Experiments and Random Assignment
A free Statistics and Data Analysis lesson from the “Collecting Data” unit, with a worked example and practice problems including step-by-step solutions.
An experiment deliberately applies treatments to compare outcomes. Random assignment helps make treatment groups comparable, supporting cause-and-effect conclusions when the design is sound. This lesson builds the habit of reading the context first, choosing the right statistical tool, calculating carefully, and then writing what the result means. By the end, students should be able to do the computation and explain why that computation answers the question.
What you'll learn
- Identify treatments and experimental units
- Explain random assignment
- Connect experiments to cause-and-effect conclusions
Worked example
Problem. A sample statistic describes:
- Worked Example: First identify exactly what the question is asking: A sample statistic describes:
- Compare each answer choice with the calculation or rule, and eliminate choices that do not satisfy the condition.
- A statistic is computed from sample data.
- A parameter describes the population.
Answer: the sample
Practice problems
1. Practice case A: A sample statistic describes:
Choices: the sample · the entire population with certainty · the placebo · the null hypothesis
Show solution
- Warm-up: First identify exactly what the question is asking: A sample statistic describes:
- Compare each answer choice with the calculation or rule, and eliminate choices that do not satisfy the condition.
- A statistic is computed from sample data.
- A parameter describes the population.
- Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.
Answer: the sample
2. Practice case B: Random sampling mainly helps a study:
Choices: prove causation by itself · remove every outlier · make all variables categorical · generalize to a population
Show solution
- Warm-up: First identify exactly what the question is asking: Random sampling mainly helps a study:
- Compare each answer choice with the calculation or rule, and eliminate choices that do not satisfy the condition.
- Random sampling helps the sample represent the population.
- That supports generalizing results.
- Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.
Answer: generalize to a population
3. Practice case C: Voluntary response samples are risky because:
Choices: they have no variables · they prove causation · people with strong opinions may be overrepresented · they are always too large
Show solution
- Warm-up: First identify exactly what the question is asking: Voluntary response samples are risky because:
- Compare each answer choice with the calculation or rule, and eliminate choices that do not satisfy the condition.
- Voluntary samples depend on who chooses to respond.
- That can create bias.
- Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.
Answer: people with strong opinions may be overrepresented
4. Practice case D: Random assignment mainly helps an experiment:
Choices: turn a table into a graph · compare treatments fairly · choose a representative sample · increase every p-value
Show solution
- Warm-up: First identify exactly what the question is asking: Random assignment mainly helps an experiment:
- Compare each answer choice with the calculation or rule, and eliminate choices that do not satisfy the condition.
- Random assignment balances other factors across treatment groups.
- That supports fair treatment comparison.
- Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.
Answer: compare treatments fairly
5. Practice case E: A placebo is:
Choices: a fake treatment used for comparison · the sample mean · the population size · a residual from a model
Show solution
- Warm-up: First identify exactly what the question is asking: A placebo is:
- Compare each answer choice with the calculation or rule, and eliminate choices that do not satisfy the condition.
- A placebo looks like a treatment but lacks the active ingredient.
- It helps measure expectation effects.
- Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.
Answer: a fake treatment used for comparison
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