In experimental design, what defines a random effect?

• A. An effect that is fixed across all experiments.
• B. An effect that cannot be generalized beyond the treatment conditions.
• C. An effect is said to be random if the experiment contains only a sample of possible treatment conditions and can be generalized beyond them.
• D. An effect that is identical to the placebo effect.

Answer: (C)

A random effect describes variation that comes from levels drawn from a larger population, with the goal of generalizing beyond the exact levels studied. If an experiment includes only a sample of all possible treatment conditions and you treat that factor as random, you can extend conclusions to the broader set of conditions not just the ones observed. In other words, the levels are considered a random sample from a population, and inferences apply to that population of conditions.

This fits the idea that you’re sampling from a larger universe of treatment conditions and want to generalize beyond the specific conditions tested. By contrast, a fixed effect refers to levels you’ve deliberately chosen and intend to interpret only at those exact levels, with results not assumed to generalize to other conditions. The option about generalizing beyond the observed conditions captures the essence of a random effect. The placebo effect is a specific phenomenon unrelated to whether a factor is random or fixed.