Quantitative research utilizes a systematic way in an orderly manner to determine a problem and a subsequent solution to the issue (McNiff, Petrick, 2018).
Experimental researches are the gold-standard for research in medicine, biology, and so on. In an Experimental study, researchers can manipulate one or more independent variables, randomly assign participants to control or experimental group (treatment group), and compare them (Statistics Solutions 2020). If done accurately, experimental studies will provide evidence for cause and effect. Highly controlled environment (McNiff, Petrick, 2018). Example: effect of smoking cessation program on smoking pregnant women. A sample of 30 women from the same hospital (or GI clinic) was assigned to an experimental or control group. Smoking status was measured by self-report and biochemical measures. Data were collected before random assignment to groups and after three follow up points: after the first week of the session, in five months and after delivery of the baby. During educational sessions, nicotine replacement gum was provided fo the experimental group while the control group received brochures about how smoking affects pregnancy and lactation.
Non-experimental research can be just as impressive, but we cannot draw the same conclusions from it as we can with experimental research. The non-experimental study is usually descriptive or correlational. That means that we are either describing a situation or phenomenon just as it is, or we are defining a correlation between two or more variables. All without any intervention from the researcher meaning that we do not manipulate any variables (e.g., change the conditions that an experimental group undergoes) or randomly assign members to a control or treatment group. Without this level of control, we cannot determine any causal effects. High chance of bias (McNiff, Petrick, 2018). While validity is still a concern in non-experimental research, the concerns are more about the validity of the measurements, rather than the validity of the effect.
Example of correlational research: a randomized trial of 100 breastfeeding mothers, we arranged to determine the relationship of maternal age and anxiety in breastfeeding women during the immediate postpartum period. The result would be: A weak but significant negative relationship exists between age and anxiety; as age increases, anxiety decreases. As we can see Correlational research measures the statistical relationship between two or more variables and the degree of the relationship (cause/effect).
References
McNiff, P., Petrick, M. (2018). Quantitative Research: Ethics, Theory, and Research. In Nursing research: Understanding methods for best practice. Retrieved from: https://lc.gcumedia.com/nrs433v/nursing-research-understanding-methods-for-best-practice/v1.1/#/chapter/3.
Statistics Solutions. (2020). Research Designs: Non-Experimental vs. Experimental. Retrieved from: https://www.statisticssolutions.com/research-designs-non-experimental-vs-experimental/

Experimental research is the most powerful qualitative method.it has a rigorous control of the variables.it It is an objective, systematic, and highly controlled investigation conducted for predicting and controlling phenomena. During the experimental design, the researcher uses a random assignment. they also manipulate a must be randomization, control a group, and manipulation of a variable while examining the direct cause or predicted relationship between variables.

Non-experimental research is research that lacks the manipulation of an independent variable, random assignment of participants to conditions or orders of conditions, or both.it focuses on examining variables as they would naturally occur. Some of the examples of experimental research are surveys, case studies, comparative studies, and descriptive studies. This research design has no random assignment, no control groups, and no manipulation of variables. The research method is observation only.

Experimental research provides convincing evidence that changes with an independent variable. this it results in the differences in a dependent variable. on the other hand, non-experimental research does not cause any change in the independent variables.

Reference: Dawson R, Algozzine R. Doing Case Study Research: A Practical Guide for Beginning Researchers. 2006. New York, NY: Teachers College Press. Qualitative content analysis in nursing research: concepts, procedures, and measures to achieve trustworthiness. Nurse Educ Today. 2004 Feb; 24(2):105–12.