Experience in Use Alpha Lattice Design in Pakistan

Field trials on each wheat, maize and potato were conducted for three years Viz. 2011 to 2014 in Agricultural Research Institute, Tarnab, Peshawar, Pakistan to gauge the efficiency of Alpha Lattice Design (ALD) in comparison to randomized complete block design. The results emphasize that randomized complete block (RCB) design should be replaced by alpha lattice when treatments exceed ten due to the less reliability of homogenous blocks under circumstances. Results depicted that Alpha Lattice design provide better control on experimental variability among the experimental units under field conditions. Improvement in the precision level in terms of decline in the mean square error, coefficient of variation and standard error of difference were recorded for the ALD. The coefficient of variation (CV) calculated for wheat, maize and potato yield trials were (9.20, 17.8 and 14.5) for alpha lattice and (17.32, 23.70 and 18.53) for RCB design respectively. The standard error of mean squares calculated for these trials were (292, 3.67 and 2.41) for alpha lattice and (437, 5.40 and 3.23) for RCB design respectively. The relative efficiency of trials shows that alpha lattice design was more efficient than RCB design. The value of relative efficiency (1.49, 1.47 and 1.34) indicates that the use of alpha lattice design instead of randomized complete block design (RCBD) increased experimental efficiency by 49, 47 and 34 percent respectively.

Heliyon, 2021

Plant breeding experiments require the use of appropriate experimental designs that will efficiently block variation due to wide heterogeneity nature of tropical soils. The primary objective of this study was to assess the effectiveness of eight different alpha-lattice designs relative to randomized complete block design for evaluating 108 genotypes of maize under rainforest agro-ecology. The maize genotypes were field-tested using three replications at two locations. Data were collected on grain yield and other agronomic traits. Data collected were subjected to analysis of variance (ANOVA) assuming randomized complete block design (RCBD) and eight alphalattice designs. Pearson's correlation and stepwise multiple regression analyses were used to analyze relationship among different designs and efficiency of the lattice designs over RCBD was computed. Result showed that all the alpha lattice designs except 27 Â 4 were effective in evaluating the genotypes for plant height. There was significant difference (p < 0.001) among genotypes for grain yield only when data were analyzed based on 9 Â 12 alpha lattice design. In addition, results showed that the proportion of variation due to blocking and R-square values of the model increased with increase in the number of blocks for grain yield. In contrast, coefficient of variation decreased with increase in the number of blocks. The result showed an increase in efficiency of the alpha lattice designs as the number of blocks increased. It could then be concluded that the more the number of blocks within replicate, the proportion of total variation due to blocking increased, the coefficient of variation (CV) reduced, coefficient of determination (R-square) increased and thus, effectiveness increased. Appropriateness of designs was trait dependent. The 9 Â 12 alpha lattice design was identified to be the best in the evaluation of grain yield for the maize genotypes.

Three trials of each wheat, maize and potato were conducted from 2011 to 2014 in Agricultural research institute, Tarnab, Peshawar, Pakistan to evaluate the efficiency of alpha lattice design in field experiments. The results emphasize that the traditional randomized complete block designs (RCBD) should be replaced by alpha lattice in the agricultural field experiments when number of varieties to be tested in an experiment increases to more than ten. In such a situation finding a homogeneous block is quite difficult in field experiments. Alpha designs are used for field trials because they provide better control on experimental variability among the experimental units under field conditions. The results show improvements in the precision level in terms of decline in the mean square error, coefficient of variation and standard error of difference. The coefficient of variation (CV) calculated for wheat, maize and potato yield trials are (9.20, 17.8 and 14.5) for alpha lattice design and (17.32, 23.70 and 18.53) for RCBD respectively. The standard error of mean squares calculated for these trials are (292, 3.67 and 2.41) for alpha lattice design and (437, 5.40 and 3.23) for randomized complete block design (RCBD) respectively. The relative efficiency of trials shows that alpha lattice design was more efficient than RCBD. The value of relative efficiency (1.49, 1.47 and 1.34) indicates that the use of alpha lattice design instead of randomized complete block design (RCBD) increased experimental efficiency by 49, 47 and 34 percent respectively.

