Introduction to Experimental Design - AP Statistics

SECTION 1

Historical Context & Motivation

For centuries, scientists relied on passive observation to draw conclusions about the natural world, but observation alone could never definitively separate cause from coincidence. The need for a rigorous, structured method of testing hypotheses gave rise to experimental design — the systematic practice of deliberately manipulating one or more factors while holding others constant so that any observed effect can be attributed to the manipulation itself rather than to lurking variables. The development of formal experimental design transformed statistics from a tool of description into a powerful engine of causal inference, and its principles now underpin research in medicine, agriculture, psychology, engineering, and virtually every empirical discipline.

1747 • Lind's Scurvy Trial

Scottish naval surgeon James Lind conducted one of the first recorded controlled experiments by dividing twelve scurvy-afflicted sailors into six pairs, each receiving a different dietary supplement. The pair given citrus fruits recovered, providing early evidence for the value of comparison groups.

1835 • Placebo-Controlled Testing

Researchers began systematically using placebos to account for psychological effects, recognizing that subjects' beliefs about treatment could influence outcomes independently of the treatment itself.

1925 • Fisher's Foundational Work

Sir Ronald A. Fisher published Statistical Methods for Research Workers and later The Design of Experiments (1935), formalizing randomization, replication, and blocking as the three pillars of experimental design at Rothamsted Experimental Station.

1948 • First Randomized Clinical Trial

The British Medical Research Council conducted the first properly randomized clinical trial, testing streptomycin against tuberculosis. This landmark study demonstrated that random assignment could credibly establish treatment efficacy and became the gold standard for medical research.

2000s–Present • Modern Adaptive Designs

Advances in computing power have enabled adaptive experimental designs, Bayesian approaches, and large-scale A/B testing (used by technology companies), all of which build on the classical principles Fisher established nearly a century ago.

The central question that experimental design addresses is deceptively simple: How can we determine whether changes in one variable actually cause changes in another? Observational studies can reveal associations and correlations, but they cannot, by themselves, rule out the influence of confounding variables. Only a well-designed experiment — with deliberate manipulation, proper controls, and random assignment — can close the gap between correlation and causation. Understanding these principles is essential not only for the AP Statistics exam but for critically evaluating the scientific claims you encounter throughout your academic and professional life.

SECTION 2

Core Principles & Definitions

An experiment differs from an observational study in one critical way: the researcher deliberately imposes a treatment on the experimental units to observe a response. The vocabulary of experimental design is precise, and mastering it is the first step toward designing and critiquing studies. The explanatory variable (also called the factor) is the variable the researcher manipulates; the specific values of the factor are called levels. The response variable is the outcome measured after the treatment is applied, and the experimental units are the individuals or objects to which treatments are applied (when these are people, we call them subjects). A treatment is a specific combination of factor levels imposed on the experimental units.

Control

Hold extraneous variables constant so that differences in the response can be attributed to the treatment. This often involves a control group that receives no treatment (or a placebo) to serve as a baseline for comparison.

Randomization

Assign experimental units to treatment groups using a chance mechanism. Random assignment balances both known and unknown confounding variables across groups, making groups roughly equivalent before treatment begins.

Replication

Apply each treatment to a sufficiently large number of experimental units so that the effects of chance variation are reduced and results can be distinguished from random noise with statistical confidence.

Blocking (Optional but Powerful)

Group experimental units into blocks of similar units before random assignment. By accounting for a known source of variability (e.g., age, gender), blocking reduces unexplained variation and increases the precision of treatment comparisons.

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KEY TAKEAWAY

Think of an experiment like a controlled laboratory recipe: you change exactly one ingredient (the treatment), keep everything else the same (control), use random selection of taste-testers (randomization), and have many people taste the dish (replication). If the results are consistently different, you can confidently attribute the difference to the ingredient you changed, not to the cook's mood or the time of day. Random assignment is what distinguishes an experiment from an observational study and is the key to establishing causation.

SECTION 3

Visual Explanation — Anatomy of an Experiment

The following diagram illustrates the general structure of a completely randomized design — the most fundamental experimental layout. Experimental units are first collected, then randomly assigned to treatment groups (including the control group), treatments are applied, and finally responses are measured and compared. This visual framework applies to experiments across every discipline, from pharmaceutical trials to agricultural field studies.

