CorrelationIn statistics, correlation or dependence is any statistical relationship, whether causal or not, between two random variables or bivariate data. Although in the broadest sense, "correlation" may indicate any type of association, in statistics it usually refers to the degree to which a pair of variables are linearly related. Familiar examples of dependent phenomena include the correlation between the height of parents and their offspring, and the correlation between the price of a good and the quantity the consumers are willing to purchase, as it is depicted in the so-called demand curve.
Pearson correlation coefficientIn statistics, the Pearson correlation coefficient (PCC) is a correlation coefficient that measures linear correlation between two sets of data. It is the ratio between the covariance of two variables and the product of their standard deviations; thus, it is essentially a normalized measurement of the covariance, such that the result always has a value between −1 and 1. As with covariance itself, the measure can only reflect a linear correlation of variables, and ignores many other types of relationships or correlations.
Correlation coefficientA correlation coefficient is a numerical measure of some type of correlation, meaning a statistical relationship between two variables. The variables may be two columns of a given data set of observations, often called a sample, or two components of a multivariate random variable with a known distribution. Several types of correlation coefficient exist, each with their own definition and own range of usability and characteristics. They all assume values in the range from −1 to +1, where ±1 indicates the strongest possible agreement and 0 the strongest possible disagreement.
Intraclass correlationIn statistics, the intraclass correlation, or the intraclass correlation coefficient (ICC), is a descriptive statistic that can be used when quantitative measurements are made on units that are organized into groups. It describes how strongly units in the same group resemble each other. While it is viewed as a type of correlation, unlike most other correlation measures, it operates on data structured as groups rather than data structured as paired observations.
Euler methodIn mathematics and computational science, the Euler method (also called the forward Euler method) is a first-order numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. It is the most basic explicit method for numerical integration of ordinary differential equations and is the simplest Runge–Kutta method. The Euler method is named after Leonhard Euler, who first proposed it in his book Institutionum calculi integralis (published 1768–1870).
Femoroacetabular impingementFemoroacetabular impingement (FAI) is a condition involving one or more anatomical abnormalities of the hip joint, which is a ball and socket joint. It is a common cause of hip pain and discomfort in young and middle-aged adults. It occurs when the ball shaped femoral head contacts the acetabulum abnormally or does not permit a normal range of motion in the acetabular socket. Damage can occur to the articular cartilage, or labral cartilage (soft tissue, ring-shaped bumper of the socket), or both.
Acetabular labrumThe acetabular labrum (glenoidal labrum of the hip joint or cotyloid ligament in older texts) is a fibrocartilaginous ring which surrounds the circumference of the acetabulum of the hip, deepening the acetabulum. The labrum is attached onto the bony rim and transverse acetabular ligament. It is triangular in cross-section (with the apex represented by the free margin). The labrum contributes to the articular surface of the joint (increasing it by almost 10%). It embraces the femoral head, holding it firmly in the joint socket to stabilise the joint.
AcetabulumThe acetabulum (ˌæsɪˈtæbjələm), also called the cotyloid cavity, is a concave surface of the pelvis. The head of the femur meets with the pelvis at the acetabulum, forming the hip joint. There are three bones of the os coxae (hip bone) that come together to form the acetabulum. Contributing a little more than two-fifths of the structure is the ischium, which provides lower and side boundaries to the acetabulum. The ilium forms the upper boundary, providing a little less than two-fifths of the structure of the acetabulum.
Cross-correlationIn signal processing, cross-correlation is a measure of similarity of two series as a function of the displacement of one relative to the other. This is also known as a sliding dot product or sliding inner-product. It is commonly used for searching a long signal for a shorter, known feature. It has applications in pattern recognition, single particle analysis, electron tomography, averaging, cryptanalysis, and neurophysiology. The cross-correlation is similar in nature to the convolution of two functions.
Spearman's rank correlation coefficientIn statistics, Spearman's rank correlation coefficient or Spearman's ρ, named after Charles Spearman and often denoted by the Greek letter (rho) or as , is a nonparametric measure of rank correlation (statistical dependence between the rankings of two variables). It assesses how well the relationship between two variables can be described using a monotonic function. The Spearman correlation between two variables is equal to the Pearson correlation between the rank values of those two variables; while Pearson's correlation assesses linear relationships, Spearman's correlation assesses monotonic relationships (whether linear or not).
