AP Statistics Experimental Design and Random Assignment Lesson (Free PDF)
This experiments lesson for AP Statistics covers experimental design and random assignment (Common Core AP STAT 3.4, AP STAT 3.5, AP STAT 3.6, HSS-IC.B.3, HSS-IC.B.5), with a free PDF to print.
An experiment imposes treatments on experimental units and measures a response; an observational study only observes. Good experiments use comparison, random assignment, control of other variables, and replication, and may use placebos and blinding. Random assignment supports cause-and-effect conclusions, while random selection supports generalizing to a population.
AP Statistics · Common Core State Standards: AP STAT 3.4, AP STAT 3.5, AP STAT 3.6, HSS-IC.B.3, HSS-IC.B.5
Key facts in this experiments lesson
- Experiments impose treatments; observational studies do not and cannot prove causation.
- Confounding occurs when the effects of two variables on the response cannot be separated.
- Good design: comparison, random assignment, control, replication; use blinding and placebos when needed.
- Designs: completely randomized, randomized block, matched pairs.
- Random assignment allows cause-and-effect; random selection allows generalization.
What is the difference between an observational study and an experiment?
In an observational study, researchers observe individuals and measure variables without influencing them. In an experiment, researchers impose treatments on experimental units and measure the response. Only well-designed experiments can support cause-and-effect conclusions.
What makes a good experiment?
- Comparison: use at least two treatments, often including a control group (no treatment or a placebo).
- Random assignment: use chance to assign units to treatments, so the groups are alike on average.
- Control: keep other variables the same for all groups.
- Replication: use enough units to see the effect despite random variation.
A placebo is an inactive treatment. In a double-blind experiment, neither the subjects nor the people measuring the response know who got which treatment.
What are the common experimental designs?
In a completely randomized design, all units are randomly assigned to treatments. In a randomized block design, units are first grouped into blocks of similar units (for example by age), and random assignment is done within each block. In a matched pairs design, each subject receives both treatments in random order, or two similar subjects are paired and one gets each treatment.
What can you conclude?
If the difference in responses is too large to be explained by chance variation in the random assignment, the result is statistically significant. Random assignment lets you conclude cause and effect; random selection lets you generalize to the population.
Experiments lesson: questions and answers
Why is random assignment important?
It creates treatment groups that are similar on every variable, measured or not, on average. Then a large difference in responses is unlikely to be caused by anything except the treatment.
What is a confounding variable?
A confounding variable is related to both the explanatory variable and the response so that you cannot tell which one caused the change. In an observational study, confounding is a major reason not to claim causation.
What is the difference between blocking and stratifying?
Both group similar units. Blocking is used in experiments before random assignment to treatments; stratifying is used in sampling before randomly selecting individuals.
When should I use a matched pairs design?
Use it when subjects can serve as their own control, such as measuring each runner’s time in both shoe types in random order, or when subjects can be paired by a strong related variable.
What does statistically significant mean?
It means the observed difference between treatment groups is larger than would be expected from random assignment alone, so it is unlikely to be due to chance.
How to use this experiments lesson
Read the definitions first, then follow the worked method line by line and redo the example on paper without looking. When every step makes sense, move on to the worksheet, then check yourself with the quiz.
Download the experiments lesson as a PDF with the button below and keep it with your notes.
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