Latin square design ( Lsd ) : In analysis of varianc context. the term “Latin square design” was foremost 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 so the selected interventions are indiscriminately allocated to experimental units within each row and each column. Such that each intervention appears precisely one time in each row and one time in each column.

Since this design is a square agreement where the interventions are denoted by Latin missive. So this is named by Latin square design. In general a Latin square is an agreement of letters in rows and columns such that each missive appears one time in each row and one time each column. Thus a Latin square is given by

Examples:

I ) In agricultural field experiments. LSD is used to extinguish the fluctuation due to dirty birthrate difference in two perpendicular waies and so to compare the outputs of several assortments of Paddy or wheat. two ) In animate being eating experiments LSD may be used to take the fluctuation due to strains and ages of cattles and so to compare the outputs of milk from cattles fed on different states.

Advantages of LSD:

I ) LSD is more efficient than RBD and CRD. Since it control more of the fluctuation than CRD or RBD. two ) Statistical analysis of informations remains simple even with losing observations. three ) LSD is an complete layout needs less figure of observations tan the corresponding complete layout. So LSD has equal economic system in the usage of experimental stuff. four ) LSD covers comparatively complete state of affairss where factors can be studied at the same time.

Disadvantages of LSD:

I ) LSD is non suited for big member of interventions.

two ) Analysis of informations in a LSD depends on the premise that there in no interaction among rows. columns and interventions. So LSD is non appropriate when interactions are present in informations. three ) Error d. degree Fahrenheit is comparatively little in a LSD. In fact. there is no mistake for Latin square. four ) Property of perpendicularity is lost by losing values in LSD.

Uses of LSD: Latin square design is used in experimentation in different manner: I ) Glass house experiments. where there may be fluctuation across the house due to light differences and along the house due to intervention differences. two ) Cow feeding experiment.

three ) Used to extinguish two immaterial beginning of variableness. four ) Field experiment.

Question: How does LSD or uncomplete three manner categorization differ from complete three manner categorization? Ans: A complete three manner categorization involves possible degree combinations. While a LSD or uncomplete three manner categorization is a design affecting observations out possible degree combinations.

Difference between LSD and RBD:

LSD differs from RBD in the undermentioned points:

I ) Where in RBD. interventions are arranged in complete blocks in one way to extinguish one immaterial beginning of variableness. In LSD interventions are arranged in complete blocks in two waies to take two immaterial beginnings of fluctuation.

two ) The figure of blocks and interventions need non be equal in RBD. While member of rows. columns and interventions must be equal in LSD. three ) RBD is a complete layout while LSD is uncomplete layout viewed from the types of blocks used.

Types of Latin squares: Harmonizing to Fisher and Yates assorted types of Latin squares are as defined below:

Standard square: A square is said to be standard square if the first row and the first column are ordered alphabetically or numerically. For illustration.

Conjugate solutions square: Two criterion squares are said to be coupled if the row of one square are the columns of the other. For illustration.

are coupled square.

Self conjugate square: A square is called self conjugate square if its agreement of rows and columns are the same. For illustration.

is self conjugate square.

Adjugate set/square: By commuting with each other the three class rows and columns and letters six set of Latin square are formed but they are non necessary different. These sets are said to be adjugate set.

Self adjugate square: A square is said to be self adjugate if the substitution of three class rows. columns and letters consequences in the same set.

Orthogonal Latin squares: Two Latin squares of same size are said to be extraneous Latin squares if each missive of one square appears precisely one time with each missive of the other square when the two Latin squares a rhenium superimposed. For illustration.

are extraneous Latin square.

Maximal figure of extraneous Latin squares of size is. Then a set of extraneous Latin squares of order is called a complete set of extraneous Latin squares. A compete set of extraneous Latin square can be constructed when is a premier figure or the power of premier figure.

Statistical analysis of LSD:

A fixed consequence theoretical account for LSD is given by

Premise:

I ) and are unknown parametric quantities

two ) There is no interaction consequence between rows. columns and intervention.