yates(x), x a REAL vector |

yates(x) performs Yates' algorithm for the effects in a 2-series factorial experiment. The argument x should be a REAL vector (univariate case) or matrix (multivariate case) containing the 2^k observations in standard order, that is, the levels of the first factor changing most rapidly. When x is a vector, the value is a vector of the (2^k)-1 effects in standard order and divisor 2^(k-1). For example, for a 2^3 experiment with data vector(x111,x211,x121,x221,x112,x212,x122,x222), the result is vector(A, B, AB, C, AC, BC, ABC), where A = (-x111 + x211 - x121 + x221 - x112 + x212 - x122 + x222)/4 B = (-x111 - x211 + x121 + x221 - x112 - x212 + x122 + x222)/4 AB = (+x111 - x211 - x121 + x221 + x112 - x212 - x122 + x222)/4 and so on. The mean, (x111+x211+x121+x221+x112+x212+x122+x222)/8, is not included. In matrix notation, the k = 3 case can be expressed as [ A ] [ -1 1 -1 1 -1 1 -1 1 ] [ x111 ] [ B ] [ -1 -1 1 1 -1 -1 1 1 ] [ x211 ] [ AB ] [ 1 -1 -1 1 1 -1 -1 1 ] [ x121 ] [ C ] = (1/4) [ -1 -1 -1 -1 1 1 1 1 ] [ x221 ] [ AC ] [ 1 -1 1 -1 -1 1 -1 1 ] [ x112 ] [ BC ] [ 1 1 -1 -1 -1 -1 1 1 ] [ x212 ] [ ABC ] [ -1 1 1 -1 1 -1 -1 1 ] [ x122 ] [ x222 ] When x is a matrix with m columns, the value is a (2^k) - 1 by m matrix, each column of which is the result of applying Yates's algorithm to the corresponding column of x.

Gary Oehlert 2003-01-15