by experimentation vs through an experiment

by experimentation and through an experiment both are adverbs.

Word	Noun	Adjective	Verb	Adverb
by experimentation	No	No	No	Yes
through an experiment	No	No	No	Yes

As adverbs, by experimentation and through an experiment are synonyms defined as:

by experimentation and through an experiment: in an experimental fashion

Other synonyms of by experimentation include experimentally.

by experimentation (adverb)	through an experiment (adverb)
in an experimental fashion	in an experimental fashion