The diagram shows the flow of a completely randomized design: all experimental units enter from the left, pass through random assignment, are divided into treatment groups and a control group, and then results are compared to determine whether the treatments produced statistically significant differences.

Notice that the random assignment step is the critical juncture in the diagram. Without it, pre-existing differences among the experimental units might systematically favor one treatment group over another — a problem known as confounding. A confounding variable is a variable associated with both the explanatory variable and the response variable, making it impossible to determine which one is truly responsible for the observed effect. Randomization does not eliminate confounding variables; rather, it distributes their effects evenly across all treatment groups so that they cannot systematically bias the comparison.

SECTION 4

How Experimental Design Works — Key Mechanisms

The Role of Random Assignment

Random assignment is not the same as random selection, and confusing these two concepts is one of the most common errors on the AP Statistics exam. Random selection refers to how experimental units are chosen from a population — it allows generalization from a sample to the broader population. Random assignment refers to how units already in the study are allocated to treatment groups — it allows causal conclusions. An experiment can use one, both, or neither; the strongest inference is possible when both are present.

Feature	Random Selection	Random Assignment
What it does	Chooses who is in the study from the population	Allocates study participants to treatment groups
Purpose	Reduces sampling bias; enables generalization to the population	Balances confounders; enables causal inference
Inference supported	Generalization	Causation
Example	SRS of 500 adults from the U.S. population	Flip a coin to decide which group each participant joins

Comparison of random selection vs. random assignment

Blinding and the Placebo Effect

Even with proper randomization, human psychology can introduce bias. The placebo effect occurs when subjects respond to the mere expectation of receiving an effective treatment. To combat this, researchers employ blinding. In a single-blind experiment, the subjects do not know which treatment they are receiving. In a double-blind experiment, neither the subjects nor the researchers who interact with them and measure outcomes know the assignment. Double-blinding prevents both the placebo effect and unconscious bias by evaluators, and it is considered the gold standard for clinical trials. A placebo is a dummy treatment (such as a sugar pill) that is indistinguishable from the real treatment to the subjects.

Scope of Inference

The combination of random selection and random assignment determines the scope of inference — what conclusions a study can support. With both random selection and random assignment, you can make causal claims about the entire population. With only random assignment (but a convenience sample), you can claim causation only for units similar to those in the study. With only random selection (an observational study), you can generalize associations to the population but cannot claim causation. With neither, the study is severely limited in its conclusions.

SECTION 5

Types of Experimental Designs

While the completely randomized design is the most straightforward layout, experimenters often need more sophisticated designs to control for known sources of variability or to study multiple factors simultaneously. The AP Statistics curriculum focuses on three primary designs: the completely randomized design (CRD), the randomized block design (RBD), and the matched-pairs design (a special case of the block design). Understanding when to use each design is as important as understanding how they work.

This diagram compares the three major experimental designs covered in AP Statistics. The CRD is simplest, the RBD adds blocking to control for known variability, and the matched-pairs design is a special block design where each block contains exactly two matched units (or the same unit measured twice).

In a completely randomized design, every unit has an equal chance of receiving any treatment, and there is no preliminary grouping. This works well when the experimental units are relatively homogeneous. In a randomized block design, units are first sorted into blocks based on a variable that is expected to affect the response (such as age, gender, or pre-existing condition), and then units within each block are randomly assigned to treatments. This ensures that each treatment group contains a representative mix of the blocking variable, reducing variability and increasing the experiment's ability to detect true treatment effects.

The matched-pairs design is a special case where each block contains exactly two experimental units that are as similar as possible (e.g., twins), or where the same subject receives both treatments in random order (a crossover design). By comparing differences within pairs rather than between separate groups, matched-pairs designs can be especially powerful at detecting small treatment effects, because much of the subject-to-subject variation is eliminated.

Participants wear headphones at matching task stations while a researcher distributes cards. Measurements taken from the same person remain linked. Compare within-person differences instead of treating the two columns as independent samples.

Six linked before-and-after pairs become six differences; within-ID sign swaps generate 64 assignments with 12 in the marked absolute tail. Suppose the same six IDs have differences 2, −1, 3, 0, 2 and 1, averaging 7/6. Under a sharp zero-effect null with randomized or exchangeable within-ID labels, 2⁶ = 64 sign assignments are allowed; 12 have absolute mean at least 7/6. Repeated measurement alone does not establish that exchangeability.

