Treatment Sum Of Squares Research Articles

AMMI and GGE biplot analysis for barley genotype yield performance and stability under multi environment condition in southern Ethiopia

AbstractBarley (Hordeum vulgare L.) is a major grain crop farmed in Ethiopia throughout the long rainy season (Meher) and the short rainy season (Belg) of the year. Barley genotypes were subjected to multi‐environment experiments in six different settings to identify stable genotypes and estimate the impact of genotype × environment interaction (GEI) on grain production. In each area, the field experiment was conducted from mid‐July to January during the primary cropping season of 2021. Three replications of a randomized complete block design were used to set up the trials. According to the additive main effects and multiplicative interaction (AMMI) study, genotype (18.19%), GEI (22.98%), and environment (58.83%) all had an impact on the major treatment sum of squares. The more variance attributed to the environments is a sign of environmental diversity. Given that the two interaction principal component analysis (IPCAs) accounted for 76.94% of the interaction sum of squares, they were sufficient for cross‐validation of the grain yield variance explained by GEI. In contrast to the GGE biplot approaches, which indicated genotypes G12, G3, and G9 as stable and high‐yielding genotypes throughout the environments, the AMMI stability value identified genotypes G3, G12, and G9 as high yielding with stable performance across environments. In general, the GGE biplot and AMMI analysis models demonstrated that genotypes G12, G3, and G9 were stable and yielded well, making G3 acceptable for cultivation in a wider range of environments and G12 and G9 suitable for release.

Variation in Seed Quality Paramertes of Off-Season Soybean of Different Planting Dates and Varieties

The work was carried out to assess the effect of varieties and dates of sowing on seed quality parameters of soybean seed produced during off-season i.e., Rabi at Rajendranagar. The seeds of varieties AISb-50, Basara and JS-335 were used for estimation of seed quality parameters which were sown on 15th December and 15th January. The seed quality parameters differed significantly due to dates of sowing and varieties. The treatment sum of squares revealed a significant difference in germination, seedling vigour index-I, seedling dry weight, speed of germination and field emergence, whereas seedling length was non-significant for varieties. While the seedling vigour index-II and electrical conductivity showed non-significant variation in the interaction between varieties and dates of sowing. The 15th December sown crop showed higher germination (91.11%), seedling length (27.63 cm), seedling vigour index-I (2518), dry weight (95.90 mg), seedling vigour index-II (8713), speed of germination (25.05) and field emergence (89.22%). The variety JS-335 exhibited higher germination (92.83%), seedling length (27.55cm), vigour index I (2558), speed of germination (28.25%), while higher seedling dry weight and vigour index II was exhibited by Basara (94.86 mg and 8097). The amount of leachates was found in Basara with electrical conductivity of 23.82 µScm-1g-1. The interaction between dates of sowing and varieties revealed that the variety JS-335 of 15th December sown exhibited higher germination (95.33%), seedling length (28.43 cm), seedling vigour index I (2711), speed of germination (29.97) among other varieties. The variety Basara of 15th December sown crop showed higher seedling dry weight (103.93 mg) and seedling vigour index II (8936). The electrical conductivity was higher in case of Basara of 15th January (24.59 µScm-1g-1).

Solving the incomplete data problem in Greco-Latin square experimental design by exact-scheme analysis of variance without data imputation

<p>This study introduced a novel exact-scheme analysis of variance to tackle the challenge of incomplete data within the Greco-Latin square experimental design (GLSED), specifically for scenarios with a single missing observation across any treatment and block level, thus eliminating the need for conventional data imputation methods. This approach innovatively addresses and mitigates the bias in the treatment sum of squares, a significant drawback of traditional missing plot techniques, by providing a precise, exact-scheme-based formula for calculating the treatment sum of squares in fixed-effect GLSED contexts with unrecorded values. Moreover, it offers a method for correcting biased treatment sum of squares values, presenting an adjustment mechanism for instances where the least squares method was previously employed to estimate missing values. This comprehensive strategy not only enhances the methodological accuracy and integrity of GLSED studies but also contributes significantly to the field by offering a solution to navigate the complexities of incomplete datasets without resorting to data imputation, thus improving the rigor and validity of experimental designs in the face of missing data challenges.</p>

Grain Yield Potential and Stability of Soybean Genotypes of Different Ages across Diverse Environments in Southern Africa

