A method is proposed to estimate the effect of long-term variations in total ozone on the error incurred in determining a trend in total ozone due to man-made effects. When this method is applied to data from Arosa, Switzerland over the years 1932--1980, a component of the standard error of the trend estimate equal to 0.6 percent per decade is obtained. If this estimate of long-term trend variability at Arosa is not too different from global long-term trend variability, then the threshold (¿2 standard errors) for detecting an ozone trend in the 1970's that is outside of what could be expected from natural variation alone and hence be man-made would range from 1.35% (Reinsel et al, 1981) to 1.8%. The latter value is obtained by combining the Reinsel et al result with the result here, assuming that the error variations that both studies measure are independent and additive. Estimates for long-term trend variation over other time periods are also derived. Simulations that measure the precision of the estimate of long-term variability are reported.