AP Statistics 3.5 Introduction to Experimental Design Study Notes
AP Statistics 3.5 Introduction to Experimental Design Study Notes- New syllabus
AP Statistics 3.5 Introduction to Experimental Design Study Notes -As per latest AP Statistics Syllabus.
LEARNING OBJECTIVE
- Well-designed experiments can establish evidence of causal relationships.
Key Concepts:
- Identify the Components of an Experiment
- Describe Elements of a Well-Designed Experiment
- Compare Experimental Designs and Methods
Identify the Components of an Experiment
Identify the Components of an Experiment
Experiments are designed studies where researchers impose treatments on individuals to measure their responses. A well-designed experiment allows us to make cause-and-effect conclusions. To analyze or design experiments, we must recognize their key components.
Key Components of an Experiment:
Experimental Units (or Subjects):
- The individuals (people, animals, objects) on which the experiment is conducted.
- Called subjects when the units are people.
- Units should represent the population of interest.
- Responses are measured on these individuals.
- Example: Patients in a clinical drug trial.
Treatments:
- The specific conditions imposed on experimental units.
- Often a combination of factor levels (e.g., different doses of a drug).
- Each unit receives exactly one treatment.
- Treatments must be clearly defined for fair comparison.
- Example: A group receives 10mg of medication daily.
Factors and Levels:
- Factors are explanatory variables manipulated by researchers.
- Levels are the specific values or categories of a factor.
- Treatments are formed by combining factor levels.
- Allows testing of how different variables influence the response.
- Example: Factor = caffeine intake; Levels = 0mg, 100mg, 200mg.
Response Variable:
- The outcome measured in the experiment.
- Shows the effect of the treatments applied.
- Must be quantitative or categorical depending on the study.
- Should directly relate to the research question.
- Example: Blood pressure after 8 weeks of treatment.
Example
A researcher wants to test if different amounts of caffeine affect memory. She recruits 90 students and randomly assigns them to three groups: no caffeine, 100mg caffeine, and 200mg caffeine. Later, she gives them a memory test and records their scores.
Identify the components of this experiment.
▶️ Answer / Explanation
Step 1: Experimental units = 90 students.
Step 2: Factors = caffeine intake; Levels = 0mg, 100mg, 200mg.
Step 3: Treatments = assignment to one caffeine level.
Step 4: Response variable = memory test score.
Conclusion: All key components (units, factors, levels, treatments, response) are clearly defined.
Describe Elements of a Well-Designed Experiment
Describe Elements of a Well-Designed Experiment
A well-designed experiment ensures valid and reliable results by reducing bias and variation. Four key principles guide the design of good experiments: control, randomization, replication, and comparison.
Key Elements:
Control:
- Keep all variables other than the treatment the same for all groups.
- Helps isolate the effect of the explanatory variable on the response.
- Controls reduce the influence of lurking or confounding variables.
- Often includes a control group that receives no treatment or a placebo.
- Ensures differences in response are due to treatment, not external factors.
Randomization:
- Use chance to assign experimental units to treatments.
- Balances out unknown or uncontrollable variables across groups.
- Prevents bias in the assignment process.
- Gives all units an equal chance of being assigned to any group.
- Creates groups that are comparable on average.
Replication:
- Use enough experimental units in each treatment group.
- Larger sample sizes reduce the impact of random variation.
- Ensures results are not due to chance or unusual individuals.
- Allows for more precise estimates of treatment effects.
- Replicating experiments in different settings increases reliability.
Comparison:
- Compare results across different treatment groups.
- Key to determining whether a treatment has an effect.
- Without comparison, we cannot judge the effectiveness of a treatment.
- Often involves at least one control group for baseline comparison.
- Clear differences between groups support cause-and-effect conclusions.
Comparison Table
| Element | Purpose | Example |
|---|---|---|
| Control | Keep outside variables the same | Placebo group in a medical trial |
| Randomization | Assign treatments using chance | Random number generator assigns patients to groups |
| Replication | Use many units to reduce variation | 100 plants per treatment group in an agricultural study |
| Comparison | Evaluate differences across groups | Drug group vs. placebo group |
Example
A company wants to test whether a new fertilizer increases plant growth. They plant 200 identical seedlings in similar pots under the same light and water conditions. Half are randomly assigned to receive the new fertilizer, and the other half receive standard fertilizer. After 8 weeks, plant heights are measured and compared.
Does this experiment include the elements of a well-designed study?
▶️ Answer / Explanation
Step 1: Control — Same pots, water, and light conditions ensure only fertilizer differs.
Step 2: Randomization — Plants were randomly assigned to treatments.
Step 3: Replication — 200 plants provide enough data to reduce chance variation.
Step 4: Comparison — New fertilizer vs. standard fertilizer allows evaluation of effect.
Conclusion: This is a well-designed experiment using all four key elements.
Compare Experimental Designs and Methods
Compare Experimental Designs and Methods
Different experimental designs allow researchers to control for variation and reduce bias in different ways. Choosing the right design is important for drawing valid cause-and-effect conclusions. Below are the major designs used in AP Statistics.
Completely Randomized Design:
- All experimental units are assigned to treatments entirely by chance.
- Simple and easy to implement.
- Balances out both known and unknown variables across groups.
- Works best when units are fairly similar.
- Example: 60 students randomly assigned to either a new teaching method or the standard method.
Randomized Block Design:
- Experimental units are first grouped into blocks based on a variable that may affect the response.
- Random assignment is carried out separately within each block.
- Reduces variation caused by differences among blocks.
- Improves accuracy by making fairer comparisons within homogeneous groups.
- Example: Students are blocked by grade level, then randomly assigned within each grade to treatments.
Matched Pairs Design:
- A special case of a block design with pairs of closely matched units.
- Each pair receives both treatments, or each individual receives both treatments in random order.
- Controls for individual differences since comparisons are within pairs.
- Useful when sample size is small.
- Example: Each person tests both brands of headphones, order randomized.
Placebo and Control Groups:
- A placebo group receives an inactive treatment (like a sugar pill).
- Used to measure the placebo effect (improvement due to belief, not treatment).
- Control groups receive no treatment or standard treatment.
- Provide a baseline for comparison against experimental groups.
- Essential for reducing bias in medical and psychological experiments.
Example
Researchers want to test whether a new sleep supplement improves sleep quality. They recruit 120 volunteers and can choose among different designs.
Which design would be most appropriate?
▶️ Answer / Explanation
Option 1: Completely Randomized — Randomly assign 60 to supplement, 60 to placebo. Simple but may not account for differences in age or stress levels.
Option 2: Randomized Block — Block volunteers by age group (young, middle-aged, older) and randomly assign within each block. Controls for age differences affecting sleep.
Option 3: Matched Pairs — Have each volunteer take the supplement for one month and a placebo for another month in random order. Each person serves as their own control, reducing individual variability.
Best Choice: Matched pairs design, since sleep quality is highly individual and comparing each person to themselves provides the most accurate results.