I notice there's no height requirment for being Amish. Look at those guys again.
I noticed that too and had to wonder about it.
My first thought was that was it possible that limiting your technology to 100 years ago or older might, some how, limit your average height to the average of that long ago?
My next bit of reasoning is the more probable cause. Since their "eligible mate" pool is pretty much limited to those of the same religion and the religion doesn't have many new converts, they are all drawn from the same basic gene pool that has belonged to the Amish since they were founded, and it looks like most of that is 5'3" or so.