Types of Experimental Designs

Why This Matters

When you're designing an experiment, the structure you choose determines everything—how well you can isolate treatment effects, how efficiently you use your subjects, and ultimately, whether your conclusions hold up to scrutiny. The AP exam doesn't just want you to name these designs; you're being tested on when and why each design is the right tool for the job. Questions will ask you to identify which design fits a scenario, explain why blocking improves precision, or describe how a researcher could reduce confounding variables.

Think of experimental designs as strategic choices that balance three competing goals: controlling variability, maximizing statistical power, and working within practical constraints. Some designs use randomization to eliminate bias, others use blocking to account for known differences, and still others use subjects as their own controls to boost sensitivity. Don't just memorize the names—know what problem each design solves and what trade-offs it introduces.

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Designs Based on Pure Randomization

These designs rely on random assignment as the primary tool for eliminating bias. By giving every subject an equal chance of receiving any treatment, randomization ensures that both known and unknown confounding variables are distributed evenly across groups.

Completely Randomized Design

• Random assignment to all treatment groups—every subject has an equal probability of landing in any condition, which is the gold standard for eliminating selection bias
• No blocking or matching—this design assumes treatment effects are uniform across subjects, making it simple but potentially less precise when subjects vary widely
• Best for homogeneous populations—when individual differences are minimal, this design maximizes simplicity without sacrificing validity

Between-Subjects Design

• Each subject experiences only one treatment—different groups receive different conditions, eliminating any possibility of carryover or practice effects
• Requires more subjects—because you can't reuse participants, you need larger sample sizes to achieve the same statistical power as within-subjects approaches
• Ideal for treatments with lasting effects—when a treatment permanently changes subjects (like surgery or intensive training), this is often your only option

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Designs That Use Blocking

Blocking designs identify a known source of variability before the experiment begins and organize subjects accordingly. By grouping similar subjects together and randomizing within those groups, blocking removes confounding variation and increases the precision of treatment comparisons.

Randomized Block Design

• Subjects grouped by a shared characteristic—blocks might be based on age, gender, prior experience, or any variable expected to influence the outcome
• Randomization occurs within each block—this ensures that treatment effects aren't confounded with the blocking variable
• Reduces experimental error—by accounting for between-block variability, this design makes it easier to detect true treatment differences

Matched-Pairs Design

• Two subjects paired on key characteristics—each pair should be as similar as possible on variables that might affect the response
• One member of each pair receives each treatment—this creates a direct, controlled comparison while accounting for individual differences
• Common in medical and psychological research—when you have exactly two treatments and can identify meaningful pairs, this design offers excellent control

Latin Square Design

• Controls for two blocking variables simultaneously—treatments are arranged so each appears exactly once in every row and column of a square grid
• Highly efficient with limited subjects—when you have the same number of treatments, row blocks, and column blocks, this design balances everything perfectly
• Requires equal levels of all factors—if you have 4 treatments, you need exactly 4 rows and 4 columns, which limits flexibility

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Designs Where Subjects Serve as Their Own Controls

These designs expose the same subjects to multiple treatments, using each individual as their own baseline. This approach dramatically reduces variability due to individual differences and increases statistical power, but introduces risks of carryover effects and order bias.

Within-Subjects Design

• Same subjects experience all treatments—this allows direct comparison of how each individual responds to different conditions
• Controls for individual differences—since each person serves as their own control, between-subject variability is eliminated from the analysis
• Watch for carryover effects—fatigue, learning, or lingering treatment effects can confound results if not properly managed

Repeated Measures Design

• Measurements taken from the same subjects over time or conditions—this is the go-to design for tracking change, development, or response patterns
• Increases statistical power with fewer subjects—you get more data points per participant, making this design efficient when subjects are scarce or expensive
• Requires careful timing—the interval between measurements must be long enough to avoid interference but short enough to maintain relevance

Crossover Design

• Subjects receive treatments in sequence with washout periods—the gap between treatments allows previous effects to dissipate before the next treatment begins
• Each participant serves as their own control—this is especially valuable in clinical trials where individual response variability is high
• Order effects are balanced—half the subjects might receive Treatment A first, half receive Treatment B first, counterbalancing any sequence bias

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Designs for Complex, Multi-Factor Experiments

When researchers want to study multiple independent variables at once, these designs allow them to examine both individual effects and interactions. Factorial and split-plot designs are efficient because they extract more information from the same number of subjects.

Factorial Design

• Studies multiple factors simultaneously—every level of one factor is combined with every level of all other factors, creating a complete grid of conditions
• Reveals interaction effects—you can see not just whether Factor A matters, but whether its effect depends on the level of Factor B
• Efficient use of data—a $2 \times 2$ factorial gives you information about two main effects and one interaction from a single experiment

Split-Plot Design

• Different factors applied at different levels—one factor is applied to whole plots (larger units), another to subplots (smaller units within each plot)
• Practical when some treatments are hard to change—in agriculture, you might apply irrigation to whole fields but fertilizer types to individual rows
• Requires specialized analysis—the error terms differ for whole-plot and subplot factors, which affects how you calculate significance

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Quick Reference Table

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Self-Check Questions

1. A researcher wants to test three teaching methods but knows that students' prior math ability varies widely. Which design would help control for this variability, and why is it better than a completely randomized design?

2. Compare and contrast within-subjects and between-subjects designs. Under what circumstances would you choose each, and what are the main trade-offs?

3. A pharmaceutical company is testing two migraine medications and wants each participant to try both drugs. What design should they use, and what critical feature must they include to ensure valid results?

4. Which two designs both control for individual differences by using subjects as their own controls, but differ in whether treatments are given simultaneously or sequentially?

5. An FRQ describes an agricultural experiment where irrigation systems are applied to entire fields, but different seed varieties are planted in rows within each field. Identify the appropriate design and explain why the factors are treated differently.