AP Statistics 3.6 Selecting an Experimental Design Study Notes
AP Statistics 3.6 Selecting an Experimental Design Study Notes- New syllabus
AP Statistics 3.6 Selecting an Experimental Design Study Notes -As per latest AP Statistics Syllabus.
LEARNING OBJECTIVE
- Well-designed experiments can establish evidence of causal relationships.
Key Concepts:
- Explain Why a Particular Experimental Design Is Appropriate
Explain Why a Particular Experimental Design Is Appropriate
Explain Why a Particular Experimental Design Is Appropriate
Choosing the right experimental design depends on the research question, the type of units being studied, and potential sources of variation. A good design minimizes bias and variation while maximizing fairness in comparison. Below are guidelines for when each design is appropriate.
Completely Randomized Design:
- Appropriate when experimental units are similar in important ways.
- Random assignment alone is enough to balance out variables.
- Simple to implement and analyze.
- Works best for large sample sizes where chance evens things out.
- Example: Randomly assigning 100 identical plants to two fertilizers.
Randomized Block Design:
- Appropriate when units differ in a characteristic that may affect the response.
- Blocking reduces variability within groups by controlling for that characteristic.
- Ensures fairer comparisons between treatments within each block.
- Improves accuracy when outside factors (age, gender, location) are important.
- Example: Blocking patients by gender in a drug trial before random assignment.
Matched Pairs Design:
- Appropriate when units can be paired based on similarity, or when one unit can receive both treatments.
- Eliminates variation between individuals by comparing within pairs.
- Useful when sample sizes are small or when individual differences are large.
- Each subject serves as their own control, reducing bias.
- Example: Testing two teaching methods by having each student experience both, in random order.
Comparison Table
| Design | When Appropriate | Why It Works | Example |
|---|---|---|---|
| Completely Randomized | Units are fairly similar; large sample size | Randomization balances groups on average | Randomly assign 200 seeds to two fertilizers |
| Randomized Block | Units differ on a key characteristic | Blocks control for known sources of variation | Block by age before assigning drug or placebo |
| Matched Pairs | Units can be paired or tested under both treatments | Each unit serves as its own control | Each person tries both diets in random order |
Example
A researcher wants to compare the effectiveness of two fertilizers on plant growth. The plants are genetically identical and grown under the same conditions. Which design is most appropriate?
▶️ Answer / Explanation
Step 1: All plants are similar; no natural grouping is necessary.
Step 2: Random assignment alone is sufficient.
Conclusion: A completely randomized design is appropriate because units are similar and chance balances groups.
Example
A medical study wants to test a new drug for reducing blood pressure. Because men and women may respond differently, researchers separate patients by gender before assigning treatments. Which design is most appropriate?
▶️ Answer / Explanation
Step 1: Gender may affect response, so blocking is needed.
Step 2: Patients are grouped into male and female blocks.
Step 3: Random assignment occurs within each block.
Conclusion: A randomized block design is appropriate because it controls for gender differences.
Example
A psychologist wants to test whether people solve puzzles faster after drinking coffee. Each participant is tested once after drinking coffee and once after drinking water, in random order. Which design is most appropriate?
▶️ Answer / Explanation
Step 1: Each person is tested under both treatments.
Step 2: Order of treatments is randomized to avoid bias.
Conclusion: A matched pairs design is appropriate because each subject serves as their own control.