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In case of random effects models for balanced designs, the analysis is simple and no problem is encountered in testing the variance components since the sums of squares are independent, sums of squares are chi-square variates, ratio of variance components follow standard F-distribution and hence exact testing is possible. When a random effects model is considered in unbalanced designs, analysis of variance technique rarely produce exact tests for testing the hypothesis. Under the conventional normality assumptions, except for the error component, the analysis of variance fails to decompose the total sums of squares into independently distributed sums of squares. Also, sums of squares are neither chi-square variates nor multiple of chi-square variate. The sums of squares are not independent either. Another standardized measure that quantifies the difference between means and relationship between independent and the dependent variable is effect-size measure. Two generally used statistics for computing effect-size are eta and omega squared statistics. But, these statistics do not yield correct estimate of effect-size that are comparable across different designs [Bakeman (2005)]. In that scenario, generalized eta and omega statistics given by Olejnik and Algina (2003) can be used. There was a conversation on two-way factorial ANOVA with mixed effects and interactions [Nelder (1977, 1982, 1994, 2008)]. The major assessments about the two-way factorial ANOVA model is no substantial rationale for the imposed constraints on random interactions and a lack of clear interpretation of its variance components, especially for the main random effects in respect of the response [Nelder (1977), Wolfinger and Stroup (2000), Lencina et al. (2007)]. As a result, the usual model is more widely used nowadays. The unbalanced mixed ANOVA models are often analyzed under the linear mixed models (LMM) framework using the restricted maximum likelihood (REML) or generalized least squares approaches [Littell (2002), Stroup (2013), Jiang (2017)]. Kaur and Garg (2020) attempted for Computer aided construction of rectangular PBIB designs. Gupta and Sharma (2020) constructed a set of balanced incomplete block designs (BIBD) against the loss of two blocks where loss of some observations lie in between at most two common treatments. Gupta (2021) worked on nested partially balanced incomplete block designs and its analysis. Singh et al. (2021) presented mixture designs generated using orthogonal arrays. In this study, the one way random effects model for unbalanced nested design in which we have given the model, hypothesis to be tested, sums of squares and testing procedure for the hypothesis along with analysis of variance table. In the next section, we have explained model, hypothesis testing, sums of squares, hypothesis testing procedure and analysis of variance table for two way unbalanced nested design. Since in two way unbalanced case the means squares are generally not independent and are not distributed as chi-square variates, exact testing is not available for the main class variance component. We have obtained the expected size of approximate tests and the actual size for both conventional and approximate tests. Then with the help of a simulated data we found out the numerical for actual size of the conventional test and the actual and expected size of the approximate tests for some assumed values of the variance components.Under unbalanced design, testing of variance ratios are generally neither independent nor distributed as chi- square variates and does not follow standard F-distribution. In this case, exact testing of variance ratios is not available in the literature. Procedure for unbalanced data (generally not independent and are not distributed as chi-square variates) has been developed for testing the variance components in one way and two way unbalanced nested designs.Not Availabl

Application GGE biplot and AMMI model to evaluate sweet sorghum (Sorghum bicolor) hybrids for genotype x environment interaction and seasonal adaptation,”

ABSTRACT The genotype × environment interaction influences greatly the success of breeding strategy in a multipurpose crop like sweet sorghum [Sorghum bicolor (L.) Moench]. Eleven improved sweet sorghum hybrids were evaluated in both seasons for three years and genotype main effects and genotype × environment interaction (GGE) biplot analysis revealed that the hybrids that performed well in rainy season are: 'ICSSH 24' and 'ICSSH 39' and post rainy season are: 'ICSSH 57' and 'ICSSH 28'. The stable hybrid, based on additive main effects and multiplicative interaction (AMMI) and GGE biplot analysis that performed well across seasons and over the years for grain yield and stalk sugar yield is: 'ICSSH 28'

Role of big data in Agriculture-A Statistical Prospective

Not AvailableData are playing an important role making good planning and policies for agricultural growth and development. Population growth and climate change are worldwide trends that are increasing the importance of using big data science to improve agriculture. Add to that land degradation increasing marginal land and loss of biodiversity are better deals with study of big data science. Crop data can be break down into bits and bytes it will give better study about the crop development by using advance data analytics tools for betterment of agriculture. Here, talk about some important tools and techniques to handle and study the big data

GGE biplot based assessment of yield stability, adaptability and mega-environment characterization for hybrid pigeon pea (Cajanus cajan

ABSTRACT GGE biplot methodology is a powerful tool to study relationship among test environments (E), genotypes (G) and genotype-by-environment interaction (GE). Present study was conducted on 10 short-duration genotypes in five test environments for two years, and 16 medium-duration genotypes in six test locations for three years in randomized complete block design with two replications. In short-maturity group three mega-environments (ME) were found-ME1 comprised of Phaltan, Patancheru and Hyderabad1; ME2 and 3 constituted Jalna and Aurangabad, respectively. In scenario of limited resources, Patancheru may be a good testing location for general adaptability of short-duration hybrids, while Aurangabad and Hyderabad1 may be right environments for testing specific adaptation of short-duration cultivars in pigeonpea. ICPH 2433 was a winning genotype in ME1 in terms of high yield and stability. In medium-maturity group, two MEs were observed. Jalna, Jalna 1, Parbhani and Hyderabad grouped together as ME1, while Patancheru and Phaltan formed the second mega-environment (ME2). Parbhani was found to be most representative of all the six test locations. Jalna (ME1) and Phaltan (ME2) produced longest environment vectors, and hence may be regarded as highly discriminating. In mediummaturity group ICPH 2673 was found to be stable and high-yielding genotype for ME1

