“Comparing apples and oranges”

Entry in progress—B.P.
 
Wikipedia: Apples and oranges
“Apples and oranges” refers to the idiom “comparing apples and oranges” or “apples to oranges”, which is used to indicate that two items or groups of items have not been validly compared. The idiom evokes the apparent differences between items which are popularly thought to be incomparable or incommensurable, such as apples and oranges. The idiom may also be used to indicate that a false analogy has been made between two items, such as where an “apple” is faulted for not being a good “orange”. Conversely, where the comparison or analogy is valid, the idiom will usually take the form “comparing apples with apples”.
 
(Oxford English Dictionary)
apples and oranges: used as the type of two things which are inherently different or incompatible, usually in contexts implying that a given comparison is invalid. Freq. in to compare apples and oranges and variants. Cf. CHALK n. 6a.
[1922 Ann. Amer. Acad. Polit. & Social Sci. Jan. p. xxiv/2 It is as impossible to add investment banking to commercial banking and get security as it is to add apples to oranges and get peaches.]
1930 Psychol. Rev. 37 160 Psychologists..adding scores in the sub-tests..have been doing something akin to adding apples and oranges.
1958 Burlington (N. Carolina) Daily Times-News 6 Feb. 8/3D To do so is..like comparing apples with oranges, because the two differ in..philosophy and mission.
1989 New Yorker 9 Jan. 56/3 Comparing the two programs is comparing apples and oranges.
2004 Mojo June 14 It’s apples and oranges… Our film is a concert DVD.., and theirs is a feature-length documentary.
 
9 February 1930, Galveston (TX) Daily News, pg. 23, col. 7:
South Texas blue stem prairie hay will not and can not compare in color with other types. It is like comparing apples with oranges and trying to reduce them both to the same color scale.