Any use of the song snippets in your App can be copyright infringement (in the US), Fair Use (U.S. Copyright Office) not withstanding. Not distributing the App and/or using the App only in a limited group for the study, or not making money from the App doesn't usually matter when it comes to copyright infringement.
Fair Use does have some educational exceptions; read the link above and see if your case may fit. But the final assessment of educational use would be made by a court if you were sued for infringement.
If the use in your App doesn't fall under the education exception, you still probably run little risk of the copyright holders finding out if the App use is private and within a small group, but that's your choice to make.
You can always Google the name of the music/recording company; most provide ways online to request licensing of samples, but the cost may be prohibitive, or permission may simply not be available for popular songs.