Correspondence analysis and the Freeman-Tukey statistic: A study of archaeological data

Traditionally, simple correspondence analysis is performed by decomposing a matrix of standardised residuals using singular value decomposition where the sum-of-squares of these residuals gives Pearson's chi-squared statistic. Such residuals, which are treated as being asymptotically normally distributed, arise by assuming that the cell frequencies are Poisson random variables so that their mean and variance are the same. However, studies in the past reveal that this is not the case and that the cell frequencies are prone to overdispersion. There are a growing number of remedies that have been proposed in the statistics, and allied, literature. One such remedy, and the focus of this paper, is to stabilise the variance using the Freeman-Tukeytransformation. Therefore, the properties that stem from performing correspondence analysis will be examined by decomposing the Freeman-Tukey residuals of a two-way contingency table. The application of this strategy shall be made by studying one large, and sparse, set of archaeological data.