Latin Square Design Analysis

Latin square design analysis tests treatment differences in an experiment where each treatment appears exactly once in every row and every column, removing two blocking sources of variation.

라틴방격 설계 분석은 각 처리가 모든 행과 모든 열에 정확히 한 번씩 놓인 실험에서 두 방향의 블록 변동을 제거한 뒤 처리 간 차이를 검정합니다.

I tested five fertilizers on a field laid out in five rows and five columns so each fertilizer appears once per row and column; do the fertilizers differ once row and column effects are removed?

비료 다섯 가지를 5행 5열 밭에 행과 열마다 한 번씩 배치해 실험했는데, 행과 열 효과를 빼고 나면 비료 간 수확량 차이가 있나요?

Fit an additive ANOVA with row, column and treatment terms, so the error mean square excludes variation along both blocking directions. Report the treatment F test with its effect size and follow a significant result with Tukey HSD comparisons based on the model error.

When to use Latin Square Design Analysis

• Two nuisance factors, such as day and operator or field row and column, each have as many levels as there are treatments
• Each treatment was assigned once in every row and every column
• You can assume the row, column and treatment effects do not interact

When to use something else

• Only one blocking factor is present; use a randomized complete block design analysis
• Row, column or treatment interactions are expected; use a factorial or replicated Graeco-Latin design instead

Assumptions and requirements

• Row, column and treatment effects are additive with no interactions
• Errors are independent and approximately normal
• Error variance is equal across treatments

What the analysis reports

• ANOVA table for rows, columns, treatments and error
• Treatment eta squared, partial eta squared and omega squared
• Treatment least-squares means and effects
• Tukey HSD pairwise comparisons with adjusted p values and intervals
• Check that the layout is a valid Latin square

How to report it

A [t] x [t] Latin square ANOVA controlling for [row factor] and [column factor] showed a significant treatment effect, F([df1], [df2]) = [value], p = [value], partial eta^2 = [value]; Tukey HSD indicated that [treatment] differed from [treatment] (mean difference = [value], p = [value]).

Related methods

• Randomized Complete Block Design Analysis
• Two way ANOVA
• Tukey HSD Post Hoc Test

Run Latin Square Design Analysis on Quorant