Latin square and factorial Design

Latin Square Design It an Experimental design frequently used in agriculture research. For example an experiment has to be made through which the effects of five different fertilizers on the yield of certain crop (i.e) wheat. The varying fertility of the soil in different blocks in which experiment is going to be performed otherwise the result obtained may not be dependable because the output happens effect not only fertilizers but also fertility of the soil

Similarly there may be impact of varying seeds on yield To overcome such difficulties, the L.S design is used when two extraneous factors such as varying fertility of soil and varying seeds. In our examples each fertilizer appears five times but is used only once in each row and in each column of design The two blocking factors may be represented through rows and columns

The following is the diagrammetic form of such design in respect of 5 types of fertilizers viz., A,B,C,D &E and two blocking factors viz., varying soil fertility and varying seeds Fertility Level I II III IV V Seed Differences X1 A B C D E X2 B C D E A X3 C D E A B X4 D E A B C X5 E A B C D

Factorial Designs Factorial designs are used in experiment where the effect of varying more than one factor are to be determined. Is is of two types. They are: (I)Simple factorial design (II)Complex factorial design

Simple factorial design In this effects of varying two factors on the dependent variable, but when experiment is done with more than two factors,we can use complex design It is also termed as “two factorial design” It may be either 2x2 simple factorial design or it may be 3x4 or 5x4 Complex factorial design: Experiment with more than two factors at a time involve the use of complex factorial design

A design which considers three or more independent variables simultaneously is called a complex factorial design. In case of three factors with one experimental variable having two treatments and two control variables, each one having two levels, the design used will termed as 2x2x2 complex factorial design which will contain total of eight cells

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