Final answer:
Stronger statistical conclusions can be drawn when known variation is large compared to unexplained variation, as it suggests that the treatment effects are primarily responsible for the differences in the response variable, indicating a cause-and-effect relationship.
Step-by-step explanation:
If known variation is large compared to unexplained variation, stronger statistical conclusions can be made regarding the effects of the treatments on the response variable. In the context of an experiment where treatments are randomly assigned, such as in pharmaceutical trials or psychology experiments, the large known variation implies that the variation we see in our response variable is mostly due to the treatments being administered, rather than random error or chance. This helps us infer a cause-and-effect relationship between the independent variable (treatment) and the dependent variable (response).
When treatments are randomly assigned, all of the potential lurking variables are spread equally among the groups, thus minimising their impact on the results. The measurable differences in the experiment's outcomes, termed as explained variation, can then be attributed mostly to the treatment effects, paving the way for significant conclusions when interpreting data.
Example of Variation in an Experiment
In an experiment conducted by a pharmaceutical company to test a new drug for lowering blood pressure, the difference in outcomes between the control group receiving a placebo and the treatment group receiving the new drug would be explained by the known variation. If this known variation is significantly larger than the unexplained variation, which is due to chance, errors, or measurement issues, one can more confidently assert that the drug is responsible for the changes in blood pressure readings.