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User modeling on the Web has rested on the fundamental assumption of Markovian behavior --- a user's next action depends only on her current state, and not the history leading up to the current state. This forms the underpinning of PageRank web ranking, as well as a number of techniques for targeting advertising to users. In this work we examine the validity of this assumption, using data from a number of Web settings. Our main result invokes statistical order estimation tests for Markov chains to establish that Web users are not, in fact, Markovian. We study the extent to which the Markovian assumption is invalid, and derive a number of avenues for further research.