the…
A Union B (Union Set)
Probability > What is “A Union B”? A Union B means that A happens or B happens (or perhaps both happens). These could be events, objects, or just about anything else. For example: A person buys a scratch off lottery…
Empty Set
Probability > The empty set (∅) has no members. This placeholder is equivalent to the role of “zero” in any number system. Examples of empty sets include: The set of real numbers x such that x2 + 5, The number…
Inverse Probability & Distribution
Bayes Theorem > Contents: What is Inverse Probability? What is an Inverse Distribution? What is Inverse Probability? Inverse probability is the probability of things that are unobserved; or, more technically, the probability distribution of an unobserved variable. It’s generally considered…
Superfactorial: Definition (Sloane, Pickover’s)
Statistics Definitions > The term superfactorial has two slightly different definitions: as a product of factorials (Sloane & Plouffe, 1995) or as a tower of factorials involving compound exponents (Pickover, 1995). Sloan and Pouffe’s form is the most common. 1.…
Pairwise Disjoint
Statistics Definitions > Pairwise disjoint events don’t have any outcomes in common. In probability, the term is often used synonymously with mutually exclusive. A subtle difference is sometimes defined in set theory. If the intersection of two events is the…
Countable Additivity
Probability > The countable additivity axiom states that the probability of a union of a finite (or countably infinite) collection of disjoint events is the sum of their individual probabilities (disjoint events can’t happen at the same time; They are…