SECTION 6

Worked Example — Designing an Experiment

A biology teacher wants to determine whether a new fertilizer increases the growth rate of tomato plants compared to the standard fertilizer currently used in the school greenhouse. She has 30 tomato seedlings of the same variety, all approximately the same height. She also knows that the greenhouse has two shelves: the top shelf receives more light than the bottom shelf. Design an experiment to test the fertilizer's effectiveness.

Designing a Randomized Block Experiment

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Step 1 — Identify the Components

The experimental units are the 30 tomato seedlings. The explanatory variable (factor) is the type of fertilizer, with two levels: new fertilizer and standard fertilizer. The response variable is the plant growth rate (measured as height increase in centimeters over four weeks).

Factor: Fertilizer type (2 levels) • Response: Growth rate (cm/4 weeks) • Units: 30 seedlings
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Step 2 — Identify the Blocking Variable

Because the top and bottom shelves differ in light exposure, shelf position is a known source of variability that could confound results. We use shelf position as the blocking variable. Place 15 seedlings on the top shelf (Block 1) and 15 on the bottom shelf (Block 2).

Block 1: 15 seedlings (top shelf) • Block 2: 15 seedlings (bottom shelf)
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Step 3 — Randomly Assign Within Blocks

Within each block, number the seedlings 1 through 15. Use a random number generator to select 7 or 8 seedlings from each block to receive the new fertilizer; the remaining seedlings receive the standard fertilizer. For example, in Block 1, assign seedlings whose numbers correspond to the first 8 unique random integers between 1 and 15 to the new fertilizer group, and the remaining 7 to the standard fertilizer group. Repeat for Block 2 with 8 receiving new and 7 receiving standard (or vice versa, as long as group sizes are balanced).

Each block has approximately equal numbers assigned to new and standard fertilizer by a chance mechanism.
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Step 4 — Apply Treatments and Control Extraneous Variables

Apply the assigned fertilizer to each seedling according to the manufacturer's recommended dosage. All other conditions — watering schedule, soil type, pot size, temperature — should be kept the same for all seedlings. These are the controlled variables. Note that this is not double-blind because the teacher knows which plants receive which fertilizer and the plants cannot exhibit a placebo effect; however, she could use single-blind measurement by having a colleague who does not know the assignment measure the plants.
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Step 5 — Measure, Compare, and Conclude

After four weeks, measure the height of every seedling and calculate the mean growth for each treatment group within each block, then compare treatments while retaining shelf as a block in the analysis. If the mean growth of the new-fertilizer group is significantly greater than the standard-fertilizer group (using a statistical analysis that accounts for shelf blocks, such as an ANOVA with treatment and shelf terms), and because the experiment used random assignment, the teacher can conclude that the new fertilizer caused the increase in growth. However, because the seedlings were not randomly selected from all possible tomato plants, generalization beyond this particular batch of seedlings should be made cautiously.

Random assignment → causal conclusion possible. No random selection → limited generalization.

A researcher examines a seedling in a greenhouse with brighter upper shelving and shaded lower shelving. The top shelf receives more light than the lower shelf. Place both fertilizer treatments on each shelf, control watering, soil and pot size, and measure height increase over four weeks.

Thirty unique plant IDs: T01–T15 on the brighter top shelf and B01–B15 on the lower shelf. Blue indicates new fertilizer and white standard; each shelf contains both treatments. For 30 seedlings, form two 15-plant shelf blocks and randomize both fertilizers within each shelf. The shown allocation assigns 7 new and 8 standard on top, 8 new and 7 standard below. Compare treatment growth within shelves so the light difference stays in the analysis.Open full diagram

SECTION 7

Strengths, Limitations, and Common Pitfalls

Experiments are the most powerful tool for establishing causation, but they are not always feasible or appropriate. Understanding the strengths and limitations of experimental design helps you evaluate research critically and recognize situations where an observational study may be the only ethical or practical option.

Aspect	Strengths	Limitations
Causal Inference	Random assignment allows researchers to attribute differences in the response to the treatment, establishing cause-and-effect relationships.	Causation claims are valid only when randomization is properly implemented and maintained.
Control of Confounders	Controlled environments and random assignment reduce the influence of confounding variables, both known and unknown.	It is impossible to control every extraneous variable; some experiments require impractical or artificially constrained settings.
Ethics	When ethically permissible, experiments provide the strongest evidence for informing medical treatments and public policy.	Many important questions (e.g., effects of smoking, poverty) cannot be ethically studied via experiments because it would require imposing harmful conditions.
Generalizability	Internal validity (confidence in the causal conclusion) is typically high when the design is sound.	External validity (ability to generalize to other populations or settings) may be limited if the sample is not representative.
Practical Feasibility	Small-scale experiments (e.g., agricultural plots, classroom studies) can be relatively inexpensive and fast.	Large-scale experiments (e.g., multi-year drug trials) can be extremely expensive and time-consuming.