Soybean [Glycine max (L.) Merrill] is an important crop in southern Africa where it is cultivated in a wide range of agro-ecologies. Both spatial and seasonal variability is high in the region. As a result, breeders aim to release varieties with a fine balance of high productivity potential and stability. Genotype × environment interaction (GEI) limits the selection of superior genotypes in heterogeneous environments consequently slowing down breeding progress. This study determined the magnitude of GEI effects and genotype superiority index of soybean genotypes of different ages across three countries in southern Africa. Forty-two soybean genotypes that were released between 1966 and 2013 were evaluated for two seasons at thirteen diverse locations across the three countries. Additive main effects and multiplicative interaction (AMMI) and genotype superiority index tools were used to analyse both productivity and stability performance of these genotypes. The AMMI analysis showed that grain yield variation due to genotypes, environments main effects and GEI were highly significant (p < 0.001). Environments explained the greatest proportion (77%) of the total treatment sum of squares followed by GEI (17.4%) and genotypes (5.6%), justifying the need for multi-environmental trials over many seasons in this region. The two methods were useful in discriminating and identifying common productive and stable genotypes of different ages. The top four high-yielding (>5.0 tha−1) genotypes displayed both stability and genotype superiority index. These findings have important implications for soybean genotype recommendations, breeding progress, and strategy.

ANOVA by means of divisions of treatment sum of squares into each component having degree of freedom of 1

ANOVA by means of divisions of treatment sum of squares into each component having degree of freedom of 1

The Role of Third-Party Intervention in Trade Dispute in Nigeria: A Study of Selected Universities

The study investigated the role of third-party intervention in trade dispute. Litigation is one of the popular ways of disputes settlements. Hence, there are other appropriate pragmatic and adaptive models of resolving disputes apart from litigation, such as arbitration, mediation, and conciliation. The study examined the challenges before the third party by way of conciliation, mediation and arbitration and conclude that motives of the third parties in disputes resolution are to prevent disputes, resolve it if it has developed, or manage it from being dysfunctional. Again, the choice of alternation/appropriate dispute resolution (ADR) model(s) to be employed depends on the peculiarities of the disputes. A sample size of 631.7 was determined from a population of 2,021 employees using Taro Yamme’s approach. Data obtained from pilot survey were committed to test of reliability using Cronbach alpha statistic and computed using SPSS version 19 and the result reported a Cronbach alpha of 0.771. In analyzing the data, the descriptive statistics of simple percentage, mean, Variance and Analysis of Variance (ANOVA) were adopted to answer the research questions and test the hypotheses. To further this research, F- value was used to calculate the test statistics, treatment mean square (TRMS), Error mean Square (EMS), and Treatment Sum of Squares (TRSS) at 5% significant level. The study however concludes that the role of third Party and the resolution model(s) it uses have significant impact in dispute resolution. Thus, recommended these model(s) in settling disputes because it is convenient, cheap, flexible, adaptive, dignity-protecting, less time-consuming, friendly enhancing, among others. Immediate and remote causes of dispute should be properly addressed and substantive effort should be made towards reducing disputes in the institutions because of its negative consequences.

Comparison of Non-parametric Stability Statistics for Selecting Stable and Adapted Soybean Genotypes under Different Environments

The objectives of this study were to investigate the comparison among non-parametric stability statistics and to evaluate seed yield stability of the sixteen soybean genotypes across four locations during the 2016, 2017 and 2018 growing seasons in Egypt. All trials were laid down in a randomized complete block design (RCBD) with three replications. The AMMI analysis showed ahighly significant effect of genotype (G), environment (E) and G x E interaction (GEI). The major contributions to treatment sum of squares were GEI, followed by G and E. The AMMI analysis also partitioned the total GEI component into eleven PCAs and Residual. The first eight PCAs were highly significant and accounted for about 99.56% of the total GEI. Based on the static and dynamic concepts, the results of spearman’s rank correlation and PCA showed that stability measures could be classified into three groups. The non-parametric stability statistics i.e., YSi, KR, TOP, RSM and δgy related to the dynamic concept and strongly correlated with mean seed soybean yield of stability. While, the other non-parametric stability statistics (Si(1) ,Si(2) ,Si(3) and Si(6),NPi(1) ,NPi(2) ,NPi(3) and NPi(4) , δr, MID, LOW) represented the concept of static stability, which were influenced simultaneously by both yield and stability. The non-parametric stability statistics in each the groups I, II, and III were positively and significantly correlated with each other, thus; any of these parameters could be considered as appropriate alternatives for each other. According to cluster analysis, soybean genotypes G6, G4, G8, G11, G9, G1, G7 and G2 were more stable varieties on the basis of mean seed yield and non-parametric stability statistics. In conclusion, both yield and stability should be considered simultaneously to exploit the useful effect of GEI and to make the selection of genotypes more precise and refined. Thus, the YSi, KR, TOP, RSM and δgy were more useful statistics in soybean breeding programmes and could be useful alternatives to parametric stability statistics. According to most non-parametric stability statistics, the genotypes G6 and G11 were more stable coupled with high seed yield; therefore, these genotypes might be used for genetic improvement of soybean and they must be released in studied regions and other regions in Egypt.

