Illustrated Use of Normality Data Tests and the Factor Analysis Model

When carrying out Factor analysis, it is the procedure, to first appreciate the form of distribution of the variables set for analysis. While doing so it is necessary however to recognise that normality of such data though useful is not a required underpinning of the properties of Factor analysis. Nevertheless, since Principle Components are linear combinations of the original variables, it is not unreasonable to expect them to be nearly normal. Nevertheless, it is often necessary to verify that the first few components (the Principle Components) are approximately normally distributed when they are to be used as the input data for additional analysis. Further still, more meaning can generally be given to the components in cases where observations are assumed to be multivariate normal. Two methods of data reduction can be adopted for use and this is consistent with the principle of triangulation that seeks to confirm results using complementary methods. Such a twofold approach respects recommendations on the conduct of factor analysis that at least two methods be used to verify its effectiveness and the authenticity of results. Accordingly, the Principle Component Factor Analysis and the Maximum Likelihood Factor Analysis methods that replicate similar procedure for conducting Factor Analysis are selected for consideration here.