Dobson total ozone data have been analyzed using two different statistical methods, time series analysis using time domain (TD) methods and frequency domain (FD) methods. The trend estimates from these two methods using a network of 36 Dobson stations have differed from between 0.5% and 1% per decade over the past few years as new data have become available in the 1980's. The reasons for the differences are found to be largely due to a combination of (1) the shorter length data record used in the FD analysis, (2) the different sensitivity of each method to the low 1982--1983 winter ozone values, (3) the different methods of seasonal weighting, and (4) the varying sensitivities to a solar adjustment. Between 1970 and 1984 the total ozone trend estimates are -0.26¿0.92% per decade and -0.70¿0.82% per decade based on the TD and FD methods, respectively. Although different by nearly 0.5% per decade, neither trend estimate is statistically significant.