Experimental Design

🔬 Experimental Design

Part 1 of 7 — Principles of Experimental Design

Three Principles of Experimental Design

Vocabulary

• Explanatory variable (factor): The variable manipulated by the researcher
• Response variable: The outcome being measured
• Treatments: The specific conditions applied to subjects
• Experimental units: The individuals being studied (called subjects if human)

Example

A pharmaceutical company tests a new drug. 200 patients are randomly assigned to receive the drug or a placebo. Blood pressure is measured after 8 weeks.

• Factor: Drug vs. placebo
• Response: Blood pressure change
• Experimental units: The 200 patients
• Treatments: Drug, placebo

Concept Check 🎯

Design Identification 🧮

A researcher wants to test whether a new teaching method improves test scores. She randomly assigns 60 students to either the new method or traditional method, then compares their exam results.

1) What is the explanatory variable?

2) What is the response variable?

3) How many treatments are there?

🎲 Randomization Techniques

Part 2 of 7 — Randomization Techniques

Why Randomize?

Randomization serves two purposes:

1. Eliminates bias in group assignment
2. Balances confounding variables (both known and unknown)

Methods of Random Assignment

Example: Using a Random Number Table

To assign 30 students to two groups:

1. Number students 01–30
2. Read two-digit numbers from the table
3. First 15 unique numbers → Group A
4. Remaining 15 → Group B

Completely Randomized Design

All experimental units are randomly assigned to treatments with no grouping.

$\text{Random Assignment} \to \begin{cases} \text{Treatment 1} \\ \text{Treatment 2} \end{cases} \to \text{Compare Results}$

Concept Check 🎯

Random Assignment 🧮

You have 40 volunteers for a study with 2 treatments.

1) In a completely randomized design, how many subjects per group?

2) If you use a random number table with numbers 01-40, what range goes to Treatment A? (e.g., 01-20)

3) What is the purpose of randomization? (bias/replication/control)

🧱 Blocking

Part 3 of 7 — Blocking

What Is Blocking?

Blocking groups experimental units by a characteristic expected to affect the response, then randomizes within each block.

🔑 Purpose: Reduce variability and increase the precision of the experiment.

Randomized Block Design

1. Identify a blocking variable (e.g., age, gender, baseline fitness)
2. Group subjects into blocks of similar units
3. Randomly assign treatments within each block
4. Analyze results

Example

Testing a new diet’s effect on weight loss. Block by gender:

Blocking vs. Confounding Variables

• Blocking variable: A variable you KNOW affects the response (you control for it)
• Confounding variable: A variable that is mixed up with the explanatory variable (uncontrolled)

Matched Pairs Design

A special case of blocking where:

• Each block has exactly 2 units (or same subject gets both treatments)
• Often: before/after measurements on the same person

Concept Check 🎯

Blocking Design 🧮

A researcher tests whether a new fertilizer increases crop yield. Fields vary in sun exposure (high/low).

1) What is the blocking variable?

2) How many blocks are there?

3) Within each block, how do you assign fertilizer vs. control? (randomly/alphabetically/by size)

📋 Types of Studies

Part 4 of 7 — Observational Studies vs. Experiments

Two Types of Studies

Key Rule

💡 Only experiments can establish causation. Observational studies can only show association.

Types of Observational Studies

Example

“People who exercise more have lower rates of heart disease.”

• This is an observational finding (no one was assigned to exercise)
• We CANNOT say exercise causes lower heart disease from this alone
• Confounders: diet, genetics, socioeconomic status

Concept Check 🎯

Study Classification 🧮

Classify each as observational (O) or experimental (E):

1) Researchers survey 500 people about their diet and measure cholesterol levels.

2) 100 volunteers are randomly assigned to take vitamin D or a placebo for 6 months.

3) Hospital records are examined to compare outcomes of two surgical approaches.

⚠️ Confounding and Bias

Part 5 of 7 — Sources of Error

Confounding Variables

A confounding variable is associated with both the explanatory and response variables, making it impossible to determine which causes the effect.

$\text{Explanatory} \leftarrow \text{Confounder} \rightarrow \text{Response}$

Types of Bias

Placebo Effect and Blinding

• Placebo: An inactive treatment that looks identical to the real one
• Single-blind: Subjects don’t know which treatment they receive
• Double-blind: Neither subjects NOR researchers know who gets what

🔑 Double-blinding prevents both placebo effect AND researcher bias.

Concept Check 🎯

Bias Identification 🧮

1) A study finds coffee drinkers live longer. Name a possible confounding variable.

2) In a drug trial, patients know whether they get the real drug. What kind of blinding is missing? (single/double)

3) A magazine asks readers to mail in a survey. What type of bias is this? (voluntary response/undercoverage/nonresponse)

🏆 Problem-Solving Workshop

Part 6 of 7 — AP-Style Practice

AP Exam Framework

Experimental design questions often ask you to:

1. Describe a completely randomized design
2. Explain why blocking is used
3. Identify confounding variables
4. Distinguish between observational and experimental studies

How to Describe a Design (AP FRQ)

1. State groups and sizes
2. Describe random assignment method
3. Identify treatments
4. State the response variable
5. Mention comparison between groups

Template Answer

“Randomly assign the 80 subjects to two groups of 40. Group 1 receives Treatment A and Group 2 receives Treatment B. After 6 weeks, compare the mean [response variable] between the two groups.”

Concept Check 🎯

Design an Experiment 🧮

A teacher wants to test whether background music improves quiz scores. She has 40 students.

1) How many students per group in a completely randomized design with 2 treatments?

2) What is the explanatory variable?

3) Should students know whether music is being played for them? (yes/no) Why?

📝 Mixed Review

Part 7 of 7 — Comprehensive Review

Key Concepts Checklist

• Three principles: Control, Randomization, Replication
• Observational vs. Experimental studies
• Completely randomized design
• Randomized block design & matched pairs
• Sources of bias (undercoverage, response, nonresponse, voluntary response)
• Confounding variables
• Blinding (single and double)
• Placebo and placebo effect

AP Exam Tips

• “Explain why” = give a reason connected to bias or variability
• Always mention random assignment when describing experiments
• Use the word cause only with experiments, never with observational studies

Concept Check 🎯

Final Review 🧮

1) In a randomized block design, you randomize WITHIN blocks. True or False?

2) Can an observational study prove causation? (yes/no)

3) What does a placebo control for? (confounding/placebo effect/sample size)