Statistician as co-author
The first rule of thumb is never do work without clarifying authorship. (This is usually harder said than done, especially if one is a graduate student). 

Based on the limited information you have provided, it seems that authorship may be warranted here. If your analysis was used, especially if your "explanations of how to interpret the results" were used verbatim, you need to be given authorship. If you are in a position to do such, I would send a short email to the professor and explain that you feel your contributions deserve authorship. It costs the professor nothing to add you as an author. Since you are outside academia, you have the option of not working with the professor further. Regardless of the outcome, you can still list the project as a project you participated in as a statistician. 

This will be somewhat field specific. Such practices could be confirmed by looking at other similar papers and seeing what type of attribution the statistician was given. This will also back your claim if statisticians are usually given authorship in the field. 

Also note that a poster is not the same as a journal article. Authorship for posters is usually somewhat loose; authorship for journal articles is much more official.