| name | design-controlled-experiment |
| description | Use when planning a physics experiment that requires controlling variables to isolate causal relationships between physical quantities |
| source | Fisher "The Design of Experiments" (1935); Box, Hunter & Hunter "Statistics for Experimenters" (2005); NIST/SEMATECH e-Handbook of Statistical Methods |
| tags | ["physics","experiment-design","controls","scientific-method"] |
| verified | true |
Design Controlled Experiment
Plan a physics experiment that isolates a single causal variable while controlling all others, enabling valid causal inference.
Why This Is Best Practice
Adopted by: NIST measurement science protocols, CERN experimental design review process, APS (American Physical Society) experimental reporting standards, NSF research grant requirements.
Impact: Factorial design (Box & Hunter) reduces the number of required experimental runs by 50–90% compared to one-factor-at-a-time approaches while simultaneously revealing interactions; NIST calibration studies using designed experiments achieve measurement uncertainty reductions of 30–60%.
Why best: Proper control structure is the only mechanism by which an experiment can support causal claims rather than correlational observations; without it, confounders are indistinguishable from true effects.
Sources: Fisher "Design of Experiments" (1935); Box, Hunter & Hunter 2nd ed. (2005) ch. 3–5; NIST/SEMATECH e-Handbook §5.
Steps
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Define the causal question — state explicitly: "Does [independent variable X] cause a change in [dependent variable Y], holding [list of control variables Z₁, Z₂, ...] constant?"
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Map all variables — categorize every variable as: independent (manipulated), dependent (measured), controlled (held constant), or nuisance (known to vary but not of interest → randomize or block).
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Choose the experimental design — select from: completely randomized design (CRD, for homogeneous material), randomized block design (RBD, for known nuisance variables), factorial design (multiple independent variables and their interactions), or response surface design (optimization).
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Define measurement protocol — specify: instrument, calibration procedure, range, resolution, sampling rate, and number of repeated measurements per condition. Reference calculate-measurement-uncertainty.
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Randomize run order — use a random number generator to determine the order of experimental runs; this distributes unknown time-dependent effects (instrument drift, temperature fluctuations) across all conditions.
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Implement blocking — if a nuisance variable cannot be controlled (e.g., different batches of material, different days), group runs into blocks where the nuisance is constant and include block as a factor in analysis.
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Replicate — perform ≥3 independent replications (not repeated measurements of the same run) to estimate run-to-run variability and support statistical inference.
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Record all conditions — log every environmental parameter (temperature, pressure, humidity, operator, instrument serial number) at the time of each run, even those believed to be controlled.
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Analyze with ANOVA or regression — test the effect of the independent variable while accounting for block effects; report effect size (η² or ω²), F-statistic, and p-value; plot residuals to verify model assumptions.
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Interpret within scope — conclusions apply only to the range of conditions tested (no extrapolation beyond the experimental domain without physical model justification).
Rules
- Control variables must be actively monitored and documented — assuming they are constant without measurement introduces undetectable confounders.
- Never change more than one variable between conditions in a controlled experiment — the entire purpose is isolation.
- Randomization is mandatory; alternating treatment-control-treatment is not randomization.
- Report all failed or excluded runs with reason for exclusion — selective omission is data fabrication.
Common Mistakes
- Confounding with time — running all treatment conditions first, then all controls, means any time-dependent drift (instrument warm-up, sample aging) is confounded with the treatment effect.
- Technical replicates only — measuring the same sample three times is not replication; it estimates measurement noise, not run-to-run experimental variability.
- No baseline or reference condition — without a reference point (zero-field, room temperature, no treatment), the magnitude of the effect cannot be quantified.
- Insufficient range of independent variable — testing X over too narrow a range may miss the functional relationship or underestimate the effect.
When NOT to Use
- For observational studies where manipulation is impossible (use matched cohort or natural experiment methods)
- For theoretical/computational studies (use sensitivity analysis and verification/validation methodology instead)
- For engineering design optimization over a large parameter space (use Design of Experiments software: JMP, Minitab, or Python pyDOE)
