The relation between the Freese (1960) accuracy test and the related test proposed by Reynolds (1984) is examined and a three-way decision rule is recommended as a circumspect alternative to the accept/reject decision rule commonly employed. Further alternatives are proposed in the form of point and interval estimates for parameters of the error distribution under scrutiny. The effect of bias correction on the test procedures and estimators is analyzed and simulated. Conditional bias correction following a pretest is shown to behave equivalently to unconditional bias correction when sample size is not too small. When errors are nonnormal, all tests and estimators degrade considerably, and the problem becomes severe for large sample sizes. For. Sci. 34(2):302-320.