Journal of Scientific Research, 2010

Journal of Cereal Research, 2022

To decrease errors and increase the precision and efficacy of crop improvement programmes, a quality experimental design is required in addition to breeding methods. In this study, ninety-six oat genotypes used to examine the relative efficiency of randomized complete block design (RCBD) and alpha lattice design (ALD). Effectiveness of ALD over RCBD was determined for green forage yield per plant and seed yield per plant. Genotypes were sown in three replications during two consecutive years 2019-20 and 2020- 21. The results of each year of experiment showed >1.0 relative efficiency for ALD while in pooled environment of each trait relative efficiency changed drastically might be due to high and significant genotype X environment interaction for studied traits. Multi-environment trials are the major concerned for evaluation of entries for economic traits. So as a consequence RCBD should be substituted by ALD in crop field experiments.

This investigation was conducted in 2010/11 and 2011/12 growing seasons at the experimental farm of the Faculty of Agriculture, Cairo University, Giza, Egypt. Twenty Egyptian bread wheat cultivars were evaluated in an alpha lattice design with three replications for nine characters. The aim was to compare the relative efficiency of two experimental designs based on error mean squares. In field trials, variation in soil fertility can result in substantial heterogeneity within blocks and thus, poor precision in treatment estimates resulted. For this purpose, two datasets were analyzed according to alpha lattice design and randomized complete blocks design (RCBD). For the two trials, alpha lattice design exhibited more efficient than randomized complete blocks design in reducing both the error mean squares and the coefficient of variation consequently, an efficient estimation of treatment differences, than RCBD. Average estimated relative efficiency (RE) was 9.5, 28.5, 30.0, 22.5, 40.0, 30.5, 35.0 and 28.5% for plant height, number of tillers plant-1 , spike length, number of spikelets spike-1 , number of grains spike-1 , 1000-grain weight, grain yield plant-1 and grain yield feddan-1 , respectively, indicating that the high precision to estimate treatment effects is gained significantly from using an alpha lattice design instead of RCBD. Whereas RE value of 0.98 for days to 50% heading indicated that the precision of both alpha lattice design and RCBD was similar. Mean rank comparisons for both RCBD and alpha lattice design were performed. The ranks were not constant across the experiments. The results showed that the traditional RCBD should be replaced by alpha lattice in the agricultural field trials when the number of treatments to be tested in an experiment increases to more than ten, where a homogeneous block is quite difficult to find in field experiments. INTRODUCTION A correct experimental design is as important as a correct statistical analysis in order to obtain valid and reliable conclusion from field experiments. Certain restrictions must be imposed when the plots are arranged in order to be able to accurately estimate the errors. The choices of experimental design as well as of statistical analysis are of huge importance in field experiments. These are necessary to be correctly in order to obtain the best possible precision of the results. Wheat breeders and agronomists are faced a problem, how to select and evaluate the available experimental designs. The available literature of the efficiency of lattice designs relative to the randomized complete blocks design in wheat variety trials was very rare. The efficiency of one analysis over another is usually measured in terms of reduced error variance, expected error mean squares, or standard error of the difference between genotype means (Cochran and Cox, 1957, Binns 1987 and Magnussen 1990). The randomized block, latin square, and other complete block types of experiments are inefficient for comparing large number of treatments, because of their failure to adequately minimize the effect of soil heterogeneity (Lentner and Bishop 1993). Also, when the number of factors and/or levels of the factors increase, the number of treatment combinations increase very rapidly and it is not possible to accommodate all these treatment combinations in a single homogeneous block. Incomplete block designs arrange the total number of varieties in relatively small blocks that contain fewer varieties. Consequently, there is a gain in precision due to use of small blocks. As far as the layout of the incomplete block designs are no more difficult than randomized blocks. Some extra planning is involved in drawing up and randomizing the experimental plan. Randomized complete block design (RCBD) is affordable when the block size is less than eight varieties/treatments. It is always useful to use alpha lattice when the number of varieties/treatments increases. As a result of use a large number of treatments, estimate of experimental error is inflated and results are low in precision, so the use of RCBD is unsuitable when the

This study examined the significant difference in the mean yield of maize in Ogun State, Nigeria with respect to the effect of fertilizer's proportion and maize varieties. For the successful execution of this research work, secondary data was collected from Ogun State Agricultural Development Programme (OGADEP), Department of Agriculture Production Survey (APS), Ogun State. There were four levels of fertilizer's proportion (50kg, 100kg, 150kg and 200kg) and three levels of maize variety (Open Pollinated, Hybrid and Local Maize). Data collected was analyzed electronically using SPSS version 21. The analysis techniques employed was a Randomized Completely Block Design (RCBD) without replicates. Results from the analysis revealed that there is significant difference in the effect of the fertilizer's proportions and maize varieties on the yield of maize in Ogun State, Nigeria. The multiple comparisons test for fertilizer proportion indicates the significant difference to be between 50kg & 200kg fertilizers and between 100kg & 200kg fertilizers. However, an evaluation of the marginal mean revealed the 200kg fertilizer to be the most suitable. The multiple comparisons test for maize varieties indicates the significant difference to be between Open pollinated and Hybrid maize. However, an evaluation of the marginal mean revealed the Hybrid type of maize to be the most suitable

