Confidence Ellipses for X Score Scatterplot Matrix

The Score Scatterplot Matrices option adds 95% confidence ellipses to the X Score scatterplots. The X scores are uncorrelated because both the NIPALS and SIMPLE algorithms produce orthogonal score vectors. The ellipses assume that each pair of X scores follows a bivariate normal distribution with zero correlation.

Consider a scatterplot for score i on the vertical axis and score j on the horizontal axis. The coordinates of the top, bottom, left, and right extremes of the ellipse are as follows:

•

the top and bottom extremes are +/-sqrt(var(score i)*z)

•

the left and right extremes are +/-sqrt(var(score j)*z)

where z = ((n-1)*(n-1)/n)*BetaQuantile(0.95, 1, (n-3)/2). For background on the z value, see Tracy et al. (1992).