Recover lost Linux files after hard drive wipe

I purchased a new hard drive to add to my home Linux server. I moved all the files I wanted to save onto a single hard drive and repartitioned the old hard drive so I could upgrade to a newer version of Linux. After going through the process of reinstalling the operating system, I mounted the backup hard drive and discovered that it was empty. I had some how mixed up the hard drive I used to back up all the data with a hard drive that I wanted to wipe. Because I had done such a poor job of retaining backups on external media, I did not have any backups of my pictures and videos...