Experimental Design: Your Guide to AP Stats Success 🚀

Hey there, future AP Stats superstar! Let's break down experimental design so you're ready to rock the exam. Remember, choosing the right design is key to getting valid results. Let's dive in!

The Big Three Experimental Designs

These are the bread and butter of experimental design. Know them well!

• Completely Randomized Design
• Blocking Design
• Matched Pairs Design

Completely Randomized Design

• How it works: Think of drawing names from a hat. Each participant has an equal chance of being assigned to any group.
• When to use it: When you have a fairly homogenous group and no specific variables you need to control for.
• Example: Testing the effectiveness of a new fertilizer on plants. Randomly assign plants to different fertilizer groups.

Blocking Design

• How it works: Like sorting socks by color before matching them. You group similar units together, then randomize treatments within those groups.
• When to use it: When you know a variable (the blocking variable) could influence your results. This helps reduce variability within treatment groups.
• Example: Testing a new drug, but you know age affects drug response. Block by age group, then randomize treatment within each age group.

Matched Pairs Design

• How it works: Think of twins. You pair them up because they're very similar, then give each twin a different treatment. Or, you could give the same person two different treatments over time.
• When to use it: When you have two treatments and want to compare them on very similar units. Great for reducing variability due to individual differences.
• Example: Testing two different running shoes. Have the same runner try both shoes, or pair runners with similar running styles and have each runner try one shoe.

Practice Problems

Let's apply what we've learned with some practice problems. Remember, understanding these scenarios is key to success on the exam!

Problem 1: Completely Randomized Design

(1) A researcher wants to test a new teaching method on 50 high school students. Describe how to set up a completely randomized design.

Problem 2: Blocking Design

(2) A researcher wants to test a new study technique on 100 college students. They know that major and course load can affect grades. How should they set up a blocking design?

Problem 3: Choosing the Right Design

(3) A researcher is considering using a completely randomized design, a blocking design, or a matched pairs design for a study. Explain the advantages and disadvantages of each and recommend the best design for the study described in problem 2.

• Confusing blocking with stratification: Blocking is used in experiments, while stratification is used in sampling.
• Not randomizing within blocks: Always randomize treatments within each block.
• Using matched pairs when it's not appropriate: Matched pairs are for comparing two treatments on very similar units.

• CRD (Completely Randomized Design): Think "Completely Random, Done!" - It's the simplest, just randomize.
• Blocking: "Block it out!" - Block out the unwanted variation by grouping similar units.
• Matched Pairs: "Pair up!" - Pair up similar units to reduce variability.

Final Exam Focus

• High-Priority Topics:
  • Identifying the correct experimental design given a scenario.
  • Understanding the purpose of blocking and matched pairs.
  • Explaining how to randomize in different designs.
• Common Question Types:
  • Multiple-choice questions that test your understanding of design differences.
  • Free-response questions that require you to design an experiment.
  • Questions that ask you to identify the best design for a given situation.

Multiple Choice Questions

(1) A researcher is studying the effect of a new fertilizer on tomato yield. They have 20 tomato plants and randomly assign 10 plants to receive the new fertilizer and 10 to receive the standard fertilizer. What type of experimental design is this?

(A) Completely Randomized Design
(B) Blocking Design
(C) Matched Pairs Design
(D) Stratified Design
(E) Cluster Design

(2) A pharmaceutical company is testing a new drug to lower blood pressure. They recruit 100 participants and measure their blood pressure before and after taking the drug. What type of experimental design is this?

(A) Completely Randomized Design
(B) Blocking Design
(C) Matched Pairs Design
(D) Stratified Design
(E) Cluster Design

(3) A researcher wants to compare two different methods of teaching reading. They have 50 students, and they know that some students have learning disabilities. They decide to group students with learning disabilities together and then randomly assign students within each group to one of the two teaching methods. What type of experimental design is this?

(A) Completely Randomized Design
(B) Blocking Design
(C) Matched Pairs Design
(D) Stratified Design
(E) Cluster Design

Free Response Question

A researcher is interested in studying the effect of different types of music on test performance. They recruit 60 students and have them take a math test while listening to one of three types of music: classical, pop, or no music. The researcher knows that students' math skills vary, so they want to control for this variable.

(a) Describe how the researcher could use a completely randomized design to conduct this study.

(b) Describe how the researcher could use a blocking design to conduct this study, controlling for students' math skills.

(c) Which of these two designs would be more appropriate for this study? Justify your answer.

*   **1 point:** Randomly assign each of the 60 students to one of the three music conditions (classical, pop, or no music).
*   **1 point:** Explain that each student has an equal chance of being assigned to any of the three groups.

*   **1 point:** Assess students' math skills (e.g., using a pre-test or previous grades).
*   **1 point:** Divide students into blocks based on math skills (e.g., high, medium, low).
*   **1 point:** Within each block, randomly assign students to one of the three music conditions.

*   **1 point:** The blocking design is more appropriate.
*   **1 point:** Justification: Blocking controls for the variability in math skills, which may affect test performance. This reduces the influence of the confounding variable (math skill) and provides a more precise estimate of the effect of music on test performance.

Remember, you've got this! Keep practicing, and you'll be an experimental design pro in no time! 🌟