Foundations of Inquiry · Lesson 017
Controlled Comparisons — How Experiments Reveal What Really Changes
Previous lesson: 016 — Baselines & Benchmarks. Academy home.
Learning objectives
By the end, you should be able to identify an independent variable, dependent variable and controlled variables; explain the role of a comparison group; calculate a difference between group means; and describe why random assignment and repeated trials matter.
What makes a comparison controlled?
A controlled experiment deliberately changes one factor while keeping other relevant conditions as similar as practical. The factor deliberately changed is the independent variable; the measured outcome is the dependent variable. A control or comparison group supplies a reference for interpreting the change. This does not guarantee causation: bias, chance, measurement errors and confounding factors still matter.
The National Institute of Standards and Technology describes design of experiments as a systematic way to study factors and responses. The CDC Field Epidemiology Manual emphasizes comparing groups and accounting for uncertainty when interpreting evidence.
Worked example: light and seedlings
Imagine 20 similar seedlings, randomly assigned to two groups of 10. Both groups receive the same soil, pot size, watering schedule and observation period. Group A receives six hours of light daily; Group B receives eight. After two weeks, the average height increase is 3.2 cm for A and 4.0 cm for B.
Difference in mean growth = 4.0 − 3.2 = 0.8 cm. Relative to the A group mean, the difference is 0.8 ÷ 3.2 × 100 = 25%. That is a descriptive comparison in this invented teaching example, not a proven 25% causal effect in real seedlings. We would need variability estimates, replication, and checks for unexpected differences before drawing a strong conclusion.
Try it: a safe paper experiment
Test whether a paper airplane’s wing width affects flight distance. Make two airplane designs differing only in wing width as far as possible. Use the same paper, thrower, launch position and approximate force. Alternate designs across ten throws each and measure distance in meters. Record all 20 distances, not only the best throws. Calculate each group’s mean: sum its ten distances and divide by 10. Compare means and ranges. Note that human throwing variation remains a limitation.
Reflection
Which variables were genuinely held constant? Could the order of trials matter? What would you change to make the comparison fairer without pretending all uncertainty disappears?
Knowledge check
- In the seedling example, what is the independent variable?
- What is the dependent variable?
- What is the absolute difference between group means?
- Does that difference alone prove the light schedule caused the change?
- Why alternate airplane designs instead of testing all of one design first?
Answer key
- Daily hours of light.
- Height increase after two weeks.
- 0.8 cm.
- No; sampling variability and other factors need consideration.
- Alternating helps reduce the influence of changing conditions or thrower fatigue over time.
Limits and next steps
Small samples, imperfect controls, biased measurements and nonrandom group assignment can undermine an inference. A measured difference is a starting point for inquiry, not a universal law. Next, we will examine how uncertainty around an estimate changes what conclusions are justified.
Nova Academy · Electric Icarus Project · Free Foundations of Inquiry education
