Virtually all social science research related to obesity studies a person's body mass index (BMI). Yet there is wide agreement in the medical literature that BMI is seriously flawed because it does not distinguish fat from fat-free mass such as muscle and bone. This paper studies data that include multiple measures of fatness and finds that many important patterns, such as who is classified as obese, group rates of obesity, and correlations of obesity with social science outcomes, are all sensitive to the measure of fatness and obesity used. We show that, relative to percent body fat, BMI misclassifies substantial fractions of individuals as obese or non-obese; in general, BMI is less accurate classifying men than women. Furthermore, when percent body fat instead of BMI is used to define obesity, the gap in obesity between white and African American men increases substantially but the gap in obesity between African American and white women is cut in half. Finally, total body fat is negatively correlated with employment for some groups and fat-free mass is not significantly correlated with employment for any group, a difference that was obscured in previous research that studied BMI. In the long run, social science datasets should include more accurate measures of fatness. In the short run, estimating more accurate measures of fatness using height and weight is not possible except by making unattractive assumptions, but there is also no reason to adhere uncritically to BMI as a measure of fatness. Social science research on obesity would be enriched by greater consideration of alternate specifications of weight and height and more accurate measures of fatness.