Many countries have a statutory minimum wage for employees. There is a strong policy interest in knowing the degree of compliance with the law. Quantitative analysis is ideally suited to this, and many countries have rich datasets for employment research. However, identifying genuine underpayment of wages is not straightforward: data quality, statistical factors and processing errors can all contribute to the under- or over-estimation of the true level of compliance. The impact is exacerbated by the binary ‘yes-no’ nature of compliance.We consider the statistical measurement of non-compliance in the UK. UK minimum wages have been extensively studied, using large-scale high-quality datasets whose characteristics are well understood and whose overlapping coverage allows triangulation of results. We focus particularly on apprentices: a survey of apprentice wages was introduced in 2011, throwing further light onmeasurement issues, even in a purpose-built survey instrument.We identify several problems leading to under- and over-estimation of compliance rates. Some are well-known statistical or methodological issues, but others relate to the way that survey data is processed; this is rarely considered by data users. The binary nature of compliance makes such problems easier to identify and evaluate. In particular, we demonstrate the value of a very detailed knowledge of the data at crucial points in the distribution, and the importance of triangulation for understanding the reliability of estimates.While concentrating on compliance with a statutory minimum wage, the paper has some wider lessons for the understanding the characteristics of large and complex datasets. We also show how the use of quantitative data can be used to effectively target complementary qualitative datacollection
