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).
Correlation does not imply causationThe phrase "correlation does not imply causation" refers to the inability to legitimately deduce a cause-and-effect relationship between two events or variables solely on the basis of an observed association or correlation between them. The idea that "correlation implies causation" is an example of a questionable-cause logical fallacy, in which two events occurring together are taken to have established a cause-and-effect relationship. This fallacy is also known by the Latin phrase cum hoc ergo propter hoc ('with this, therefore because of this').
Finite element methodThe finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat transfer, fluid flow, mass transport, and electromagnetic potential. The FEM is a general numerical method for solving partial differential equations in two or three space variables (i.e., some boundary value problems).
PelvisThe pelvis (: pelves or pelvises) is the lower part of the trunk, between the abdomen and the thighs (sometimes also called pelvic region), together with its embedded skeleton (sometimes also called bony pelvis, or pelvic skeleton). The pelvic region of the trunk includes the bony pelvis, the pelvic cavity (the space enclosed by the bony pelvis), the pelvic floor, below the pelvic cavity, and the perineum, below the pelvic floor. The pelvic skeleton is formed in the area of the back, by the sacrum and the coccyx and anteriorly and to the left and right sides, by a pair of hip bones.
Finite difference methodIn numerical analysis, finite-difference methods (FDM) are a class of numerical techniques for solving differential equations by approximating derivatives with finite differences. Both the spatial domain and time interval (if applicable) are discretized, or broken into a finite number of steps, and the value of the solution at these discrete points is approximated by solving algebraic equations containing finite differences and values from nearby points.
Coefficient of multiple correlationIn statistics, the coefficient of multiple correlation is a measure of how well a given variable can be predicted using a linear function of a set of other variables. It is the correlation between the variable's values and the best predictions that can be computed linearly from the predictive variables. The coefficient of multiple correlation takes values between 0 and 1.
Kendall rank correlation coefficientIn statistics, the Kendall rank correlation coefficient, commonly referred to as Kendall's τ coefficient (after the Greek letter τ, tau), is a statistic used to measure the ordinal association between two measured quantities. A τ test is a non-parametric hypothesis test for statistical dependence based on the τ coefficient. It is a measure of rank correlation: the similarity of the orderings of the data when ranked by each of the quantities.
HipIn vertebrate anatomy, hip (or coxa in medical terminology; : coxae) refers to either an anatomical region or a joint. The hip region is located lateral and anterior to the gluteal region, inferior to the iliac crest, and overlying the greater trochanter of the femur, or "thigh bone". In adults, three of the bones of the pelvis have fused into the hip bone or acetabulum which forms part of the hip region. The hip joint, scientifically referred to as the acetabulofemoral joint (art.
Iterative methodIn computational mathematics, an iterative method is a mathematical procedure that uses an initial value to generate a sequence of improving approximate solutions for a class of problems, in which the n-th approximation is derived from the previous ones. A specific implementation with termination criteria for a given iterative method like gradient descent, hill climbing, Newton's method, or quasi-Newton methods like BFGS, is an algorithm of the iterative method.
Heun's methodIn mathematics and computational science, Heun's method may refer to the improved or modified Euler's method (that is, the explicit trapezoidal rule), or a similar two-stage Runge–Kutta method. It is named after Karl Heun and is a numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. Both variants can be seen as extensions of the Euler method into two-stage second-order Runge–Kutta methods.
Rank correlationIn statistics, a rank correlation is any of several statistics that measure an ordinal association—the relationship between rankings of different ordinal variables or different rankings of the same variable, where a "ranking" is the assignment of the ordering labels "first", "second", "third", etc. to different observations of a particular variable. A rank correlation coefficient measures the degree of similarity between two rankings, and can be used to assess the significance of the relation between them.