2013

This investigation was conducted in 2010/11 and 2011/12 growing seasons at the experimental farm of the Faculty of Agriculture, Cairo University, Giza, Egypt. Twenty Egyptian bread wheat (Triticum aestivum L.) cultivars were evaluated in an alpha lattice design with three replications for nine characters. The aim was to compare the relative efficiency of two experimental designs based on error mean squares. In field trials, variation in soil fertility can result in substantial heterogeneity within blocks and thus, poor precision in treatment estimates resulted. For this purpose, two datasets were analyzed according to alpha lattice design and randomized complete blocks design (RCBD). For the two trials, alpha lattice design exhibited more efficient than randomized complete blocks design in reducing both the error mean squares and the coefficient of variation consequently, an efficient estimation of treatment differences, than RCBD. Average estimated relative efficiency (RE) was 9.5, 28.5, 30.0, 22.5, 40.0, 30.5, 35.0 and 28.5% for plant height, number of tillers plant-1, spike length, number of spikelets spike-1, number of grains spike-1, 1000-grain weight, grain yield plant-1 and grain yield feddan-1, respectively, indicating that the high precision to estimate treatment effects is gained significantly from using an alpha lattice design instead of RCBD. Whereas RE value of 0.98 for days to 50% heading indicated that the precision of both alpha lattice design and RCBD was similar. Mean rank comparisons for both RCBD and alpha lattice design were performed. The ranks were not constant across the experiments. The results showed that the traditional RCBD should be replaced by alpha lattice in the agricultural field trials when the number of treatments to be tested in an experiment increases to more than ten, where a homogeneous block is quite difficult to find in field experiments.

Euphytica, 1980

Efficiencies of lattice designs, check plot designs, and moving means were compared in seven environments for control of error in wheat breeding trials. Lattice analyses of lattice designs and check plot covariance analyses of check plot designs gave similar CV's and intra-site heritabilities and were superior to direct RCBD analyses of these designs. Moving mean covariance analyses were generally only slightly less efficient than lattice analyses or check plot covariance analyses. Differences between designs and methods ofanalysis, which were evident on an intra-site basis, were not evident from combined analyses indicating that genotype x environment interaction is much more important than intra-site error in limiting progress from selection, Moving mean covariance analyses with 2 replicates per location and as many locations as feasible is suggested as a useful strategy for early generation wheat breeding trials.

Two field experiments were conducted at Giza Research Station, ARC, Egypt, during 2013/14 and 2014/15 seasons. Twenty faba bean genotypes were evaluated in this study in an Alpha Lattice design with three replications for seven traits. The aim was to assess the efficiency of two experimental designs to minimizing experimental error and the coefficient of variation for yield variable, and to identify the more suitable design. Thus, data were analyzed according to alpha lattice design and randomized complete blocks design (RCBD). The results showed an improvement in the precision level thought decline in both the mean square error and the coefficient of variation. The relative efficiency (R.E.%) of trials showed that alpha lattice design was more efficient than RCBD. The estimated average of R.E.% indicated that the use of alpha lattice design instead of RCBD increased the experimental accuracy by 10.46, 8.01, 22.47, 13.60, 17.56 and 55.00% for days to 50% maturity, plant height, number of branches/plant, 100-seed weight, seed yield/plant and seed yield ard/fed, respectively. Mean rank comparisons for both randomized complete block and alpha lattice design were performed. Data showed that the ranks for both designs were not constant across the experiments. Generally, the results showed that the traditional RCBD should be replaced by alpha lattice in the agricultural field trials when the number of treatments tested in an experiment is high, where a homogeneous block is quite difficult to find in field experiments. Results performed that the estimation of heritability according to alpha lattice was higher than the RCBD; therefore, the results indicated a greater efficiency for alpha design, enabling more precise estimates of genotypic variance, greater precision in the prediction of heritability in broad sense.