In an experiment, researchers impose treatments on experimental units and measure a response. A well-designed experiment uses comparison, random assignment, control of other variables, and replication. Here, 40 volunteers test a new workout plan. Fitness level affects the result too. See how each design handles it.
Response: increase in push-ups after 6 weeks. Treatments: new workout plan vs. the usual plan. Fitter volunteers tend to improve more no matter which plan they get.
Unbiased: average estimate near the true effect. Precise: small SD. Changing the effect or n clears the table.
What you can conclude depends on two questions: were individuals randomly selected from a population, and were treatments randomly assigned? Click a cell.
Experimental units (called subjects if they are people) receive treatments. A factor is an explanatory variable the researcher manipulates; its values are levels. A treatment is a specific condition applied, such as one level or a combination of levels.
Assigning treatments by chance tends to create groups that are similar in every variable, known or unknown. Then a large difference in the response can be attributed to the treatments.
Hold other variables constant for all units, and include a control group (placebo, no treatment, or the current standard) for comparison. Blinding keeps expectations from affecting results.
Use enough experimental units in each group so that real differences can be told apart from chance variation.
A block is a group of units that are similar in a way expected to affect the response. Randomly assign treatments within each block. Blocking reduces variability from that variable, giving more precise comparisons.
Pair very similar units (or use each subject twice, in random order) and randomly assign the two treatments within each pair. Analyze the differences within pairs.
Each design uses randomization differently.
| Design | How treatments are assigned | Why use it |
|---|---|---|
| Completely randomized | All units are randomly assigned to treatments, e.g., put 40 names on slips, shuffle, the first 20 drawn get the new plan. | Simple; works when units are fairly similar |
| Randomized block | Split units into blocks by a variable related to the response (fitness), then randomly assign treatments within each block. | Removes the block variable's effect; more precise |
| Matched pairs | Pair the two most similar units, randomly assign one of each pair to each treatment; or give each subject both treatments in random order. | Most control over differences between units |
| Double-blind | Neither the subjects nor the people measuring the response know who got which treatment. | Prevents expectations from biasing results |
| Placebo control | The control group gets a fake treatment that looks like the real one. | Accounts for the placebo effect |
AP-style multiple choice. Pick an answer to see the explanation.
The vocabulary for topic 1.13. Read the list, flip through flashcards, or quiz yourself. For every term in the unit, see the Unit 1 terminology guide.