Die Robustheit der Schätzer wurde überprüft durch

This is primarily used in formal or semi-formal writing, especially in academic papers, research reports, technical documentation, or presentations. You'd use it when describing the methodology or results section. For instance, you might say, 'Die Robustheit der Schätzer wurde überprüft durch eine Monte-Carlo-Simulation.' (The robustness of the estimators was verified through a Monte Carlo simulation.) It’s a precise way to state that validation has occurred. Think about explaining how you tested a new app feature: 'Die Leistung wurde unter verschiedenen Netzwerkbedingungen überprüft.' (The performance was verified under different network conditions.) It’s about showing you’ve done your homework to prove something works as expected or is reliable.

This phrase leans heavily towards formal and academic contexts. You wouldn't typically use it in a casual chat with friends about your weekend plans, unless you're both deeply into statistics or science. It sounds quite technical and precise. Imagine using it in a job interview for a data analyst role – perfect! Using it in a text message about pizza toppings? Probably not, unless you're making a joke about the structural integrity of the crust. It signals a serious, evidence-based approach. It’s the kind of phrase you’d find in a thesis, a scientific journal, or a technical manual. So, keep it for when you need to sound knowledgeable and thorough.

In a research paper: 'Die Robustheit der Schätzer wurde überprüft durch Kreuzvalidierung.' (The robustness of the estimators was verified through cross-validation.) This shows the statistical methods used. On a company report: 'Die Stabilität der neuen Software wurde überprüft durch Belastungstests.' (The stability of the new software was verified through stress tests.) This confirms the software's reliability. In a scientific presentation: 'Die Ergebnisse sind konsistent, und die Robustheit der Modelle wurde überprüft durch Sensitivitätsanalysen.' (The results are consistent, and the robustness of the models was verified through sensitivity analyses.) This highlights the confidence in the model's predictions. In an engineering proposal: 'Die Widerstandsfähigkeit des Materials wurde überprüft durch zyklische Belastungstests.' (The resistance of the material was verified through cyclic load tests.) This is crucial for safety and performance guarantees.

Use this phrase when you need to explicitly state that the reliability or stability of a method, model, or result has been tested. It's perfect for academic writing, scientific research, technical reports, and any situation where you need to demonstrate thoroughness and validate your findings. If you're presenting data analysis, discussing algorithm performance, or explaining the quality of a measurement, this phrase fits right in. It's also great when you want to preemptively address potential doubts about your conclusions. Think of it as a signal that you've gone the extra mile to ensure accuracy and dependability. It's like saying, 'Don't worry, we checked this thoroughly!'

Avoid this phrase in everyday conversations, casual emails, or social media posts unless you're being intentionally humorous or ironic. It's too formal and technical for discussing weekend plans, movie reviews, or your favorite recipe. Using it in a casual setting would sound out of place, like wearing a tuxedo to a barbecue. It's also not suitable for situations where the 'robustness' isn't really a quantifiable or testable aspect, or when the verification method is extremely simple and obvious. If you just asked a friend if they liked a movie, don't say, 'The validity of your opinion was verified through direct inquiry.' They'll just give you a weird look.

One big mistake is using it in the wrong context – like in a casual text. Another is misplacing it grammatically. Sometimes, people might use a less precise verb. It's also easy to forget the durch (through/by) part, which is crucial for explaining the verification method. A common error is trying to translate it too literally without considering the statistical context. For example, saying 'The toughness of the guessers was checked by...' doesn't make sense. The key is understanding Schätzer refers to statistical estimators, not people guessing.

✗ Die Robustheit der Schätzer wurde überprüft mit

✓ Die Robustheit der Schätzer wurde überprüft durch

✗ Die Stärke der Schätzer wurde überprüft durch

✓ Die Robustheit der Schätzer wurde überprüft durch

While the core phrase is quite specific, related ideas can be expressed more broadly. In less formal settings, you might hear things like: 'Wir haben die Ergebnisse nochmal gecheckt.' (We checked the results again.) or 'Die Daten sind abgesichert.' (The data is secured/validated.) In very technical fields, you might see more specific terms like 'Die Validität der Ergebnisse wurde durch ... bestätigt.' (The validity of the results was confirmed by...) or 'Die Zuverlässigkeit der Messungen wurde mittels ... ermittelt.' (The reliability of the measurements was determined by means of...). The key is that the original phrase is quite formal and specific to statistical 'estimators'.