Randomized Complete Block Design Analysis

Randomized complete block design analysis compares treatments that were each applied once within every block, removing block-to-block variation from the error term with a two-way additive ANOVA.

난괴법(완전 확률화 블록 설계) 분석은 모든 처리를 각 블록 안에서 한 번씩 적용한 실험에서 이원 가법 분산분석으로 블록 간 변동을 오차에서 제거하고 처리 효과를 비교합니다.

Each of my six batches of raw material was split and run under all four machine settings; do the settings differ in output after accounting for batch?

원료 여섯 배치를 각각 나눠 기계 설정 네 가지로 모두 돌려 봤는데, 배치 차이를 감안하면 설정에 따라 생산량이 다른가요?

Fit a two-way additive ANOVA with treatment and block, test the treatment effect against the residual mean square, and check additivity with Tukey's one-degree-of-freedom test. Report the relative efficiency of blocking versus a completely randomized design and use Tukey HSD for pairwise treatment comparisons.

When to use Randomized Complete Block Design Analysis

• Experimental units were grouped into homogeneous blocks and every treatment appears in every block
• Block differences such as batch, day or subject are a nuisance you want to remove
• There is one observation per treatment within each block

When to use something else

• There are two crossed blocking factors with as many levels as treatments; use a Latin square design analysis
• Many blocks lack some treatments by design; use an incomplete block design or a linear mixed model

Assumptions and requirements

• Block and treatment effects are additive (no block-by-treatment interaction)
• Errors are independent and approximately normal
• Error variance is equal across treatments
• Every treatment appears in every block; incomplete blocks are dropped and repeated cells are averaged

What the analysis reports

• ANOVA table for treatments, blocks and error
• Treatment eta squared, partial eta squared and omega squared
• Relative efficiency of the block design versus a completely randomized design
• Tukey's one-degree-of-freedom test for nonadditivity
• Tukey HSD pairwise comparisons of treatment means

How to report it

A randomized complete block ANOVA ([t] treatments, [b] blocks) showed a significant treatment effect, F([df1], [df2]) = [value], p = [value], partial eta^2 = [value]; blocking had a relative efficiency of [value], and Tukey's test for nonadditivity was not significant, F(1, [df]) = [value], p = [value].

Related methods

• Latin Square Design Analysis
• Repeated Measures ANOVA
• Friedman Test

Run Randomized Complete Block Design Analysis on Quorant