Why can a completely randomized design produce misleading results when another factor affects the response?

A completely randomized design can produce misleading results because it does not account for extraneous variables that influence the response variable. In this design, treatments are assigned to experimental units purely by chance.1

If an unmeasured factor—such as a specific manufacturer in a fuel efficiency study—significantly impacts the outcome, random assignment might inadvertently group more units from that category into one treatment group. Consequently, the observed differences in the response may be incorrectly attributed to the treatment rather than the underlying influence of the uncontrolled factor.1

To mitigate this, statisticians often use a randomized block design. By grouping units into homogeneous blocks before assigning treatments, researchers ensure that the effects of these external factors are balanced across all treatment groups, allowing for more precise and reliable comparisons.1