Strengths and limitations of experimental design

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Common AP Exam Pitfall

Students frequently confuse random selection with random assignment. Remember: random selection determines who is in the study (generalization), while random assignment determines which treatment each participant receives (causation). Free-response questions often ask you to describe a complete design — always explicitly state the random assignment mechanism and what is being compared.

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KEY TAKEAWAY

Think of experimental design like a controlled scientific audit. Just as a financial auditor isolates one account variable at a time to find discrepancies while holding the rest of the books constant, an experimenter isolates one factor at a time while controlling everything else. The auditor's ability to pinpoint the source of an error depends on their systematic methodology — and so does the experimenter's ability to pinpoint a cause. Without systematic control and randomization, you may find a suspicious pattern, but you cannot prove what caused it.

SECTION 8

Connections to Inference and Advanced Topics

The principles of experimental design you have learned in this lesson lay the groundwork for the inferential statistics you will study later in the AP Statistics course. When you encounter hypothesis testing and confidence intervals, you will see that the validity of these procedures depends entirely on how the data were collected. A statistically significant p-value is meaningless if the experiment was poorly designed, because the observed effect could be due to confounding rather than the treatment. Conversely, a well-designed experiment with proper randomization and replication provides data that can be analyzed with confidence.

Concept in This Lesson	Connection to Later Topics
Random assignment creates comparable groups	Justifies the independence assumption in two-sample t-tests and ANOVA
Replication provides multiple observations	Increases statistical power and reduces the standard error of estimates
Blocking reduces within-group variability	Connects to paired t-tests, which analyze within-pair differences rather than between-group differences
Confounding threatens internal validity	Leads to the study of Simpson's Paradox and multiple regression in advanced courses
Scope of inference (causation vs. generalization)	Directly tested in free-response conclusions — students must match their language to the study design

How experimental design concepts connect to inference

In more advanced statistics and data science courses, you will encounter factorial designs (experiments with multiple factors varied simultaneously), Latin square designs, and response surface methodology. These are extensions of the principles covered here. Modern technology companies use A/B testing — essentially a completely randomized design applied at massive scale — to test everything from website layouts to pricing strategies, demonstrating that Fisher's century-old principles remain central to contemporary data-driven decision-making. As you move forward, remember that no statistical method can rescue a poorly designed study; good inference begins with good design.

SECTION 9

Practice Problems

Question 1: CONCEPTUAL

A researcher wants to determine whether a new study technique improves exam scores. She recruits 60 volunteers from her university and randomly assigns 30 to use the new technique and 30 to use their usual methods. After two weeks, she compares their exam scores. Which of the following is the best description of why this study can support a causal conclusion?

A. Because the sample size of 60 is large enough to eliminate all confounding variables.
B. Because the volunteers chose to participate, ensuring they are motivated and representative of the population.
C. Because random assignment tends to balance both known and unknown confounding variables across the two groups, so differences in exam scores can be attributed to the study technique.
D. Because the researcher selected volunteers from a university, which is a random sample of all students.
E. Because the two-week time period is long enough to eliminate the effects of prior knowledge.

Show answer (C)

Correct answer: C. Random assignment is the mechanism that allows causal inference. By using a chance process to allocate participants to groups, random assignment tends to distribute potential confounders — both known (like prior GPA) and unknown (like motivation level) — evenly across groups. Choice A is incorrect because no sample size can eliminate all confounders; randomization balances them, not eliminates them. Choice B is incorrect because voluntary participation introduces potential volunteer bias and has nothing to do with causal inference — that is a selection issue. Choice D is incorrect because volunteers from one university are a convenience sample, not a random sample of all students; this limits generalizability but does not affect the causal claim within the study. Choice E is incorrect because the length of the study does not address confounding; a longer study might reduce some transient effects but is not the reason causal inference is valid.

