The Variable That Wasn't Controlled
A team tests whether a paper airplane's design affects flight distance. Design A has a pointed nose; Design B has a blunt nose. Each design is thrown 10 times. The student throwing Design A is a different person from the one throwing Design B, and Design A is thrown in the gym while Design B is thrown in the hallway. Distances for Design A average 9.2 m; Design B averages 6.8 m. The team concludes the pointed nose flies farther. The teacher asks them to list every difference between the two conditions and judge whether the 2.4 m gap can be attributed to nose shape.
1. List the uncontrolled variables and explain how each could inflate Design A's apparent advantage.
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Uncontrolled variables:
- Thrower - different people have different arm strength and technique. A stronger thrower assigned to Design A would raise its average regardless of design.
- Location - gym vs. hallway differ in air currents, ceiling height, and obstacles. A draft-free gym could allow longer flights.
- Order/other conditions - time of day, paper stock, and folding consistency are not stated as matched.
How each inflates A: Any of these could produce a 2.4 m gap on its own. Because thrower and location both favor Design A, the comparison confounds design with person and place. The 2.4 m difference cannot be attributed to nose shape.
2. Propose a controlled version of the test and describe how the data should be summarized to support a design claim.
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Controlled version:
- Same thrower (or several throwers who each throw both designs) to remove skill differences.
- Same location and conditions for all throws.
- Same paper and folding protocol, verified by checking dimensions/mass.
- Alternate throws (A, B, A, B…) to balance any drift in conditions.
- Many trials per design and, ideally, multiple throwers so the result generalizes beyond one person.
Summarizing: Report the mean distance for each design and the spread (range or standard deviation). Compare whether the difference in means exceeds the trial-to-trial variability. A design claim is supported only if A's advantage is larger than the noise and holds across throwers.
3. Suppose, after controlling everything, Design A still averages 2.4 m farther with small spread. What can the team conclude, and what can they not conclude?
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Can conclude: Under these controlled conditions, with this paper and these throwers, the pointed-nose design flew farther on average by about 2.4 m, and the gap exceeds the trial variability.
Cannot conclude:
- Why it flies farther - the data show a difference, not a mechanism (e.g., aerodynamics of the nose).
- Generalization to other paper types, sizes, indoor/outdoor conditions, or throwers outside the sample.
- That nose shape is the only factor - other design features that differ between the planes could still contribute.
Reasoning: A controlled experiment supports a limited causal claim about the tested conditions. Explaining the cause and extending the result require further tests.