📊 Power Analysis, Sampling, and Statistics for Apiary Studies

About this simulation

This field represents a population of colonies spread across an apiary site with a real environmental gradient — forage quality rises from one side of the field to the other, exactly the kind of confound that biases small, badly-placed studies. Each time you draw a sample, some colonies are assigned to a control group (teal) and some to a treatment group (amber); unsampled colonies stay grey. The floating bars above sampled hives show a simulated yield outcome for each colony.

How it works

• Sample size (n) — colonies drawn per group. More colonies shrink the standard error of the estimated effect and raise statistical power.
• Effect size (Cohen's d) — the true standardized difference the treatment produces. Larger effects are easier to detect with fewer colonies.
• Significance level (α) — the false-positive rate you're willing to accept; a stricter α (0.01) demands a larger sample for the same power.
• Sampling method — "Random" scatters the sample across the whole gradient, so it is representative of the population. "Clustered" grabs one contiguous row of hives — cheaper to walk to, but it confounds the forage gradient with the treatment and produces a sampling bias, shown as the quality gap statistic.

Power is computed analytically with the standard two-sample normal-approximation formula power = Φ(d·√(n/2) − z_(1−α/2)), and the "n needed for 80% power" panel solves the same formula for n at the conventional 0.80 target. The curve on the right plots power against sample size for your current effect size and α, with a marker at your chosen n.

Controls

• Sample size / Effect size / α / Sampling method — as above.
• ↺ New apiary population — redraws the underlying colony noise so you can see how power and bias estimates behave across different random populations.
• Drag to rotate the scene, scroll to zoom.

Did you know?

Underpowered apiary trials are common in beekeeping research because colonies are expensive and slow to replicate — a published meta-analysis is often the only practical way to reach adequate power, which is exactly why pre-registering a power analysis before data collection is considered best practice.