Reliable measures of body composition are essential in order to develop effective policies to tackle the costs of obesity. To date the lack of an acceptable gold-standard for measuring fatness has made it difficult to evaluate alternative measures of obesity. In this paper we draw on work in other areas of epidemiology and use latent class analysis to evaluate alternative measures of obesity in the absence of a gold standard. Using data from a representative sample of US adults we show that while measures based on Body Mass Index and Bioelectrical Impedance Analysis appear to misclassify large numbers of individuals, this is not the case for classification based on waist circumference. The error rates associated with waist circumference are of the order of 3% for most of our samples compared to error rates as high as 40-50% with the other measures. These results have implications for racial differences in obesity. Our estimated true prevalence rates imply that the obesity rate among black women is substantially higher than among white women. However, the opposite is true for men, with the black men having a significantly lower obesity rate among black men. The fact that neither the BMI nor the BIA based measures of obesity are capable of capturing both these features highlights the dangers associated with measuring obesity and the potential costly policy mistakes that may arise from arbitrarily adopting a single measure as a gold standard.