Die Stichprobengröße wurde mittels G*Power ermittelt

You usually find this in the 'Method' section of a thesis or paper. It almost always uses the passive voice (wurde ... ermittelt). This keeps the focus on the science, not the scientist. If you want to sound like a pro, keep it exactly as it is. Don't try to make it 'flowery'. In German academia, dry and precise is the highest compliment.

Use this when writing your Master's thesis or a doctoral dissertation. It's perfect for research proposals or defending your methodology to a professor. If a colleague asks how you decided to recruit 100 people, dropping this line will end the argument immediately. It shows you understand statistical power and didn't just pick a random number.

Never use this in a casual setting. If you say this at a bar, people will think you've spent too much time in the library. Avoid it when talking to non-academics. They won't know what G*Power is. Also, don't use it if you actually just guessed your sample size. German professors have a sixth sense for 'statistical bluffing'.

G*Power was actually developed at the Heinrich Heine University in Düsseldorf. Because it's a 'homegrown' German tool that became a global standard, German universities are very proud of it. Using it is a nod to German precision and the high standards of their psychological and social science departments. It’s part of the 'Ordnung muss sein' (there must be order) mentality applied to data.

You might see berechnet (calculated) instead of ermittelt. Some people use anhand von (based on) instead of mittels. You could also say: Die Power-Analyse wurde mit G*Power durchgeführt (The power analysis was conducted with G*Power). All of these carry the same 'nerdy but professional' energy.