Switching between different alternative polyadenylation (APA) sites plays an important role in the fine tuning of gene expression. New technologies for the execution of 3'-end enriched RNA-seq allow genome-wide detection of the genes that exhibit significant APA site switching between different samples. Here, we show that the independence test gives better results than the linear trend test in detecting APA site-switching events. Further examination suggests that the discrepancy between these two statistical methods arises from complex APA site-switching events that cannot be represented by a simple change of average 3'-UTR length. In theory, the linear trend test is only effective in detecting these simple changes. We classify the switching events into four switching patterns: two simple patterns (3'-UTR shortening and lengthening) and two complex patterns. By comparing the results of the two statistical methods, we show that complex patterns account for 1/4 of all observed switching events that happen between normal and cancerous human breast cell lines. Because simple and complex switching patterns may convey different biological meanings, they merit separate study. We therefore propose to combine both the independence test and the linear trend test in practice. First, the independence test should be used to detect APA site switching; second, the linear trend test should be invoked to identify simple switching events; and third, those complex switching events that pass independence testing but fail linear trend testing can be identified.