Compositional Data Methods in Customer Survey Analysis

Customer satisfaction is usually measured by questionnaires with statements scored on an anchored scale. Responses to such surveys consist of compositional data (CoDa) by considering the frequency distribution of ratings across questions or respondents. By CoDa, we mean vectors whose elements contain relative information, that is, its total sum is not informative. In this paper, we explore the contribution of CoDa methodology to the analysis of customer satisfaction surveys. Compositional methods are based on the principle of working on coordinates, that is, values obtained by the logarithm of ratios of the parts in a composition. We present common compositional tools such as descriptive statistics, TC2 control chart and principal component analysis (among others), and show an example of application to the annual customer satisfaction survey of the ABC Company. We highlight the advantage of the compositional approach in dealing with non response, which turns into a difficulty when dealing with zeros. We finally underline the pros and cons of the proposed analysis.