<p><strong>Update</strong></p>

<p>Here is one of the two projects identified by @whuber. Please vote up/down this particular idea depending on whether you want to this to be our first polystats project. I am going to post the other project as a separate answer.</p>

<blockquote>
  <p>"Predictive Segmentation of Populations." Help improve clinical trials by distinguishing subpopulations of people into potential responders (to a treatment) and non-responders. </p>
</blockquote>

<p>To spice it up a bit, what about engaging in a real problem <em>with a prize offered for the best solution</em>?  Instances are easy to come by at places like <a href="http://www2.innocentive.com/" rel="nofollow">http://www2.innocentive.com/</a> .  Advantages include having a well-defined problem and ready access to appropriate data.  Disadvantages include a time limit (usually a few months) and figuring out what to do with a prize if it's won ;-).</p>
