Final answer:
A controlled experiment is required to establish a cause-and-effect relationship between two variables, involving manipulation of one variable and observation of its effect on another within a structured setup.
Step-by-step explanation:
The only way to establish a cause-and-effect relationship between two variables is to conduct a controlled experiment. In such an experiment, researchers manipulate one variable (the independent variable) to observe the effect on another variable (the dependent variable), while all other variables are kept constant. This experimental design includes an experimental group that receives the manipulation and a control group that does not, thereby allowing any differences in outcomes to be attributed to the manipulation of the independent variable. For instance, in a study examining the effects of aspirin on heart attack risk, participants would be randomly assigned to either receive aspirin (experimental group) or a placebo (control group), and the incidence of heart attacks would be compared after a set period. This rigor in design enables researchers to make causal statements about the relationship between variables.