Randomized Block Design: 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

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 (Monte Carlo, n=400)

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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: pairs each block's
  control & treatment at adjacent positions
    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

Because the block design pairs each treatment plot with a control plot at the same field position, the gradient term cancels in the difference — only the true treatment effect and noise remain. In the completely randomized design the gradient does not cancel, so it inflates the variance of the effect estimate and lowers statistical power for the same replication and noise level.

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 same logic researchers use to choose a sample size before running a real field study.

Bar height = measured response.
Ground colour = field fertility (blue → low, amber → high).

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