ANALISIS VARIANSI PADA RANCANGAN BUJUR SANGKAR YOUDEN DENGAN DUA DATA HILANG

Youden Square Design (YSD) is an incomplete latin square design with at least one row/column which can’t run in an experiment. In this research we took 5x4 YSD (one column is not runned in an experiment). This design has a balance characteristic from a balanced incomplete block design where all treatments appears with the same number in each row. Missing data can occur in YSD. In this discussion, YSD with two missing data was used. Missing data is estimated by an iterative method then we arrange analysis of variance and LSD test. Analysis of variance with two missing data in YSD is calculated by adjusting the treatment sum of squares with it’s bias value and the total degrees of freedom and error degrees of freedom are substracted by two. LSD test is carried out if the treatment has a significant effect to the response. To clarify the discussion in YSD, example of application in the field of industry is given by observing the effect of the assembly method to the length of assembly time of X component. The assembly method has an effect to the length of assembly time of X component and if the missing data are and so the suggested assembly method is E method because it has the fastest average assembly time. Keywords: YSD, Missing Data, Analysis of Variance, LSD Test

Stability Parameters and AMMI Analysis of Quinoa ( Chenopodium quinoa Willd.)

SCREENING for stable genotype entails estimating the genotype (G)×environment (E) interaction (GEI) in multi-environmental trials (MET). Quinoa is a nutritionally rich crop as a source of vitamins, minerals and essential amino acids. It has been introduced to many countries in diverse regions worldwide. We evaluated five genotypes of quinoa under ten environments including irrigated and rain-fed conditions across Egypt. We used several stability parameters as well as additive main effects and multiplicative interaction (AMMI) analysis to determine the best genotype for each environment/location across Egypt. Based on AMMI analysis of variance, the sum of squares (SS) of E, G, and GEI explained ≈ 78%, 14%, 8%, respectively, of the treatment sum of squares. The SS of interaction principal components analysis axis1 (IPCA1) and IPCA2 explained 75 and 18%, respectively. KVL-SRA3 was the most stable genotype according to ecovalence value (Wi), to deviation from regression coefficient value (S2di) of Eberhart and Russell and to IPCA1, IPCA2 and AMMI stability value (ASV). Regalona was the most unstable genotype based on the same parameters. These results were visualized using AMMI biplot analysis, which revealed that KVL-SRA3 was widely adapted to all environments unlike Regalona that was poorly adapted to most environments. The Spearman’s rank correlation among different stability parameters was significantly variable for both the five-quinoa genotypes and the ten investigated environments. Our results indicated that most stability parameters were consistent with AMMI parameters in identifying stable genotypes with some exceptions according to the concept of each of stability parameter (agronomic or biological). This study is an important step to open doors for the adoption of an extraordinary nutritional crop in Egypt.

