Durbin Test for Balanced Incomplete Blocks
The Durbin test is a Friedman-type rank test for balanced incomplete block designs, in which each block receives only some of the treatments.
Durbin 검정은 각 블록이 처리 일부만 받는 균형 불완전 블록 설계에 쓰는 Friedman 형태의 순위 검정입니다.
Each taster rated only three of the seven products in a balanced design; do the products differ?
시식자 한 명이 일곱 제품 중 세 개만 평가하는 균형 설계였는데, 제품 간 차이가 있나요?
The Durbin test ranks observations within each block, sums the ranks for each treatment and compares those sums with their expected value under no treatment effect, scaled by the constants of the balanced incomplete block design. The statistic is referred to a chi-square or, as Conover recommends, an F distribution, and pairwise rank-sum comparisons follow.
When to use Durbin Test for Balanced Incomplete Blocks
- Each block (judge, subject, batch) can only receive a subset of the treatments in a balanced incomplete block design.
- The outcome is ordinal or not normal, so a parametric BIB analysis is doubtful.
- Sensory panels or tasting studies where each assessor evaluates only a few products.
When to use something else
- Every block receives every treatment; use the Friedman test.
- Blocks have different sizes or treatments different replication; use a mixed model.
Assumptions and requirements
- Blocks are independent of each other.
- Each block has the same number of treatments and each treatment appears equally often.
- Each pair of treatments appears together in the same number of blocks.
What the analysis reports
- Chi-square statistic T1 and F statistic T2 with degrees of freedom and p values
- Design constants (t, b, k, r, λ) and a balance check
- Pairwise comparisons of rank sums with critical difference and Holm-adjusted p values
How to report it
A Durbin test for a balanced incomplete block design (t = [value], b = [value], k = [value]) indicated that treatments differed, F([df1], [df2]) = [value], p = [value].
Related methods
Run Durbin Test for Balanced Incomplete Blocks on Quorant
- Data you need
- a table (CSV or Excel) with an outcome variable, a grouping variable and a cluster ID
- Price
- 400 credits for one analysis up to 10,000 rows (complexity level 3); larger or wider data costs more. Optional methodologist review: 1800 credits.
- Checking
- Checked by property tests in every deployment
- Before you pay
- A free pre-analysis diagnosis checks your data and gives an exact quote; nothing is deducted until you approve it.