INTRODUCTION Experimental design refers to the process by which an experiment is planned so that the appropriate data is collected and analyzed using statistical methods to achieve valid and objective conclusion Montgomery (1976). Experimental design is concerned with detailed methods of carrying out an experiment in order to achieve maximum desired response objective. In his first paper on field experimental designs, Fisher (1926) emphasized the importance of randomized arrangements in estimating experimental error and described the randomized complete block and Latin square designs. In agricultural field experimentation use of proper design play an important role in attaining precision of results. To maximize the information that can be extracted from such experiments, the use of efficient experimental design is crucial. Experimental designs have been widely used for control of experimental error. Some of the natural variations between the set of experimental units are physically handled in these designs these designs in order to make a minimum contribution to the differences between the means of treatment. Various experimental designs are available to meet the requirements of the experimenter in different practical situations in order to control the nature of variation. The best design to be used in any given situation is the one that provides the maximum precision (efficiency) for estimating the desired effects and contrasts and has a simple layout and analysis. Thus, the experimental design with adequate variability control or with minimum error variance is said to be more efficient than the one with relatively larger variance. The design, which is found to be more efficient, is used to carry out the experiments and to obtain better results. In general, the relative efficiency of one design to another is measured in relation to reduced error, expected error mean squares or standard error of difference between genotype means (Cochran and Cox, 1957, Binns 1987; Magnussen 1990). The Relative Efficiency (RE) of the design say A to another design say B denoted as RE (A:B) in experimental design is defined in terms of number of design a replicates needed to achieve same result as one replicate of design A. The design an analysis of field experiments is complicated by soil heterogeneity. In order to mitigate experimental error, an acceptable experimental design is chosen from several available designs to satisfy the requirements of the experimenter under various circumstances. MATERIAL AND METHODS The experiment was designed in a randomized, complete block design and latin square design consisting of 3 replicates for RCBD and 7 replicates for LSD with leaf samples of different sizes (10, 20, 30, 40, 50, 60, 70) as an treatment and an apple tree(variety “Red Delicious”) as an experimental unit. The leaf samples were analyzed for various macro and micro nutrients, and the results were used to compute the efficiency of experimental designs. Relative efficiency of latin square design (LSD): In estimating the efficiency of LSD over RCBD, we have to consider the type of blocks. If the LSD had been RCBB with columns as blocks it is termed as column blocking. Similarly, if LSD had been RCBD with rows as blocks it is termed as row blocking. Using rows as blocks and columns as blocks, the approximate relative accuracy of LSD over RCBD can be obtained as When the error degrees of freedom is less than 20, the precision factor is taken into account. The precision factor is computed as Therefore, when error degrees of freedom is less than 20, the relative efficiency can be estimated by the formula Where, Ee (LS) and Ee (RB) are error mean squares of LSD and RCBD respectively and n1 and n2 are their respective degrees of freedom. Since, the rows and columns are equal in number the precision factor formula holds good for both row and column blockings. If rows are the only blocks, the mean square error of the randomized block design can be calculated as But, if the columns are the only blocks, i.e. row blocking is ignored, then we obtain Where, Ec, Er and Ee are mean squares for columns, rows and error in RCBD and nc, nr and ne are their respective degrees of freedom. The efficiency of LSD relative to CRD is given as When the error degrees of freedom is less than 20, the precision factor is taken into account. The precision factor is computed as Therefore, when error degrees of freedom is less than 20, the relative efficiency can be estimated by the formula Where, Ee (LS) and Ee (CR) are error mean squares of Latin Square Design and CRD respectively and n1 and n2 are their respective degrees of freedom. Error mean square of CRD can be estimated as Where, Ec, Er and Ee are the mean squares for columns, rows and error in Latin Square, respectively and nc, nr and ne are the degrees of freedom for columns, rows and error in LSD. RESULTS AND DISCUSSION The relative efficiency of the latin square design of order 7 with number of experimental units per replication 1, 2, 3, 4, 5, 6 with respect to the randomized complete block were determined and are shown in Table 1. The study found that the latin square design was superior to the randomized complete block design to control the experimental error. The improvement in efficiency of the latin square design over randomized complete block design was 52% when the number of experimental units per replication was one. When the number of experimental units per replication was two, the efficiency of the latin square design increased by 40% over the randomized complete block design. However, with the increase in the number of experimental units per replication, the efficiency of the latin square design is reduced over the randomized complete block design. It was found that randomized complete block design was superior to Latin square design when the number of experimental units per replication were 6. Therefore, it is evident that RCBD becomes more efficient than LSD as the number of replications is increased significantly. Moreover, RCBD is more efficient than LSD in the sense that it uses relatively small amount of experimental material as compared to latin Square design. Nishu et al. (2017) also found that randomized complete block design is more effective than completely randomized design in reducing error variation, and Latin square design is superior to both completely randomized design and randomized complete block design. Syed et al. (2017) also concluded that in wheat yield trials, randomized complete block design is optimal of experimental designing compared to Latin square design