Stability analysis for grain yield of coriander (Coriandrum sativum L.) genotypes in Bale, South-East Ethiopia

Yield data of 10 coriander ( Coriandrum sativum L.) genotypes tested across 9 rain-fed environments during the 2014-2016 growing season using RCBD in 3 replications were analyzed using the AMMI model. The AMMI analysis tested in nine environments (years) were showed that the yield was significantly affected (P<0.001) by genotypes and environment main effects as well as GxE interaction. The model revealed that differences between the environments accounted for about 58.16% of the treatment sum of squares. The genotypes and the GxE interaction also accounted significantly for 12.79 % and 29.05% respectively of the treatment SS. The first principal component axis (PCA1) of the interaction captured 41.97% of the interaction sum of squares. Similarly, the second principal component axis (PCA2) explained a further 39.05% of the GEI sum of squares. The mean squares for the PCA1 and PCA2 were significant at P=0.01 and cumulatively contributed to 81.02% of the GxE interaction SS, leaving 18.98% of the variation in the GxE interaction in the residual. The AMMI and AMMI stability value (ASV) identified G8 and G3 as the stable and high yielding genotypes. Therefore, release of these genotypes for production in the mid and lowlands of Bale will result in increased production and productivity of coriander in the country.

Multivariate analysis for adaptability and yield stability of rapeseed (Brassica napus L.) strains in different agro-climatic zones

Plant breeders always look for high yielding genotypes based on both genotype and G ? E (interaction of genotype with environment) for stability and adaptability in diversified environmental conditions. This present study consists of eight Brassica napus L. strains using RCBD design with three replications and conducted at eight locations in Punjab province, Pakistan to determine general and specific adaptability in 2014-2015. Additive main effects and multiplicative interactions (AMMI) study showed that the environments (86.65%) have more influence to treatment sum of squares as compare to the interaction of genotype with environment (9.4%) and genotypes (2.65%) respectively, indicating the presence of adequate genetic variation for useful selection to identify stable genotypes. G x E interaction was further partitioned by principal component analysis (PCA). The first four multiplicative axis terms (IPCA1, IPCA2, IPCA3 and IPCA4) give detailed 54.0%, 28.0%, 9.9% and 5.6% of GEI sum of squares (SS), respectively. The AMMI method was used to recognize suitable genotype / genotypes to specific locations / environments. The results showed that genotypes RBN-08004, RBN-04021 and 11-CBN 006 were more stable with the lowest interaction and have general adaptability with yield near about their mean yield. Genotype RBN-08004 has more than average yield, IPCA value closer to zero (1.8), genotype selection index (GSI) is 4 and least AMMI stability value (ASV) of 3.6 therefore considered the most stable. According to AMMI analysis, KN-253, KN-256 and RBN-08004 (adaptive group 1) exhibited specific adaptability for Bhakar and Khanpur with yield greater than mean and positive interaction. Genotype RBN-04047 (adaptive group 2) which has yield lesser than mean yield and positive interaction showed specific adaptability for Chakwal and Karore. It was observed that stability evaluation through AMMI analysis may be used for selection of genotypes from experiments performed under different environmental conditions.

Stability analysis for grain yield of black cumin (Nigella sativa L.) genotypes in Bale, South-East Ethiopia

Yield data of 12 black cumin ( Nigella sativa L.) cultivars tested across 9 rain-fed environments during the 2013-2015 growing season using RCBD in 3 replications. The AMMI analysis tested in nine environments (years) were showed that the yield was significantly affected (P<0.001) by genotypes and environment main effects. But non significant for GxE interaction. The model revealed that differences between the environments accounted for about 90% of the treatment sum of squares. The genotypes and the GxE interaction also accounted significantly for 4% and 6% respectively of the treatment SS. The first principal component axis (PCA 1) of the interaction captured 51.32% of the interaction sum of squares. Similarly, the second principal component axis (PCA2) explained a further 18.20% of the GEI sum of squares. The mean squares for the PCA 1 and PCA 2 were significant at P=0.01 and cumulatively contributed to 69.52% of the GxE interaction SS, leaving 30.37% of the variation in the GxE interaction in the residual. The AMMI and AMMI stability value (ASV) identified G10 as the most stable and high yielding genotype.

