Professional societies often have student paper competitions to encourage and reward student research.  These paper competition are usually centered around a conference.  Monetary awards are given to winners to help defray part of the travel costs.  Paper competition award winners present their research at the conference.  

Below are a few links to student paper competitions.

• ASA Biometrics Section's David B. Byar Young Investigator Award - Available for new recipients of a Ph.D. in addition to students
• ASA Biopharmaceutical Section's student paper competition for the Joint Statistical Meetings
• ASA Statistical Computing Section's student paper competition for the Joint Statistical Meetings
• John M. Chambers Statistical Software Award for the Joint Statistical Meetings
• ENAR Student Awards for the ENAR meetings - See the "Meeting information" link.  
• Oklahoma State University's Annual Research Symposium for graduate and undergraduate students
• The Society of Clinical Trials meeting's student scholarship program  

Many conferences defray some costs to students who are presenting a paper or giving a poster without having a "student paper competition".  For example, the Kansas State University Conference on Applied Statistics in Agriculture gives support to graduate students with preference given to a paper or poster presenter. 

For more specific information about student paper competitions, talk to your major advisor or another faculty member.