Anyway, Anyways, or Any Way
The adverb anyways is extremely informal, and indicates the speaker is resuming a narrative thread or changing the topic of discussion. It’s not a word you should use in formal writing.
I never did understand numbers very well. Anyways, I’ve decided to move from financing into tech support.
Anyway can be used to mean in any case. This adverb is acceptable in formal writing, but intentions may be better expressed by the use of a variation of in any case. Consider your audience when choosing the adverb.
Paris is expensive, but many people would like to vacation there, anyway.
Paris is expensive, but many people would like to vacation there, in any case.
When written as two words, any way can be replaced by in any manner or by by any means.
To get students to read, teachers often bribe them any way they can.
To get students to read, teachers often bribe them in any manner they can.
To get students to read, teachers often bribe them by any means they can.
All of these adverbs are acceptable in formal writing.
I don’t mind staying home from the party because I don’t feel all that well, any way.
Because any way cannot be replaced with in any manner, it should be written as one word: anyway.