Experimental Design & Causation Cheat Sheet

A printable reference covering random assignment, control groups, blinding, bias, confounding, sample size, and causation for grades 10-12.

Download PNG

Related Tools

Related Labs

Related Worksheets

Related Infographics

Experimental design helps students understand how researchers collect evidence to answer cause-and-effect questions. This cheat sheet explains how treatments, control groups, random assignment, and blinding make experiments more reliable. Students need these ideas to judge whether a study supports causation or only shows an association. It also helps with interpreting real research claims in science, medicine, sports, and social studies. The most important idea is that well-designed experiments control outside variables so differences in outcomes can be linked to the treatment. Random assignment helps create comparable groups, while replication and larger sample sizes reduce the role of chance variation. A study can show causation only when the design rules out major alternative explanations such as confounding and bias. Measures such as proportions, means, and differences like $\bar{x}_1 - \bar{x}_2$ help compare treatment results.

Key Facts

An experiment imposes a treatment on subjects and measures a response variable to study whether the treatment causes a change.
Random assignment means each subject has a known chance, such as $\frac{1}{2}$ in a two-group experiment, of receiving each treatment.
A control group receives no treatment, a placebo, or the standard treatment so researchers can compare outcomes against a baseline.
A randomized comparative experiment can support causation when the groups are similar except for the treatment being tested.
The treatment effect can be measured with a difference in means, $\bar{x}_{\text{treatment}} - \bar{x}_{\text{control}}$ , or a difference in proportions, $\hat{p}_{\text{treatment}} - \hat{p}_{\text{control}}$ .
Replication means using enough subjects in each group so that random variation is less likely to explain the observed difference.
Blinding reduces bias because subjects, researchers, or both do not know who received each treatment.
Confounding occurs when the effect of the treatment is mixed with another variable, making it unclear which variable caused the response.

Vocabulary

Treatment: A condition or action applied to subjects in an experiment to see how it affects the response variable.
Response Variable: The outcome measured in an experiment, such as test score, blood pressure, or reaction time.
Random Assignment: A method that uses chance to place subjects into treatment groups so the groups are likely to be comparable.
Control Group: A group used as a baseline comparison because it receives no treatment, a placebo, or the current standard treatment.
Placebo Effect: A change in response caused by a subject's belief that they received a treatment, even when the treatment has no active ingredient.
Confounding Variable: A variable that is related to both the treatment and the response, making the cause of an observed effect unclear.

Common Mistakes to Avoid

Confusing random sampling with random assignment is wrong because random sampling helps generalize to a population, while random assignment helps support cause-and-effect conclusions.
Claiming causation from an observational study is wrong because researchers did not assign treatments and may not have controlled confounding variables.
Ignoring the need for a control group is wrong because without a baseline, a change in the response may be due to time, placebo effects, or outside factors.
Using too small a sample is wrong because a result from very few subjects may be mostly due to random variation rather than a real treatment effect.
Forgetting about blinding is wrong because subjects or researchers who know the treatment can unintentionally influence the response or measurement.

Practice Questions

1 A study randomly assigns $80$ students to two groups: $40$ use a new study app and $40$ use paper notes. The app group has mean score $86$ and the paper group has mean score $81$ . Find the difference $\bar{x}_{\text{app}} - \bar{x}_{\text{paper}}$ .
2 In a two-treatment experiment with $120$ volunteers, researchers want equal group sizes. How many volunteers should be assigned to each group if the assignment is balanced?
3 A vaccine trial reports infection proportions of $\hat{p}_{\text{vaccine}} = 0.04$ and $\hat{p}_{\text{placebo}} = 0.10$ . Calculate $\hat{p}_{\text{placebo}} - \hat{p}_{\text{vaccine}}$ and interpret the difference.
4 A survey finds that students who eat breakfast have higher math scores than students who do not. Explain why this result alone does not prove that eating breakfast causes higher scores.

Sign in to save