Evaluation of Performance of Introduced Yam Bean (Pachyrhizus spp.) in Three Agro-Ecological Zones of Rwanda

The yam bean (Pachyrizhus spp) was recently introduced as a root crop with high-yield potential, considerable protein and micro-nutrient concentration to investigate its potential for food production in Rwanda. Except for Chuin types (Pachyrizhus tuberosus) which have high storage root dry matter (RDM) (26 to 36%), most accessions are consumed raw and are reported to have low RDM. The present study aimed to evaluate and identify adapted high yielding yam bean accessions in major agro-ecological zones of Rwanda. Field experiments with 22 accessions were conducted in 2012 at three research sites representing the major agro-ecologies of Rwanda. Strict reproductive pruning was followed to enhance fresh storage root yields. Across locations, ANOVA indicated highly significant differences (p < 0.01) for genotypes (G), locations (L), seasons (S) and G x L effects for storage root yield, vine yield and harvest index and accounted for 21.88%, 43.41%, 1.43% and 13.25% of the treatment sum of squares, respectively. The GGE bi-plot revealed that EC209018 is high yielding but unstable. However, genotypes, AC209034, AC209035 and EC209046, were outstanding in terms of adaptation and relative stability across the 3 locations, suggesting consistent root yields irrespective of location and environmental conditions. The GGE scatter plot showed that all genotypes formed one mega-environment for storage root yield (Karama, Musanze and Rubona) and two mega-environments for biomass yield (Karama and Rubona as one mega-environment and Musanze the second one). This study revealed that Karama is the most suitable environment for evaluation and selection of yam bean for yield components in Rwanda.

Proportional subclass numbers in two-factor ANOVA

ABSTRACTThe between-within split of total sum of squares in one-way analysis of variance (ANOVA) is intuitively appealing and computationally simple, whether balanced or not. In the balanced two-factor setting, the same heuristic and computations apply to analyse treatment sum of squares into main effects and interaction effects sums of squares. Accomplishing the same in unbalanced settings is more difficult, requiring development of tests of general linear hypotheses. However, textbooks treat unbalanced settings with proportional subclasss numbers (psn) as essentially equivalent to balanced settings. It is shown here that, while psn permit an ANOVA-like partition of sums of squares, test statistics for main effects of the two factors generally test the wrong hypotheses when the model includes interaction effects.

Stability analysis of pigeon pea genotypes by deployment of AMMI model under rainfed environment

Twenty one genotypes of pigeon pea were evaluated in a randomized complete block design during the Kharif season of 2007-08, 2008-09 and 2009-10 based upon number of primary branches per plant, pod length, number of grains per pod, 100-seed weight and seed yield per plant. The stability was studied by deploying AMMI (additive main effects and multiplicative interaction) model. The significant differences among the years were observed and measured more than 50% of the treatment sum of squares. First principal component axis (PCA1) of the interaction captured more than 60% of the interaction sum of squares for almost all the traits studied. The mean seed yield per plant was found highest (39.15 g) and at par similar in all the three years. Nine stable and high yielding genotypes viz., PUSA 2003-1; CORG-2001-5; WREG- 28; PANT-A-286; H-94-6; GT 101; ICPL-99004; ICPL-85010 and UPAS-120 exhibited stable performance under the rainfed environmental conditions for more than one traits studied and also under more than one year.

Stability performance of extra early maturing maize (Zea mays L.) varieties under high and low nitrogen environments in Sudan Savanna

AbstractEvaluating stability performance and range of adaptation is becoming increasingly important. If cultivars are to be selected for a large group of environments, stability and mean yield across all environments are more important than yield for specific environments. This study was conducted to assess the stability of 3 extra early maize under high and low nitrogen environments. The experiments were conducted at two locations in 2009 and 2010 wet season under high and low N applications. Additive Main Effect and Multiplicative Interaction (AMMI) and GGE biplot were used to assess the genotype-by-environment interactions. The mean square analysis reveals a significant difference for environments effect and a lack of significant mean squares for varietal effects under high and low N and across the research environments. 2004-SYNEEW gave the highest grain yield under combined analysis. Environment sum of squares under AMMI model accounted for about 98.79% of the treatment sum of squares. The first PCA ...

Genetic Variability in Growth and Seed Traits of Jatropha curcas L. Germplasm for Genetic Tree Improvement

