This paper deals with the hypotheses of symmetry of distributions with respect to a location parameter when the response variables are subject to measurement errors. Rank tests of hypotheses about the location parameter are studied in an asymptotic set up.
It is shown, when and under what conditions, these rank tests can be used effectively, and indicate the effect of measurement errors on the power of the test. Some simulation results are provided to illustrate the influence of measurement errors on the power of the tests.