When should similar units be compared together?
You will be able to: Design randomized blocks and matched pairs and justify the blocking variable.
When should similar units be compared together?
Beginning and experienced typists may respond differently to keyboard layouts. Comparing layouts within experience groups can keep that background variation from obscuring the comparison.
A useful starting point: What makes an experiment a fair comparison? →
Words and symbols before equations
- Block
- Units grouped by a pre-treatment characteristic expected to affect the response.
- Randomized block design
- Assign all treatments randomly within every block.
- Matched pairs
- A block design with two treatments and paired units or repeated measurements on each unit.
- Order effect
- A change caused by which treatment is received first.
What this picture assumes
24 synthetic units: IDs 1–12 are beginners and 13–24 experienced. A and B receive 12 units each. Skill is a potential influence on the response. No outcomes or treatment effect are simulated.
Read the picture in three steps
- Read the axes and labels first. Identify what each symbol and line represents. Read the units and fixed conditions before comparing quantities.
- Treatment A: 3, 5, 7, 11, 13, 16, 18, 19, 20, 21, 22, 23. A has 4 beginners and 8 experienced units; B has the remaining units. Allocation does not simulate an effect.
- Check what the picture assumes below. Use the Explore task to predict one change before moving a control.
Connect the picture to the mathematics
Choose a blocking variable related to the response before assigning treatments. Group by that variable, then randomize within every block. Assigning one treatment to an entire block would confound treatment with the block characteristic.
Matched pairs can match two similar individuals and randomly assign opposite treatments. Alternatively, each participant receives both treatments in randomized order. Analyze within-pair differences rather than treating all observations as unrelated.
Blocking can improve precision by separating known background variation. It does not replace random assignment, and it cannot fix every bias. For repeated treatments, consider learning, fatigue, carryover and ethical feasibility.
A worked example, step by step
Twelve beginners and twelve experienced typists compare layouts A and B. Create a block design.
- Make two blocks using pre-study experience: 12 beginners and 12 experienced typists.
- Within beginners, randomly allocate 6 to A and 6 to B.
- Within experienced typists, independently allocate 6 to A and 6 to B.
- Measure typing accuracy under common conditions and compare layouts within blocks; do not compare all beginners on A with all experienced people on B.
Strata concern selecting a sample; blocks concern assigning treatments among the units already in an experiment.
Can each person be their own matched pair?
Compare with an explanation
Yes, if both treatments can be applied appropriately; randomize order and account for carryover and learning.
Predict. Change one thing. Explain.
Choose blocked assignment and compare with unrestricted assignment. Explain how both treatments appear within each skill level. Connect this pattern to the idea of a fair comparison.
On narrow screens, swipe or scroll diagrams sideways to read all labels.
Treatment A: 3, 5, 7, 11, 13, 16, 18, 19, 20, 21, 22, 23. A has 4 beginners and 8 experienced units; B has the remaining units. Allocation does not simulate an effect.
| Group | Selected IDs / treatment A |
|---|---|
| 1 | 3, 5 |
| 2 | 7, 11 |
| 3 | 13, 16, 18 |
| 4 | 19, 20, 21, 22, 23 |
24 synthetic units: IDs 1–12 are beginners and 13–24 experienced. A and B receive 12 units each. Skill is a potential influence on the response. No outcomes or treatment effect are simulated.
Explain what you noticed: Answer the investigation prompt above. State one observation and explain it using the data values, graph scales, summary statistics or study-design conditions. Identify what the representation cannot tell you.
Apply the idea to a fresh problem Practice →Show what you understand.
Two original questions are a starting check, not proof of mastery. Explain your choice before revealing the answer.
Original written challenge
4 points · self-check · not an official AP questionTen volunteers each test two app interfaces. Propose a matched-pairs procedure and name two concerns.
This response is not submitted or saved. Copy it before leaving.
Compare with the answer and four-point rubric
- 1 point: Have each volunteer use both interfaces on comparable tasks.
- 1 point: Randomize which interface is used first for each volunteer.
- 1 point: Compare each volunteer’s paired completion-time difference.
- 1 point: Control task difficulty and consider learning or fatigue; the volunteer sample also limits population generalization.
Accept equivalent correct methods and explanations. This is a Refresh Kid teaching rubric, not an official AP scoring guideline.
Retrieve it before you reveal it.
RECALL 1Why block?
To separate relevant background variation and improve treatment comparisons.
RECALL 2What happens inside every block?
Random assignment to the treatments.
RECALL 3Why randomize order in paired trials?
To reduce systematic order effects such as practice or fatigue.
Revisit these tomorrow and a week later. Try a fresh problem and explain why the method applies.
When should similar units be compared together?
- Block first, then randomize treatments within every block.
- Matched pairs use two treatments.
- For each participant receiving both, randomize order and manage carryover.
Remember: Strata concern selecting a sample; blocks concern assigning treatments among the units already in an experiment.
Conditions: 24 synthetic units: IDs 1–12 are beginners and 13–24 experienced. A and B receive 12 units each. Skill is a potential influence on the response. No outcomes or treatment effect are simulated.
Refresh Kid · AP Statistics Unit 1 · Objectives 1.13.B, 1.13.C · Review edition
Framework, scope and review status
Mapped to College Board, AP Statistics CED, Topic 1.13, objectives 1.13.B, 1.13.C. Framework effective Fall 2026, checked September 17, 2026. Unit 1 includes one-variable data and data collection; it is part of the revised five-unit course.
Examples and datasets are synthetic, independently authored teaching material. Quartile calculations state a median-of-halves convention. Outlier screens identify values to investigate, not data to discard. Random selection and random assignment have different inferential roles. These lessons introduce design and descriptive reasoning; formal inference comes in later units.
The Organic Chemistry Tutor companion title and destination were checked; the full video was not reviewed. Khan Academy’s destination was checked, but its lesson content was not fully readable by the research tool. OpenStax provides optional reference reading. No provider scripts, questions or graphics were copied. Refresh Kid is not affiliated with these providers.
GitHub’s 3D website collection informed optional spatial inspection. Our original sampling model uses self-hosted Three.js with its MIT license. It shows labeled units in four groups; camera rotation does not change the sampling procedure. Quantitative graphs remain 2D to avoid perspective distortion. Complete labeled diagrams, selected IDs and explanations remain available without 3D.
Independent teacher review and observation of students remain pending. Technical checks do not certify statistical accuracy, accessibility or learning effectiveness. This is a review edition.
Released AP Statistics questions and scoring guides are optional. Older exams use the earlier framework, so check alignment before selecting parts. All practice on this page is original, not official AP material.
Learn → Explore → Practice → Review is informed by the IES learning guide. This implementation has not yet been evaluated with learners.
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