"Chiropracty" isn't my invention (try an Internet search). I prefer it simply because it sounds more like a noun than an adjective.
Chiropractic is a moderately successful business technique based on the (extremely powerful and very real) placebo effect.
There is still some controvery regarding the meaning of the results known as the "placebo effect". One needn't appeal to it in this case. Anecdotes are sufficient for the success of chiropracty.
I did an Internet search and you are, of course, correct. "Chiropracty" seems to be used in Great Britain more commonly.
Like most successful medical fraud, there are many success stories with chiropractic treatment. These successes are real, but are due to the extemely powerful placebo effect on very desparate people. The Chiropracty business technique has no scientific basis beyond this, and in fact is overtly hostile to the scientific method or intellectual honesty, as one can see on this thread.
Chiropracty has no place in a university.