Gaining from discretization of continuous data: The correspondence analysis biplot approach

According to Stevens's classification of measurement, continuous data can be either ratio or interval scale data. The relationship between two continuous variables is assumed to be linear and is estimated with the Pearson correlation coefficient, which assumes normality between the variables. If researchers use conventional statistics (t test or analysis of variance) or factor analysis of correlation matrices to study gender or race differences, the data are assumed to be continuous and normally distributed. If continuous data are discretized, they become ordinal; thus, discretization is widely considered to be a downgrading of measurement. However, discretization is advantageous for data analysis, because it provides interactive relationships between the discretized variables and naturally measured categorical variables such as gender and race. Such interactive relationship information between categories is not available with the ratio or interval scale of measurement, but it is useful to researchers in some applications. In the present study, Wechsler intelligence and memory scores were discretized, and the interactive relationships were examined among the discretized Wechsler scores (by gender and race). Unlike in previous studies, we estimated category associations and used correlations to enhance their interpretation, and our results showed distinct gender and racial/ethnic group differences in the correlational patterns.