You already know conduct research ('do research' is fine in speech but casual on the page; 'make research' is simply wrong). Two more to add. To test a hypothesis is to run an experiment to see whether a proposed explanation holds, where a hypothesis is the theory you set out to test. Extensive means wide-ranging and thorough, so extensive research is a large, in-depth body of work, not a single small study.
The verbs that go with research
conduct research /kənˈdʌkt rɪˈsɜrtʃ/ — The team conducted research on sleep patterns over three winters.
test a hypothesis /tɛst ə haɪˈpɑθəsɪs/ — They designed an experiment to test the hypothesis that noise slows recovery.
extensive /ɪkˈstɛnsɪv/ — After extensive research, the authors found no link between the two factors.
Not ""The scientists did extensive research." ('do research' is informal here)" — say ""The scientists conducted extensive research."". In formal science writing you conduct research; 'do research' is fine in speech but reads as casual on the page.
Try it: Which sentence uses the standard academic collocations? (The lab conducted extensive research to test its hypothesis. / The lab did extensive research to check its hypothesis. / The lab made extensive research to prove its hypothesis.) Answer: The lab conducted extensive research to test its hypothesis. — 'Conduct research' and 'test a hypothesis' are the fixed academic pairings. 'Did research' and 'check its hypothesis' are too casual for formal writing, and 'made research' isn't English; you never 'make' research.
Words for solid methods and evidence
These three words praise different parts of a study, so don't swap them. To praise a study's method, call it rigorous, meaning strict, thorough and careful, a step beyond plain 'strict'. Evidence that comes from real observation or experiment, rather than from theory or opinion, is empirical. A study that other experts have checked before publication is peer-reviewed, which describes how it was vetted, not the method or the evidence. All three are formal, neutral-to-positive words at home in academic writing.
rigorous /ˈrɪɡərəs/ — The findings held up because the methodology was so rigorous.
empirical /ɛmˈpɪrɪkəl/ — Their claim rests on empirical evidence, not on theory alone.
peer-reviewed /ˈpɪr rɪˌvjud/ — She only cites peer-reviewed studies in her literature review.
Not ""The study needs experiencial evidence to back the claim." (not an English word)" — say ""The study needs empirical evidence to back the claim."". Empirical evidence comes from observation or experiment, so it is the broad term. (Experimental evidence is also standard, but narrower, it means evidence from controlled experiments only.)
Try it: A reviewer praises a paper's careful, strict method. Which word fits best? (rigorous / empirical / peer-reviewed) Answer: rigorous — 'Rigorous' is the standard word for a strict, careful method. 'Empirical' describes evidence from observation, not the method's strictness, and 'peer-reviewed' means other experts checked the work, which is about publication, not how careful the method itself was.
Try it: Which sentence uses 'empirical' correctly? (The conclusion is supported by empirical evidence from field observations. / The professor gave an empirical lecture on the topic. / They felt empirical about the results before seeing the data.) Answer: The conclusion is supported by empirical evidence from field observations. — 'Empirical' describes evidence gathered from observation or experiment, so it pairs naturally with 'evidence from field observations.' A lecture isn't 'empirical,' and 'empirical' is never a feeling, so the other two misuse the word.