Question 2: BASIC CALCULATION

A pharmaceutical company is testing three dosage levels (10 mg, 20 mg, 40 mg) of a new drug and a placebo on 200 patients. The researchers use a completely randomized design. How many treatments are there, and approximately how many patients should be in each treatment group?

A. 3 treatments; approximately 67 patients per group
B. 4 treatments; approximately 50 patients per group
C. 3 treatments; approximately 50 patients per group, with 50 unassigned
D. 4 treatments; approximately 40 patients per group, with 40 in reserve
E. 2 treatments; 100 patients per group (drug vs. placebo)

Show answer (B)

Correct answer: B. A treatment is any specific condition imposed on the experimental units. Here there are three dosage levels (10 mg, 20 mg, 40 mg) plus a placebo, yielding 4 treatments. With 200 patients divided equally among 4 groups: 200 ÷ 4 = 50 patients per group. Choice A is incorrect because it counts only the three drug dosages and excludes the placebo as a treatment; the placebo group is a treatment group (the control treatment). Choice C incorrectly leaves patients unassigned. Choice D invents a reserve group, which is not part of standard CRD. Choice E incorrectly collapses the three dosage levels into a single 'drug' treatment, ignoring that each dosage level is a separate treatment.

Question 3: INTERMEDIATE

A school psychologist wants to compare two types of anti-anxiety interventions (deep breathing exercises vs. guided meditation) on test anxiety. She has 40 students: 20 freshmen and 20 seniors. She suspects that grade level affects baseline anxiety. Which experimental design is most appropriate, and why?

A. Completely randomized design, because it is the simplest and most widely used approach.
B. Matched-pairs design, pairing each freshman with a senior and randomly assigning one to each treatment.
C. Randomized block design, blocking by grade level, then randomly assigning students within each block to one of the two treatments.
D. Observational study, because it would be unethical to impose anxiety-reducing treatments on students.
E. Stratified random sample of 40 students from the school, then assign treatments randomly.

Show answer (C)

Correct answer: C. Because the psychologist suspects that grade level (freshman vs. senior) is a source of variability in baseline anxiety, she should block on grade level. This means creating two blocks — one of 20 freshmen and one of 20 seniors — and then randomly assigning students within each block to deep breathing or guided meditation. This ensures each treatment group contains equal numbers of freshmen and seniors, reducing variability due to grade level and increasing the precision of the treatment comparison. Choice A is not ideal because a CRD ignores the known source of variability (grade level) and may produce unbalanced groups. Choice B is incorrect because a matched-pairs design pairs similar individuals into blocks of two, but pairing a freshman with a senior creates blocks of dissimilar individuals, which defeats the purpose of matching. Choice D is incorrect because providing anxiety-reduction techniques is not harmful, so an experiment is ethically appropriate. Choice E confuses sampling methods with experimental designs; stratified random sampling is a method for selecting a sample, not for assigning treatments.

Question 4: APPLIED

4 pts

A tech company wants to test whether a redesigned checkout page increases the proportion of customers who complete a purchase (the conversion rate). They have access to 10,000 daily visitors and want to compare the current page (Page A) with the new design (Page B). The company knows that conversion rates tend to differ between mobile users and desktop users. (a) Identify the experimental units, the factor and its levels, and the response variable. (b) Describe a complete experimental design that accounts for the known difference between mobile and desktop users. Include a description of randomization. (c) Explain why the company can conclude that any difference in conversion rates was caused by the page design. (d) Describe one limitation of this experiment in terms of generalizability.

Show answer

Rubric (4 points): Part (a) — 1 point: The experimental units are the 10,000 daily website visitors. The factor is checkout page design with two levels: Page A (current) and Page B (redesigned). The response variable is whether each visitor completes a purchase (conversion rate, measured as the proportion of visitors who complete checkout). Part (b) — 1 point: Use a randomized block design. First, classify each visitor as a mobile user or desktop user (these are the two blocks). Within each block, use a computer's random number generator to assign each visitor with equal probability to see either Page A or Page B. For example, when a mobile user visits the site, the server generates a random number; if it is even, the user sees Page A, and if odd, the user sees Page B. The same process applies independently for desktop users. This ensures that each page version is tested on approximately equal numbers of mobile and desktop users. Part (c) — 1 point: Because visitors within each block are randomly assigned to Page A or Page B, any confounding variables (such as time of day, browsing intent, or demographics) should be approximately balanced across the two treatment groups. Therefore, if a statistically significant difference in conversion rates is observed, the company can attribute it to the page design rather than to confounding variables. Random assignment is the key feature that supports a causal conclusion. Part (d) — 1 point: The visitors in the experiment are only those who visited the website on the days the experiment was conducted; they were not randomly selected from all possible future customers. The results may not generalize to visitors during different seasons (e.g., holiday shopping), visitors from different geographic regions, or visitors to a different version of the website. Additionally, the experiment tests only an immediate effect; long-term user behavior may differ as users become familiar with the new design.

