Conceptually correct tests are performed of the Heckscher-Ohlin proposition that trade in commodities can be explained in terms of an interaction between factor input requirements and factor endowments. An exact specification of this interaction in a multicountry, multicommodity, multifactor world is derived in the form of the Heckscher-Ohlin-Vanek (H-O-V) theorem. The relationships are tested using data on the 367-order US input-output tables for 1967 and the 1967 trade and the 1966 supply of 12 resources for 27 countries. The Leontief-type sign and rank propositions, whether tested across countries or across factors, generally are not supported. The hypothesis that the H-O-V equations are exact also is not supported by the data. The data indicate errors in measurement in both trade and national factor supplies and favor the hypothesis of neutral technological differences across countries. The H-O-V equations are rejected in favor of weaker models that permit technological differences and measurement errors.