Jolliffe I. Principal Component Analysis (2ed., Springer, 2002)(518s)

4.1. Anatomical Measurements 65Table 4.1. First three PCs: student anatomical measurements.Component number 1 2 3⎫WomenHand 0.33 0.56 0.03Wrist 0.26 0.62 0.11Height ⎪⎬0.40 −0.44 −0.00Forearm Coefficients 0.41 −0.05 −0.55Head 0.27 −0.19 0.80Chest 0.45 −0.26 −0.12⎪⎭Waist 0.47 0.03 −0.03Eigenvalue 3.72 1.37 0.97Cumulative percentageof total variation 53.2 72.7 86.5⎫MenHand 0.23 0.62 0.64Wrist 0.29 0.53 −0.42Height ⎪⎬0.43 −0.20 0.04Forearm Coefficients 0.33 −0.53 0.38Head 0.41 −0.09 −0.51Chest 0.44 0.08 −0.01⎪⎭Waist 0.46 −0.07 0.09Eigenvalue 4.17 1.26 0.66Cumulative percentageof total variation 59.6 77.6 87.0The PCA was done on the correlation matrix, even though it could beargued that, since all measurements are made in the same units, the covariancematrix might be more appropriate (see Sections 2.3 and 3.3). Thecorrelation matrix was preferred because it was desired to treat all variableson an equal footing: the covariance matrix gives greater weight to larger,and hence more variable, measurements, such as height and chest girth, andless weight to smaller measurements such as wrist girth and hand length.Some of the results of the PC analyses, done separately for women andmen, are given in Tables 4.1 and 4.2.It can be seen that the form of the first two PCs is similar for the twosexes, with some similarity, too, for the third PC. Bearing in mind the smallsample sizes, and the consequent large sampling variation in PC coefficients,it seems that the major sources of variation in the measurements, as givenby the first three PCs, are similar for each sex. A combined PCA using all 28