Statistics How To

Statistics Definitions > Scale Invariance What is Scale Invariance? A system, function, or statistic has scale invariance if changing the scale by a certain amount does not change the system, function, or statistic’s shape or properties. Fractals are one of the more well known examples of this. For example, if you zoom in on a … Read more

Descriptive Statistics > A peak of a distribution is a “bump” or high point in a graph. In statistics, the peaks are more formally called modes; The data count is higher in these areas than in any other parts of the graph. In calculus, the peaks are often called local maximums or global maximums. A … Read more

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 x 2 contingency table (Kaden et al., 2014). The coefficient takes into account true negatives, … Read more

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 unknown distribution of examples; It is the probability a single randomly drawn example will be … Read more

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 of dogs sitting the PSAT. We can also define it as “the set of all … Read more

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 an obsolete term. Nowadays, the basis of inverse probability (determining the unobserved variable) is usually … Read more

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. Sloane & Plouffe’s Superfactorial A superfactorial is defined by Sloane and Plouffe as the product … Read more

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 empty set, then the events are sometimes called pairwise disjoint events. Two events are mutually … Read more

Statistics Definitions > In probability, the trinomial coefficient (sometimes called the central trinomial coefficient) is the number of ways of partitioning a set of objects into three disjoint subsets. The value of the trinomial coefficient can be calculated as (Hilton et al., 2002; Kuri-Morales & Simari, 2002): Where: ! is a factorial, k is the … Read more

Types of Variables > Simply put, a measurement variable (sometimes called a numeric variable) expresses some type of measurement and has a number associated with it. For example: 12 cm, 5 feet, or 310 meters. The measured quantity doesn’t have to be something you’d crack out a ruler to find. It can be anything represented … Read more