A 23 candidate plus trees of Jatropha curcas were selected from the states of Maharashtra, Chhattisgarh and Haryana in India. A total 14 seed traits and growth parameters were measured and their genetic values and correlation was calculated to serve as base information for further tree improvement and breeding program of J. curcas. Significantly treatment sum of squares were observed for all these traits under the study indicating an existence of a substantial variability revealed high PCV and GCV values for number of branches, number of primary branches, initial collar diameter of plant and seed yield per plant. The PCV values were higher than GCV values for all the traits, while the difference between PCV and GCV magnitude were minimum for number of seeds per fruit. High heritability was observed for number secondary branches and seed yield per plant with high genetic advance. These traits may be considered for selection and improvement of Jatropha accessions/genotypes. Positive and significant correlation exists between number of fruit per plant, number seed per fruit, 100 seed weight and seed yield. Accessions RJ-88, RJ-90, RJ-92, RJ-93, RJ- RJ-123, RJ-124 and RJ- 133 showed above average higher values for growth and seed traits attributes (viz. number of secondary branches, number of fruits per plant, 100 seed Test weight, shelling percentage, oil content and seed yield per plant. Identified promising genotype with favorable traits for future establishment of elite seedling seed orchard for varietal and hybridization programme of tree.

Genotype × environment interaction effects on early fresh storage root yield and related traits in cassava

Cassava (Manihot esculenta Crantz) is an important root crop worldwide. It exhibits substantial differential genotypic responses to varying environmental conditions, a phenomenon termed genotype×environment interaction (GEI). A significant GEI presents challenges in the selection of superior genotypes. The objective of this study was to examine the effect of genotype, environment and GEI on early fresh storage root yield (FSRY) and related traits in cassava. Accordingly, 12 cassava genotypes were evaluated in a randomised complete block design at three contrasting locations (Jinja, Nakasongola and Namulonge) in Uganda. Trials were harvested nine months after planting and the data collected were analysed using the additive main effects and multiplicative interaction (AMMI) model. The AMMI analysis of variance showed significant variation among genotypes for early FSRY and all other traits assessed. Locations were significantly different for all traits except for cassava brown streak disease root necrosis. The GEI effect was non-significant for early FSRY, but significant for other traits. For early FSRY, 48.5% of the treatment sum of squares was attributable to genotypes, 27.3% to environments, and 24.1% to GEI, indicating a predominance of genotypic variation for this trait. Predominance of genotypic variation was also observed for all the other traits. A majority of the genotypes (67%) had low interaction effects with locations for early FSRY, with Akena, CT2, CT4 and NASE14 being the most stable genotypes for the trait. Significant negative correlation was observed between cassava mosaic disease severity and early FSRY and storage root number, indicating significant negative effects of cassava mosaic disease on early FSRY and stability in cassava. The information generated will inform future selection initiatives for superior early-yielding cassava genotypes combining resistance to cassava mosaic and brown streak diseases in Uganda.

Comments on the Neyman–Fisher Controversy and Its Consequences

The Neyman-Fisher controversy considered here originated with the 1935 presentation of Jerzy Neyman's Statistical Problems in Agricultural Experimentation to the Royal Statistical Society. Neyman asserted that the standard ANOVA F-test for randomized complete block designs is valid, whereas the analogous test for Latin squares is invalid in the sense of detecting differentiation among the treatments, when none existed on average, more often than desired (i.e., having a higher Type I error than advertised). However, Neyman's expressions for the expected mean residual sum of squares, for both designs, are generally incorrect. Furthermore, Neyman's belief that the Type I error (when testing the null hypothesis of zero average treatment effects) is higher than desired, whenever the expected mean treatment sum of squares is greater than the expected mean residual sum of squares, is generally incorrect. Simple examples show that, without further assumptions on the potential outcomes, one cannot determine the Type I error of the F-test from expected sums of squares. Ultimately, we believe that the Neyman-Fisher controversy had a deleterious impact on the development of statistics, with a major consequence being that potential outcomes were ignored in favor of linear models and classical statistical procedures that are imprecise without applied contexts.

Pattern in interaction in the maize yield trial

In making decisions on the development of varieties and the identification of certain growing regions, the effects of genotype (G) and genotype by environment (GxE) are very important. Although the main genotype effect and the interaction effect should be partitioned, there is still a need for their integration in the yield, as both simultaneously affect a ranking of the particular genotype within a certain environment. The AMMI (Additive Main Effect and Multiplicative Interaction) analysis, as a hybrid model, provides appropriate partitioning. The AMMI2 model, capturing 98.4% of the treatment sum of squares, was used, and 12 observed environments were classified into three target environments. Hence, out of 15 commercial maize hybrids, used in the trial, the hybrids ZP-677, ZP-570 and ZP-732 were selected as carriers of maximum yields in three target environments. In this way, it was shown that even in a relatively small region a narrow adaptation of genotypes can be exploited.