Latin Square Design
Latin square design(Lsd): In analysis of varianc context, the term “Latin square design” was first used by R.A Fisher.
Latin square design is a design in which experimental units are arranged in complete blocks in two different ways, called rows and columns and then the selected treatments are randomly allocated to experimental units within each row and each column. Such that each treatment appears exactly once in each row and once in each column.
Since this design is a square arrangement where the treatments are denoted by Latin letter. So this is named by Latin square design.
In general a Latin square is an arrangement of letters in rows and columns such that each letter appears once in each row and once each column.
Thus a Latin square is given by
Example:
i) In agricultural field experiments, LSD is used to eliminate the variation due to soil fertility difference in two perpendicular directions and then to compare the yields of several varieties of paddy or wheat. ii) In animal feeding experiments LSD may be used to remove the variation due to breeds and ages of cows and then to compare the yields of milk from cows fed on different nations.
Advantages of LSD:
i) LSD is more efficient than RBD and CRD. Since it control more of the variation than CRD or RBD. ii) Statistical analysis of data remains simple even with missing observations. iii) LSD is an complete layout needs less number of observations tan the corresponding complete layout. So LSD has adequate economy in the use of experimental material. iv) LSD covers relatively complete situations where factors can be studied simultaneously.
Disadvantages of LSD:
i) LSD is not suitable for large member of treatments. ii) Analysis of data in a LSD depends on the assumption that there in no interaction among rows, columns and treatments. So LSD is not appropriate when interactions are present in data. iii) Error d.f is relatively small
Latin square design is a design in which experimental units are arranged in complete blocks in two different ways, called rows and columns and then the selected treatments are randomly allocated to experimental units within each row and each column. Such that each treatment appears exactly once in each row and once in each column.
Since this design is a square arrangement where the treatments are denoted by Latin letter. So this is named by Latin square design.
In general a Latin square is an arrangement of letters in rows and columns such that each letter appears once in each row and once each column.
Thus a Latin square is given by
Example:
i) In agricultural field experiments, LSD is used to eliminate the variation due to soil fertility difference in two perpendicular directions and then to compare the yields of several varieties of paddy or wheat. ii) In animal feeding experiments LSD may be used to remove the variation due to breeds and ages of cows and then to compare the yields of milk from cows fed on different nations.
Advantages of LSD:
i) LSD is more efficient than RBD and CRD. Since it control more of the variation than CRD or RBD. ii) Statistical analysis of data remains simple even with missing observations. iii) LSD is an complete layout needs less number of observations tan the corresponding complete layout. So LSD has adequate economy in the use of experimental material. iv) LSD covers relatively complete situations where factors can be studied simultaneously.
Disadvantages of LSD:
i) LSD is not suitable for large member of treatments. ii) Analysis of data in a LSD depends on the assumption that there in no interaction among rows, columns and treatments. So LSD is not appropriate when interactions are present in data. iii) Error d.f is relatively small