After doing something wrong while installing CyanogenMod 13, I flashed a google marshmallow stock rom. I wanted to go back to CyanogenMod 12, so I backed up my data using CWM recovery, factory reset, and installed CM12. After making sure it was working, I flashed Gapps and restored from my recovery. My apps were back, but I was also back with the google stock rom. Is there any way to only back up the app data?
As mentioned in the comments by Firelord and me, there are multiple approaches:
TiBu and ES File Manager require root to work. ADB and Adebar don't.
Adebar a.o. creates a script to backup each of your (user) apps into a separate archive using adb backup (and another one for the data of system apps, and two others for restore). While you could do a similar thing with TiBu (which uses its own backup format), Adebar runs from the command line while with TiBu you must use a GUI. Side effect from using Adebar: you'll have your device documented: tech specs, apps installed, etc :)
Adebar is pretty easy to install, but will require adb to be available on your computer (see our adb tag-wiki for details on that). It runs fine on Linux, and recently was reported to run on Windows as well via Cygwin.
Disclaimer: I'm the dev of Adebar.
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