Summary. The Knox method, as well as other tests for space-time interaction, are biased when there are geographical population shifts, i.e., when there are different percent population growths in different regions. In this paper, the size of the population shift bias is investigated for the Knox test, and it is shown that it can be a considerable problem. A Monte Carlo method for constructing unbiased space-time interaction tests is then presented and illustrated on the Knox test as well as for a combined Knox test. Practical implications are discussed in terms of the interpretation of past results and the design of future studies.