The test devised by Tukey, 1959, to Duckworth's specifications was intended to test for the difference in location of two populations by counting the number of the sample from one population exceeding the highest observation of the sample from the second population together with the number from the second sample which are lower than the lowest observation in the first sample. In much experimental work only the high or low end (but not both) of the scale can be effectively quantified or even observed. This note gives a simple modification of the test for this case.