There are two main types of research, experimental and non-experimental. A misconception revolves around research that non-experimental ones are non-scientific, so it is important to understand the difference between the two research methods. The most common type of research is experimental, which most refer to as scientific (Hadiyat et al., 2022). It employs scientific approaches in manipulating many control variables and measuring their defect on dependent variables. On the contrary, non-experimental research is used to classify the research that is not experimental and does not entail manipulating the control variables.
Adding more support to your example of experimental research, another good instance is an experiment done in laboratories that involves mixing different chemical components to observe the effect of one element on another (Hadiyat et al., 2022).
For example, consider a laboratory technician carrying out research in the lab and performing a test to determine the effects that Nitrogen gas could have on Hydrogen gas when mixed together. It could be deduced that Nitrogen gas could be created through the Haber process (Hadiyat et al., 2022). Understanding experimental research further is classified into three types, namely, quasi-experimental, experimental research, and true experimental research. These kinds of research are normally quantitative, multivariable, and controlled. As you indicated in the hospital example in your post, the data used within this research method are collected through observational studies and surveys.
I agree with your understanding of the non-experimental research method, where you highlighted that the researcher could not manipulate, control, or even alter the subject or the predictor variable; instead, they rely on the observed data for their conclusions. Expounding on the given example of researching who is violent between men and women, I would add another example of a laboratory test on Ammonia gas to determine its characteristics, nature, and behaviors with other chemical components. It is very hard to tell the characteristics of Ammonia until it is observed; therefore, the research is non-experimental.
Reference
Hadiyat, M. A., Sopha, B. M., & Wibowo, B. S. (2022). Response surface methodology using observational data: A systematic literature review. Applied Sciences, 12(20), 10663. Web.