It's a test developed by some fictional psychologist and named after the same (like the Turing Test). In the same vein as Voigt-Kampf I suppose, but AIs eventually managed to pass even this test too.
Don't know if the link will work for you, but looking it up in Google Books gave me this.
Jill was the oldest thinking being on Earth, a fabulous figure, the first thinker to achieve bona fide self-awareness, as defined by the Atkins test.
Decades before Jill and Roger Atkins, Alan Turing had proposed the Turing test for equality between human and machine...