How Spurious is the Relationship Between Food Price and Energy Density? A Simple Procedure and Statistical Test

An important ongoing debate in the literature is whether or not the relationship between food price per kilocalorie and energy density is real or spurious. No closure has come on this debate because no formal statistical tests have been performed. Rather, the arguments against a real relationship have been more anecdotal or analogy based. The goal of this paper is to develop and demonstrate a simple test for the degree of spurious correlation between price of food per kilocalorie and energy density and apply it to a large number of foods. Whereas previous studies have considered rather small sample sizes (e.g. 300 foods or less), here the test is applied to 4430 different foods and 25 different food sub groups from the National Health and Nutrition Examination Study (NHANES) 2003-04. The results indicate that over all foods the relationship is spurious between price per kilocalorie and energy density. When the analysis is broken down by food groups, 92% of the relationships between price per kilocalorie and energy density are spurious. Because this is such an important issue and has been cast within the context of an economic argument, a brief discussion outlines the more appropriate economic framework for discussing the relationships between price and food attributes, such as energy density.