What test checks for adequate tire tread?

It is called a "tread depth measurement"

There is a special tool for this or you can use a caliper set that will do depth measurement or a "Machinist rule"

A very easy test is to take a Lincoln penny and insert it between the treads head down. If you can see the top of lincoln's head your tires need replacing. This means the tread is worn to below 2/32" which is the danger level. The tires have very little grip and are prone to hydroplaning when worn this much.