Experimental Design Examples in Statistics

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Experimental Design.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Statistics.

Concept Recap

The careful planning of experiments to establish cause-and-effect relationships by controlling variables and using comparison groups.

Want to know if a new fertilizer helps plants grow? You can't just use it on some plants and see if they grow - maybe they would've grown anyway! You need identical plants, give fertilizer to some (treatment) but not others (control), and keep everything else the same.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Good experiments use random assignment and control groups to isolate the effect of one variable, making causation (not just correlation) provable.

Common stuck point: Students often design experiments without a control group, making it impossible to know if the treatment actually caused any change.

Worked Examples

Example 1

easy
A farmer wants to test whether a new fertiliser improves crop yield. She applies the new fertiliser to Field A and uses the old fertiliser on Field B. She finds Field A produces more. Can she conclude the new fertiliser is better? Identify the flaw in the experiment.

Solution

  1. 1
    Step 1: The two fields may differ in soil quality, sunlight, water drainage, or other factors that affect yield. These are confounding variables.
  2. 2
    Step 2: The experiment has no randomisation — the fields were not randomly assigned. The farmer compared two different fields, not two equivalent groups.
  3. 3
    Step 3: A better design would split a single field into random plots, randomly assigning the new fertiliser to half the plots and the old fertiliser to the other half.

Answer

No, she cannot conclude the new fertiliser is better. The two fields may differ in soil quality and other factors (confounding variables). Random assignment within the same field would be a better design.
Good experimental design requires controlling for confounding variables. Using two entire fields introduces many uncontrolled differences. Random assignment of treatments to equivalent units helps ensure that any observed differences are due to the treatment rather than pre-existing conditions.

Example 2

medium
Describe the key components of a well-designed experiment to test whether a new study method improves exam scores. Include: treatment and control groups, random assignment, and what should be kept constant.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

medium
A doctor tests a new headache medicine. She gives the medicine to patients who ask for it and compares their recovery to patients who didn't ask. Identify at least two problems with this experimental design.

Example 2

hard
Design a double-blind experiment to test whether caffeine improves reaction time. Specify: (a) how participants are assigned, (b) what the treatment and control conditions are, (c) what 'double-blind' means and why it matters, (d) the response variable.
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Related Concepts

Correlation vs Causation

Background Knowledge

These ideas may be useful before you work through the harder examples.

correlation vs causationvariables