Economists have usually called the proportion of the average wage gap between two groups which could not be explained by individual characteristics 'discrimination'. Recently, several theories have suggested that labour market discrimination, on the one hand, lowers the wages of the 'minority' group, and on the other, leads to higher pay for the 'majority' group. In a recent survey of the various methods used to decompose the overall wage differential between two groups, Oaxaca and Ransom compared five approaches in the contexts of race and gender discrimination. This paper checks whether there are significant differences between the various decomposition procedures which have appeared in the literature. The tests are based on bootstrap techniques.