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Latin Square Design. Price Valuations for 8 Varieties of Tea, Prepared on 8 Days in 8 Orders Harrison and Bose (1942), Sankhya , Vol6,#2,pp151-166. Data Description. Response: Mean Price Valuation among 6 judges 8 Tea Varieties (Crossing of Seed and Field Type):

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latin square design

Latin Square Design

Price Valuations for 8 Varieties of Tea, Prepared on 8 Days in 8 Orders

Harrison and Bose (1942), Sankhya, Vol6,#2,pp151-166

data description
Data Description
  • Response: Mean Price Valuation among 6 judges
  • 8 Tea Varieties (Crossing of Seed and Field Type):
    • 4 jats (tea seed) – BJ,KK,PG,CH
    • 2 Field Types - Pruned previous December, Unpruned
  • 8 Dates of Manufacture (7/28 – 9/29)
  • 8 Orderings of Preparation
  • All varieties prepared on each date
  • All varieties receive each order position of preparation
latin square design model
Latin Square Design - Model

Model (8 Varieties, Dates, Orders, N=82=64) :

latin square design anova f test
Latin Square Design - ANOVA & F-Test

Note: We can partition Variety SS into main effects for jat and pruning, and their interaction (next slide)

analysis of variance
Analysis of Variance

Evidence of Jat and Pruning Main Effects, Interaction not significant at 0.05 significance level

pairwise comparison of jat means
Pairwise Comparison of Jat Means

Tukey’s - q from Studentized Range Dist. k=4,n = (t-1)(t-2)=42

Note: Each Jat Mean is based on 2t=16 observations

  • Bonferroni’s Method - t-values from table on class website with n = (t-1)(t-2)=42 and C=4(4-1)/2=6

Very close to significant difference

relative efficiency
Relative Efficiency

Relative Efficiency of LS to CRD (how many times as many replicates would be needed for CRD to have as precise of estimates of treatment means as LS does):

Would need approximately 56 reps per variety to have as precise of estimates of variety means if experiment conducted as completely randomized design

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