Mittels Exact-Tests wurden bei kleinen Stichproben

This phrase acts as a sophisticated 'intro' for a sentence. You use it to set the stage before revealing your findings. Because it uses the word mittels and the passive voice wurden, it sounds very objective and professional. You would typically follow this phrase with a verb like analysiert (analyzed) or nachgewiesen (proven). For example, you might say that certain trends were identified 'by means of' these tests. It is a linguistic power move that makes you sound like an expert who doesn't cut corners. It is the academic equivalent of wearing a perfectly tailored suit to a meeting.

You will mostly find this in the 'Methodology' or 'Results' section of a university thesis or a scientific paper. It is also perfect for high-stakes business presentations where your pilot group was small, but you need to convince the board that the results are valid. If you are a doctor, a researcher, or a data analyst, this is part of your daily toolkit. You can also use it ironically with friends to sound 'over-educated' when discussing something trivial, like testing which of your three cats prefers which brand of food.

Do not use this at a casual dinner party or while chatting at a bar. It is far too stiff for social settings. If you tell a waiter that 'by means of exact tests' you found the soup too salty, you will get some very strange looks. Also, avoid this if you actually have a massive amount of data. If your sample size is 10,000 people, using an 'Exact-Test' is often unnecessary and mathematically 'overkill.' Finally, don't use it if you want to sound warm and approachable; this phrase is cold, logical, and strictly business.

Germany has a deep-seated cultural respect for Wissenschaft (science) and Genauigkeit (accuracy). Being precise isn't just a technical requirement; it is a sign of integrity. This phrase reflects the German desire to be 'gründlich' (thorough). Historically, German academia has always favored complex, precise terminology to distinguish professional work from amateur observations. Using mittels instead of the simple mit (with) shows that you value the formal traditions of German intellectual life. It is the linguistic version of 'Vorsprung durch Technik.'

If you want to sound slightly less formal, you could use Mithilfe von exakten Tests. If you are talking about the sample size specifically, you might say Bei geringen Fallzahlen (with low case numbers). Some people prefer the fully Germanized Exakte Tests instead of the English-influenced Exact-Tests. You might also see Aufgrund der kleinen Stichprobe (due to the small sample). However, mittels remains the gold standard for formal reporting because it sounds definitive and authoritative.