Ordered pair

In mathematics, an ordered pair (a, b) is a pair of mathematical objects. The order in which the objects appear in the pair is significant: the ordered pair (a, b) is different from the ordered pair (b, a) unless a = b. (In contrast, the unordered pair {a, b} equals the unordered pair {b, a}.)

Ordered pairs are also called 2-tuples, or sequences of length 2; ordered pairs of scalars are also called 2-dimensional vectors. The entries of an ordered pair can be other ordered pairs, enabling the recursive definition of ordered n-tuples (ordered lists of n objects). For example, the ordered triple (a,b,c) can be defined as (a, (b,c)), i.e., as one pair nested in another.

In the ordered pair (a, b), the object a is called the first entry, and the object b the second entry of the pair. Alternatively, the objects are called the first and second coordinates, or the left and right projections of the ordered pair.

Cartesian products and binary relations (and hence functions) are defined in terms of ordered pairs.

A&B

A&B may refer to:

AB

AB, Ab, or ab may refer to:

People

Personal and ranks

Places

Companies, universities, organizations, and groups

A/B testing

In marketing and business intelligence, A/B testing is a term for a randomized experiment with two variants, A and B, which are the control and variation in the controlled experiment . A/B testing is a form of statistical hypothesis testing with two variants leading to the technical term, two-sample hypothesis testing, used in the field of statistics. Other terms used for this method include bucket tests and split-run testing but these terms can have a wider applicability to more than two variants. In online settings, such as web design (especially user experience design), the goal of A/B testing is to identify changes to web pages that increase or maximize an outcome of interest (e.g., click-through rate for a banner advertisement). Formally the current web page is associated with the null hypothesis.

As the name implies, two versions (A and B) are compared, which are identical except for one variation that might affect a user's behavior. Version A might be the currently used version (control), while version B is modified in some respect (treatment). For instance, on an e-commerce website the purchase funnel is typically a good candidate for A/B testing, as even marginal improvements in drop-off rates can represent a significant gain in sales. Significant improvements can sometimes be seen through testing elements like copy text, layouts, images and colors, but not always. The vastly larger group of statistics broadly referred to as Multivariate testing or multinomial testing is similar to A/B testing, but may test more than two different versions at the same time and/or has more controls, etc. Simple A/B tests are not valid for observational, quasi-experimental or other non-experimental situations, as is common with survey data, offline data, and other, more complex phenomena.