Assumptions Underlying Principal Component Analysis

Because a principal component analysis is performed on a matrix of Pearson correlation coefficients, the data should satisfy the assumptions for this statistic. These assumptions were described in detail in Chapter 6, “Measures of Bivariate Association,” and are briefly reviewed here:

• Interval-level measurement. All variables should be assessed on an interval or ratio level of measurement.

• Random sampling. Each participant will contribute one response for each observed variable. These sets of scores should represent a random sample drawn from the population of interest.

• Linearity. The relationship between all observed variables should be linear.

• Bivariate normal distribution. Each pair of observed variables should display a bivariate normal distribution (e.g., they should form an elliptical scattergram when plotted).