A statistical analysis of stratospheric ozone profile data from the Umkehr method is considered for the detection of trends which may be associated with the release of chlorofluoromethanes (CFMs), where possible effects of atmospheric aerosols on the Umkehr measurements are also taken into account. In the statistical trend analysis, time series models have been estimated using monthly averages of Umkehr data over the past 15 to 20 years through 1980 at each of 13 Umkehr stations and at each of the five highest Umkehr layers, 5-9, which cover an altitude range of approximately 24-48 km. The time series regression models incorporate seasonal, trend, and noise factors and an additional factor to explicitly account for the effects of atmospheric aerosols on the Umkehr measurements. At each Umkehr station, the explanatory series used in the statistical model to account for the aerosol effect is a 5 month running average of the monthly atmospheric transmission data at Mauno Loa, Hawaii, the only long running aerosol data available. A random effects model is used to combine the 13 individual station trend estimates from the time series models to form an overall estimate of trend for each Umkehr layer. The analysis indicates statistically significant trends in the upper Umkehr layers 7 and 8 of the order of -0.2 to -0.3% per year over the period 1970--1980, with little trend in the lower layers 5 and 6. The results of the estimation of trends as well as aerosol effects for the Umkehr data are compared with recent corresponding theoretical predictions.