The annual mean rainfall data from Tucumán, Argentina for the years 1884–1996 is revisited for an in-depth change-point analysis. Applying classical change detection statistics, we first demonstrate that change-point analysis under independence is invalid. Upon properly adjusting for dependence, it is found that a significant change has occurred in the mean of the data in and around 1956. The data analysis demonstrates that change detection statistics are sensitive to how the model variance is estimated. Moreover, the analysis shows that even marginally significant serial correlations among the observations can have a highly significant effect upon the variance estimate. Finally, the analysis illustrates that one should exercise care while implementing parametric or non-parametric methods in estimating the model variance, and one should be prepared for one of the methods outperforming the other. Copyright © 2010 John Wiley & Sons, Ltd.