Search results
Results From The WOW.Com Content Network
A contrast is defined as the sum of each group mean multiplied by a coefficient for each group (i.e., a signed number, c j). [10] In equation form, = ¯ + ¯ + + ¯ ¯, where L is the weighted sum of group means, the c j coefficients represent the assigned weights of the means (these must sum to 0 for orthogonal contrasts), and ¯ j represents the group means. [8]
Example of orthogonal factorial design Orthogonality concerns the forms of comparison (contrasts) that can be legitimately and efficiently carried out. Contrasts can be represented by vectors and sets of orthogonal contrasts are uncorrelated and independently distributed if the data are normal.
A contrast in cell means is a linear combination of cell means in which the coefficients sum to 0. Contrasts are of interest in themselves, and are the building blocks by which main effects and interactions are defined. In the 2 × 3 experiment illustrated here, the expression
In mathematics, an orthogonal polynomial sequence is a family of polynomials such that any two different polynomials in the sequence are orthogonal to each other under some inner product. The most widely used orthogonal polynomials are the classical orthogonal polynomials , consisting of the Hermite polynomials , the Laguerre polynomials and ...
The structure matrix is simply the factor loading matrix as in orthogonal rotation, representing the variance in a measured variable explained by a factor on both a unique and common contributions basis. The pattern matrix, in contrast, contains coefficients which just represent unique contributions. The more factors, the lower the pattern ...
Hence, coefficients can also be found by solving a linear system, for instance by matrix inversion. Fast algorithms to calculate the forward and inverse Zernike transform use symmetry properties of trigonometric functions, separability of radial and azimuthal parts of Zernike polynomials, and their rotational symmetries.
In contrast to a Fourier series where the coefficients are fixed numbers and the expansion basis consists of sinusoidal functions (that is, sine and cosine functions), the coefficients in the Karhunen–Loève theorem are random variables and the expansion basis depends on the process.
Geometric representation (Argand diagram) of and its conjugate ¯ in the complex plane.The complex conjugate is found by reflecting across the real axis.. In mathematics, the complex conjugate of a complex number is the number with an equal real part and an imaginary part equal in magnitude but opposite in sign.