The term "half-assed" is used to refer to something being sloppy or partially completed. For example, "You really did a half-assed job on those TPS reports, Bob." What is the etymology of this phrase? If half-assed means partial or incomplete, can something be "full assed" or "fully assed"?
The normal expression is half-assed (or half-arsed in the UK) and "full assed" or "fully assed" aren't commonly used expressions.
"Half-arsed* usually means half-hearted today, and appears to follow on from an earlier use of the phrase meaning inferior or incompetent. Perhaps the suggestion was that a half-assed person is not entirely effective, a bit like a donkey, or half like an ass.
There a similar British expression "I can't be arsed" meaning "I can't be bothered".
The OED has half-assed from 1932 in American Speech:
Half-assed, mediocre; insignificant.
They say it's originally American slang meaning "ineffectual, inadequate, mediocre; stupid, inexperienced"; no mention is made of haphazard.
The British half-arsed is recorded much later, in 1961.
However, The New Partridge Dictionary of Slang and Unconventional English (2008) gives an earlier meaning:
half-assed; half-arsed adjective 1 inferior, unsatisfactory, incompetent US, 1865. 2 incomplete, not serious, half-hearted US, 1933
I found this earlier "incompetent" meaning in General Orders of the War Department: Embracing the Years 1861, 186" & 1861 Adapted Specially For the Use Army and Navy of the United States (Volume 2, published 1864) by Thomas M. O'Brien and Oliver Diefendorf, Military Attorneys of Kansas.
It appears as evidence in a general court martial of July 2, 1863 of an incident in January 1862:
Specification 1st -- In this; that he, the said Captain John H. Behan, Company F, 16th Regiment Virginia Volunteers, while on duty in camp, on or about the 12th day of December 1862, did use abusive and grossly insulting language to Joseph B Hamilton, 2d Lieutenant of said Company F, before and in the presence of said Company F, while he, the said Joseph B. Hamilton, was on duty and was acting Adjutant of said 16th Regiment Virginia Volunteers, in words as follows, to wit: 'There goes our half-assed Adjutant;' which was calculated to impair and weaken the influence and control of said Lieutenant Joseph B. Hamilton as Adjutant of said Regiment, and also his influence and control over said Company.
According to the Online Etymology Dictionary, half-assed made its first appearance in the early 20th century. It is most likely a mispronunciation of the word haphazard.
"ineffectual," 1932, perhaps a humorous mispronunciation of haphazard.
With this in mind, I don't think full-assed or fully assed would make any sense. Though some people may probably still use it like how the word mentee is invented by adding a suffix after back-forming the word mentor. And that is rather ridiculous. Unlike professor or escalator, the word mentor is originated from the Greek word Méntōr which is the name of the son of Anchialus and Asopis.
So is it a compound or just a word originated from another word?
I think it is a combination of both. The word haphazard more or less played a role in the formation of the word. Linguistic evolution that results in neologism is always driven by various factors.
In the UK we would say half-arsed, which might be connected to this discussion of "can't be arsed".
I couldn't find an etymology online except for Urban Dictionary which says arsed comes from the north of England (that's where I have heard it). UD also says half arsed is:
From the latin Halficus Arseicus meaning British Builder
-- jokingly implying that British builders are not very good, or perhaps a reference to "Builder's Bum" - where a builder bending down or leaning over reveals more than you would ever want to see (half his arse).
I'm pretty sure you would never hear fully arsed.