Household Socioeconomic Status (HSES) scales are among the most common measurement instruments used by social scientists concerned with stratification among nuclear families and other kinds of households. Nevertheless, the theoretic adequacy of such instruments has remained in doubt. Drawing on what is likely the only data set in existence that includes measures of the four main dimensions of the stratification structure of social systems—political, economic, social and informational power—as well as a well-constructed HSES scale, this paper provides a critical test of the theoretic adequacy of an HSES scale. The scale is found to measure the variability shared by the four power variables, thus showing that it is indeed acceptable theoretically, at least within the isolated rural Brazilian area in which the test was performed. Finally, it is noted that retests should be conducted on samples from contrasting contexts, such as urban Brazil and areas in within richer nations.