The Amish are practicing what scientists call “Authoritative Parenting” (cf. Baumrind’s seven parenting styles, UC Berkeley). It’s highly Nurturing, highly Demanding (setting appropriate limits on behaviour) and highly Responsive (consistently enforcing those limits).
By Baumrind’s own definition (who coined the term) one of the hallmarks of Authoritative Parenting is that they universally spank to enforce compliance
From a HuffPost article (May 2011) read it HERE