Statistical inference using the T index to quantify the level of comparability between accounts

Abstract

The extent to which the accounts of companies are comparable is considered important to users and regulators. However, prior research has been restricted by a lack of appropriate statistical methods for testing comparability indices. This has made it difficult to assess the true level of comparability from sample data and to test research hypotheses such as whether the level of comparability (a) differs by policy, (b) differs by country, and (c) changes over time. This paper fills this gap by exploring the statistical properties of the Tindex. The Tindex generalises the H, C, I and various modifications of these indices and represents a unified framework for the measurement of the extent to which the accounts of companies are comparable. Formulae for the bias and standard error for any index under this framework are provided and proved. The bias is shown to equal zero or be negligible in most practical situations. Using historical data, the standard error is used to illustrate the accuracy with which comparability is estimated and to perform formal statistical inference using confidence intervals and p-values. Furthermore, the sampling distribution of the T index is assessed for normality. Implications for research design and sample size determination are also discussed.