Final answer:
A controlled experiment allows researchers to claim causation between variables due to direct manipulation and control of variables, as well as random assignment of subjects to groups.
Step-by-step explanation:
The type of study that allows a researcher to claim causation between an explanatory variable and a response is a controlled experiment. Unlike observational studies, which can generally establish correlation but not causation, a controlled experiment involves the direct manipulation of the independent variable by the researcher. This manipulation, combined with random assignment of subjects to experimental and control groups, helps to isolate the explanatory variable. By minimizing the influence of other potential lurking variables and using a carefully designed structure, any observed difference in the response variable can more confidently be attributed to the independent variable, thus supporting a cause-and-effect claim.
For example, in an experiment investigating the effects of aspirin on heart attack risk, researchers would randomize participants into two groups, with one group receiving aspirin and the other a placebo. If the group taking aspirin shows a significantly different rate of heart attacks compared to the placebo group, and all other variables are controlled, the researchers can safely conclude that aspirin's presence is causing the difference in outcomes.