Experimental Design Fundamentals

Trial setup

Sample size / group 40

True effect size 1.2

Noise (variability) 1.5

Control mean

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Treatment mean

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Measured difference

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t-statistic

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Verdict

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How it works

Each floating sphere is one simulated subject. Blue spheres are the control group (no treatment); teal spheres are the treatment group. Every subject's height (y) is its measured outcome: a shared baseline plus random noise, and — for the treatment group only — the true effect being tested. The two glowing rings mark each group's mean outcome, and the amber bridge between them shows the measured gap the experiment would report.

outcome = baseline + effect·isTreated + noise·N(0,1)
t ≈ (mean_T − mean_C) / (noise / √n)
"significant" when |t| exceeds ~2 (roughly p < 0.05)

Sample size / group — more subjects (replication) shrinks the random wobble in each group's mean, making a real effect easier to detect and a false one easier to rule out.
True effect size — the actual, hidden difference the treatment causes. Set it to 0 to watch a "null" experiment — any measured gap you see is pure noise.
Noise (variability) — how much individual subjects differ for reasons unrelated to treatment. High noise can bury a real effect or fake one that isn't there.
Randomized assignment — toggle it off to inject a confound: subjects are no longer assigned by coin-flip, so a hidden variable (visualized as a color-position bias) drifts the treatment group's baseline upward on its own, mimicking a fake effect even when the true effect is 0. This is exactly why real experiments randomize who gets the treatment.

Real-world relevance: this is the same logic behind clinical trials, A/B tests and lab experiments — a control group isolates the baseline, randomization rules out confounds, replication (sample size) tames noise, and only then does a measured difference count as evidence rather than chance.

Control group Treatment group Group mean Confound bias (unrandomized)

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