What's the difference between rigor and rigorousness?
Which should I use in the following?
Rigorousness and clarity are not synonymous in pedagogy.
The relationship between rigor and rigorousness is that rigor is similar in meaning to “severity” or “strictness”, but rigorousness is primarily “the abstract property of having to do with, or being inclined to, rigor”. As for which is best in your sentence, it simply comes down to which one you mean.
The suffixes -ous and -ness are productive, meaning they are used by English speakers as part of habits or “rules” for producing new words. These compound words, in the ears of English speakers, will generally mean what the individual parts mean.
The suffix -ous takes a noun X and creates an adjective X-ous which stands for “having X”, “full of X”, “having to do with X”, “doing X”, or “inclined to X”.¹
The suffix -ness can take an adjective Y and create a noun Y-ness which stands for the abstract action, quality, or state which Y has to do with.² You can think of this as converting a description of something to a property which it possesses.
As you might expect, then, when these productive suffixes are used together with a noun Z, the resulting compound Z-ous-ness will mean “the abstract action, quality or state of having/being full of/having to do with/doing/being inclined to Z”. You can think of this as converting a thing to an abstract property having to do with such a thing.
Because these habits or “rules” of new word production are instilled into the minds of English speakers, they will find it possible to make sense of words which are invented using this method, even when the combinations have never been seen before.
Such habits or “rules” are not, of course, the whole story. Once a new word is coined by compounding with suffixes and becomes a popular word, it is tossed and buffeted by the same social forces which cause all words to evolve in meaning. The compound may acquire unique connotations which do not wholly apply to its parts. A good dictionary will provide this information.
There are many other pairs of words like this in English, just as joy and joyousness (or joyfulness), or somewhat more indirectly, pugnacity and pugnaciousness. Most of them mean the same in the longer and shorter form, but some can sometimes carry additional nuance and so do not always allow complete swapping.
In this particular case, I believe they are identical, and that you can replace rigorousness with rigor in your example sentence:
However, when rigor means “severe”, I don’t think you can do so as easily. For example:
I really don’t think you can swap that one the way you can with your own example.
The OED defines rigorousness as
And rigorous has in turn several senses of its own. One of these is very strict and exacting, but another is very harsh weather. I think only the first swaps for rigor very easily.
Rigorousness is a general word that can be applied in any context.
Rigor is an established term used in the pedagogical field, and in its critique.
For an interesting report, see DEFINING RIGOR IN HIGH SCHOOL: Framework and Assessment Tool [pdf 160kB]
When writing on pedagogy, never use one term for the other.