GIFSQ Tools · Module 16 — Statistics, Experimental Design & Research · Tool 318 of 500
Analyse a randomised complete block design: the treatment effect after removing the block (batch, day, operator) effect — the standard analysis when samples arrive in natural groups.
Try sample values — fills the form with the worked example below.
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F — treatments
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p-value
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Error SS
Equation: SSTreat = b·Σ(x̄ᵢ − x̄)²; SSBlock = t·Σ(x̄ⱼ − x̄)²; SSTotal = Σ(x − x̄)²; SSE = SSTotal − SSTreat − SSBlock. F = (SSTreat ÷ (t − 1)) ÷ (SSE ÷ ((t − 1)(b − 1))).
Method: Randomised complete block design ANOVA (Fisher), per Montgomery, Design and Analysis of Experiments, and ISO 16269-1. The p-value is computed from the F distribution itself (incomplete beta function).
Assumptions: every treatment appears once in every block; treatment and block effects are additive (no interaction); errors are independent, approximately normal, with equal variance.
Limitations: a missing cell breaks the design — this tool requires a complete rectangle. If treatment and block interact, the additive model misleads and a different design is needed.
Rounding: F to 4 decimal places; p to 4 decimal places; sums of squares to 2 decimal places; intermediates unrounded.
This is a calculation aid, not a laboratory report — confirm against your accredited method before citing a value.
Method: Randomised complete block design ANOVA (Fisher), per Montgomery, Design and Analysis of Experiments, and ISO 16269-1. The p-value is computed from the F distribution itself (incomplete beta function).
Assumptions: every treatment appears once in every block; treatment and block effects are additive (no interaction); errors are independent, approximately normal, with equal variance.
Limitations: a missing cell breaks the design — this tool requires a complete rectangle. If treatment and block interact, the additive model misleads and a different design is needed.
Rounding: F to 4 decimal places; p to 4 decimal places; sums of squares to 2 decimal places; intermediates unrounded.
This is a calculation aid, not a laboratory report — confirm against your accredited method before citing a value.
Worked example: 4 treatments × 3 blocks, values (12,15,11), (15,17,16), (10,13,9), (18,19,17): SSTreat = 97.33, SSBlock = 17.17, SSE = 4.17, F = 46.7200, p = 0.0001.
Enter values above to see results.
Blocking only helps if the blocks really differ — check the block sum of squares too. Tool 318 of 500 — GIFSQ
