Randomized Block Design 2D: Field Experiment Simulator

Experimental Design

Randomized Block Design

Replicates (blocks) 6

Treatment effect size 0.8

Measurement noise (σ) 0.6

Field fertility gradient 1.5

Control Treatment Rejection region

Live Analysis

Mean control

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Mean treatment

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t-statistic

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p-value (two-tailed)

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Power (this design, n=400 MC)

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Power (other design)

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Blocking gain

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How it works

A field has an unobserved fertility gradient. Each plot's true response is baseline + gradient(position) + treatment effect (if treated) + random noise.

Randomized Block: each block sits at ONE
  field position; its control & treatment
  share that position, so the gradient term
  is IDENTICAL for both and cancels exactly
    diff_i = T_i - C_i  (gradient cancels)
    t = mean(diff) / (sd(diff)/√n),  df = n-1

Completely Randomized (CRD): treatment
labels are shuffled across ALL positions
    t = (T̄-C̄) / (s_pooled·√(2/n)),  df = 2n-2

Fixed from the 3D source: the original 3D version placed a block's control and treatment plots at two adjacent but distinct field positions. With a linear gradient that leaves a small constant residual (gradient-slope × plot spacing) in every diff, which is not random noise — it's the same non-zero offset on every replicate. Numerically simulating 5,000 null-hypothesis (effect = 0) trials confirmed it: the 3D version rejected H₀ at α = 0.05 about 9–11% of the time instead of the correct 5%, i.e. its own "the gradient cancels" claim didn't hold. Here each block is pinned to one shared field position for both plots, which restores the textbook guarantee and the correct ~5% false-positive rate under the null.

Replicates — number of blocks (pairs of plots); more blocks shrink the standard error.
Treatment effect size — the true mean difference the experiment is trying to detect.
Measurement noise (σ) — random variability at the individual-plot level (weather, measurement error, micro-habitat).
Field fertility gradient — how strongly the underlying environment varies across the field; this is exactly the nuisance variable that blocking is designed to neutralise.
Power is estimated by re-running the whole random experiment 400 times at the current settings and measuring the fraction of runs where p < 0.05 — the "other design" and "blocking gain" boxes run the same 400 trials for the design you're not currently viewing, so you can see the benefit of blocking directly.
Drag the field panel to pan, scroll/pinch to zoom — it's a genuine spatial view of the plot row.

Top strip: field plots (drag to pan, scroll to zoom).
Middle: t-distribution & rejection region.
Bottom: Monte Carlo power, this vs. other design.