This paper develops the statistical treatment necessary to calculate the error bars associated with the average summer peak UV-B irradiance (ASPUV), a measure of annual solar UV-B irradiance similar to the summertime peak UV Index introduced by McKenzie et al. These errors include the effects of autocorrelation among daily average values of the solar UV-B irradiance at local noon as measured by a variance inflation factor (VIF), which increases the variance of the ASPUV beyond its value for no autocorrelation by amounts ranging from 14% to 52% depending on the year. Including the VIF in the error estimates of the ASPUV allows one to gauge the significance of possible changes in this quantity. As an example, the treatment is applied to broadband radiometric measurements carried out at Georgetown, TX (30.6¿N, 97.7¿W) and it is found that from summer 1995 to summer 2001 the ASPUV has decreased, the values for 1995 and 2001 differing by about 3 standard deviations.