AP Statistics 3.2 Introduction to Planning a Study Study Notes
AP Statistics 3.2 Introduction to Planning a Study Study Notes- New syllabus
AP Statistics 3.2 Introduction to Planning a Study Study Notes -As per latest AP Statistics Syllabus.
LEARNING OBJECTIVE
- The way we collect data influences what we can and cannot say about a population.
Key Concepts:
- Identify the Type of a Study
- Identify Appropriate Generalizations and Determinations Based on Observational Studies
Identify the Type of a Study
Identify the Type of a Study
In statistics, we study data to make conclusions about a larger group. To judge whether results are reliable, we must know the type of study used and how the data were collected.
Population and Sample:
- Population: The entire group of individuals we want to learn about.
- Sample: A subset of the population from which data are collected. Ideally chosen using chance (random sampling).
- Census: Data are collected from every individual in the population.
- Survey: A method of collecting data from a sample of individuals, usually through questions.
Types of Studies:
Observational Study: Researchers observe and record data without interfering.
- Describes existing conditions or relationships.
- Can identify association but not causation.
Experiment: Researchers impose treatments on individuals and measure the results.
- Uses random assignment to reduce bias.
- Can establish cause-and-effect (if well designed).
Comparison Table
| Study Type | Characteristics | What We Can Conclude |
|---|---|---|
| Observational Study | No treatment imposed; data collected naturally | Can show association, not causation |
| Experiment | Treatment imposed; random assignment used | Can show cause-and-effect |
| Survey | Sample is asked questions about opinions/behaviors | Provides information about the population (if random sample) |
| Census | Data collected from every individual in the population | Complete information, but often impractical |
Example
A researcher records the heights and shoe sizes of 500 randomly chosen students to see if there is a relationship between height and shoe size.
What type of study is this?
▶️ Answer / Explanation
Step 1: No treatment was imposed; students were simply measured.
Step 2: The sample (500 students) represents the population (all students).
Conclusion: This is an observational study.
Example
In a medical study, 200 patients with high blood pressure are randomly assigned to two groups. One group receives a new drug, while the other receives a placebo. Their blood pressure is measured after 8 weeks.
What type of study is this?
▶️ Answer / Explanation
Step 1: A treatment (new drug vs placebo) was imposed.
Step 2: Random assignment helps ensure fair comparison between groups.
Conclusion: This is an experiment. Cause-and-effect conclusions are possible.
Example
A school wants to know the average number of hours of homework its students complete weekly. It collects data from every single student enrolled in the school.
What type of data collection method is this?
▶️ Answer / Explanation
Step 1: Data were collected from all individuals in the population.
Step 2: This is not a sample, but rather a complete count.
Conclusion: This is a census.
Identify Appropriate Generalizations and Determinations Based on Observational Studies
Identify Appropriate Generalizations and Determinations Based on Observational Studies
An observational study records data without imposing a treatment. This means that the conclusions depend on how the data were collected.
What We Can Do:
- If the sample was chosen using a random sampling method, then we may generalize the results to the population.
- Observational studies can identify associations (relationships) between variables.
What We Cannot Do:
- We cannot establish cause-and-effect because no treatments were imposed.
- Bias in data collection (e.g., voluntary response, convenience sampling) prevents valid generalization to the population.
Exam Tip: Observational studies = Association only. To generalize → need random sample. To claim cause-and-effect → need an experiment.
Example
Researchers randomly sample 1000 adults across the country and record whether they smoke and whether they have high blood pressure.
What generalizations and determinations can be made?
▶️ Answer / Explanation
Step 1: A random sample was used, so results can be generalized to the adult population.
Step 2: No treatment was imposed, so causation cannot be concluded.
Conclusion: We can say smoking is associated with high blood pressure in the population, but we cannot say smoking causes high blood pressure based on this study alone.
Example
A health club surveys its members about their eating habits and exercise routines to draw conclusions about the general public.
What generalizations and determinations can be made?
▶️ Answer / Explanation
Step 1: The sample is not random; it includes only health club members, not all adults.
Step 2: Because the sample is biased, results cannot be generalized to the population.
Step 3: No treatment was imposed, so causation cannot be concluded.
Conclusion: The study only shows an association among health club members, not the general population.