It Is well known that nonindependent errors arising from autoregressive (AR) or moving average (MA) processes may reverse the conclusions oftorFtests for estimable functions of regression coefficients. We show that these conclusions can be reversed only if observedtorFvalues based on ordinary least squares (OLS) computations lie between certain lower and upper bounds. Our tabulations of these bounds are based on the Imhof [5] distribution of a ratio of quadratic forms in normal variables, and avoid some of the approximations used by Watson and Hannan [16].