Question 5: CRITICAL THINKING

4 pts

A medical researcher reads a headline: 'People who eat dark chocolate daily have 20% lower rates of heart disease.' The study was observational — researchers surveyed 50,000 adults about their diets and followed their health outcomes over 10 years. (a) Explain why this study cannot establish that eating dark chocolate causes lower heart disease rates. Identify at least one specific confounding variable. (b) Design a randomized experiment that could establish a causal relationship between dark chocolate consumption and heart disease rates. Be specific about the experimental units, treatments, randomization procedure, and what would be measured. (c) Discuss at least two practical or ethical challenges that might make the experiment you described in part (b) difficult to carry out. (d) Given these challenges, suggest a modification to your experimental design that would make it more feasible while still being an experiment.

Show answer

Rubric (4 points): Part (a) — 1 point: The study is observational, meaning the researchers did not randomly assign participants to eat or avoid dark chocolate. Therefore, any observed association could be due to confounding variables rather than a causal effect of dark chocolate. For example, people who eat dark chocolate daily may also tend to have higher incomes, better access to healthcare, healthier overall diets, or more active lifestyles — all of which are associated with lower heart disease rates. Without random assignment, it is impossible to isolate the effect of dark chocolate from these confounders. A specific confounding variable: overall diet quality — dark chocolate consumers may eat more fruits, vegetables, and whole grains in general. Part (b) — 1 point: Recruit a large sample (e.g., 2,000) of adult volunteers with no current heart disease. Use a random number generator to assign each participant to one of two groups: the treatment group (consume 30 grams of dark chocolate daily for 5 years) and the control group (consume a placebo that looks and tastes similar to chocolate but contains no cocoa). Ideally, make the study double-blind so that neither the participants nor the physicians monitoring outcomes know which group each participant is in. After 5 years, compare the incidence of heart disease (diagnosis of coronary artery disease, heart attack, or related conditions) between the two groups. Part (c) — 1 point: Challenge 1 (Practical): A 5-year study with 2,000 participants would be extremely expensive and logistically difficult — researchers must maintain contact, ensure compliance with daily chocolate consumption, and track medical records over a long period. Many participants may drop out (attrition), which can introduce bias if dropout rates differ between groups. Challenge 2 (Ethical/Practical): It may be difficult to ensure that control-group participants completely avoid dark chocolate for 5 years, and it is ethically questionable to require participants to change their diets for such a long time. Additionally, if preliminary evidence during the trial strongly suggests one group is worse off, the study may need to be stopped early. Part (d) — 1 point: A more feasible modification would be to shorten the study duration and use intermediate biomarkers (surrogate endpoints) instead of actual heart disease incidence. For example, conduct a 12-week randomized double-blind experiment measuring changes in blood pressure, cholesterol levels (LDL and HDL), and markers of inflammation (e.g., C-reactive protein). While these biomarkers are not the same as heart disease itself, they are well-established risk factors. This shorter-term experiment retains random assignment (so causal conclusions about the biomarkers are valid), is far less expensive, and has much lower attrition. The trade-off is that the conclusion applies to intermediate risk factors rather than to heart disease directly.

SUMMARY

Summary — Introduction to Experimental Design

Summary

Experimental design is the cornerstone of statistical reasoning about causation. An experiment deliberately imposes a treatment on experimental units and measures a response variable. The four pillars — control, randomization, replication, and blocking — work together to minimize the effects of confounding variables and allow researchers to draw causal conclusions. Random assignment is the key mechanism enabling causation claims, while random selection enables generalization to a broader population.

The three designs you need to know for AP Statistics are the completely randomized design (simplest; units assigned entirely by chance), the randomized block design (group similar units first, then randomize within blocks), and the matched-pairs design (blocks of size two). Additional techniques like blinding and placebos prevent psychological biases from distorting results. On the AP exam, always specify how randomization is performed, what is being compared, and why the design supports (or does not support) a causal conclusion.