Forecasting of growth rates of wheat yield of Uttar Pradesh through non-linear growth models

Wheat production in India is about 70 million tonnes per year which counts for approximately 12 per cent of world’s production. Being the second largest in population, it is also the second largest in wheat consumption after China, with a huge and growing wheat demand. Major wheat growing states in India are Uttar Pradesh, Punjab, Haryana, Rajasthan, Madhya Pradesh, Gujarat and Bihar. All of north is replenished with wheat cultivation. Uttar Pradesh, the largest wheat growing region of the country, produces around 28 million tonnes of wheat and Bihar produces around 5 million tonnes. The usual parametric approach for growth rate analysis is to assume multiplicative error in the underlying nonlinear geometric model and then fit the linearized model by ‘method of least squares'. This paper deals with a critical study of wheat yield of Uttar Pradesh with a non-linear approach. The available data of rice during different years is taken into consideration and different statistical models are fitted for that. The time series data on annual yield of wheat in UP from 1970-2010 were collected from various sources. Growth rates are computed through non-linear models, viz. Logistic, Gompertz and Monomolecular models. Different nonlinear procedures such as Gauss-Newton Method, Steepest-Descent Method, Levenberg-Merquadt Technique and Do Not Use Derivative (DUD) Method were used in this study to estimate the nonlinear growth rates. The results showed that logistic model performed better followed by Gompertz and monomolecular

Multiple novel prostate cancer susceptibility signals identified by fine-mapping of known risk loci among Europeans

Genome-wide association studies (GWAS) have identified numerous common prostate cancer (PrCa) susceptibility loci. We have fine-mapped 64 GWAS regions known at the conclusion of the iCOGS study using large-scale genotyping and imputation in 25 723 PrCa cases and 26 274 controls of European ancestry. We detected evidence for multiple independent signals at 16 regions, 12 of which contained additional newly identified significant associations. A single signal comprising a spectrum of correlated variation was observed at 39 regions; 35 of which are now described by a novel more significantly associated lead SNP, while the originally reported variant remained as the lead SNP only in 4 regions. We also confirmed two association signals in Europeans that had been previously reported only in East-Asian GWAS. Based on statistical evidence and linkage disequilibrium (LD) structure, we have curated and narrowed down the list of the most likely candidate causal variants for each region. Functional annotation using data from ENCODE filtered for PrCa cell lines and eQTL analysis demonstrated significant enrichment for overlap with bio-features within this set. By incorporating the novel risk variants identified here alongside the refined data for existing association signals, we estimate that these loci now explain ∼38.9% of the familial relative risk of PrCa, an 8.9% improvement over the previously reported GWAS tag SNPs. This suggests that a significant fraction of the heritability of PrCa may have been hidden during the discovery phase of GWAS, in particular due to the presence of multiple independent signals within the same regio

MUSiC : a model-unspecific search for new physics in proton-proton collisions at root s=13TeV

Results of the Model Unspecific Search in CMS (MUSiC), using proton-proton collision data recorded at the LHC at a centre-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 35.9 fb(-1), are presented. The MUSiC analysis searches for anomalies that could be signatures of physics beyond the standard model. The analysis is based on the comparison of observed data with the standard model prediction, as determined from simulation, in several hundred final states and multiple kinematic distributions. Events containing at least one electron or muon are classified based on their final state topology, and an automated search algorithm surveys the observed data for deviations from the prediction. The sensitivity of the search is validated using multiple methods. No significant deviations from the predictions have been observed. For a wide range of final state topologies, agreement is found between the data and the standard model simulation. This analysis complements dedicated search analyses by significantly expanding the range of final states covered using a model independent approach with the largest data set to date to probe phase space regions beyond the reach of previous general searches.Peer reviewe

Measurement of prompt open-charm production cross sections in proton-proton collisions at root s=13 TeV

The production cross sections for prompt open-charm mesons in proton-proton collisions at a center-of-mass energy of 13TeV are reported. The measurement is performed using a data sample collected by the CMS experiment corresponding to an integrated luminosity of 29 nb(-1). The differential production cross sections of the D*(+/-), D-+/-, and D-0 ((D) over bar (0)) mesons are presented in ranges of transverse momentum and pseudorapidity 4 < p(T) < 100 GeV and vertical bar eta vertical bar < 2.1, respectively. The results are compared to several theoretical calculations and to previous measurements.Peer reviewe

Search for new particles in events with energetic jets and large missing transverse momentum in proton-proton collisions at root s=13 TeV

A search is presented for new particles produced at the LHC in proton-proton collisions at root s = 13 TeV, using events with energetic jets and large missing transverse momentum. The analysis is based on a data sample corresponding to an integrated luminosity of 101 fb(-1), collected in 2017-2018 with the CMS detector. Machine learning techniques are used to define separate categories for events with narrow jets from initial-state radiation and events with large-radius jets consistent with a hadronic decay of a W or Z boson. A statistical combination is made with an earlier search based on a data sample of 36 fb(-1), collected in 2016. No significant excess of events is observed with respect to the standard model background expectation determined from control samples in data. The results are interpreted in terms of limits on the branching fraction of an invisible decay of the Higgs boson, as well as constraints on simplified models of dark matter, on first-generation scalar leptoquarks decaying to quarks and neutrinos, and on models with large extra dimensions. Several of the new limits, specifically for spin-1 dark matter mediators, pseudoscalar mediators, colored mediators, and leptoquarks, are the most restrictive to date.Peer reviewe

Combined searches for the production of supersymmetric top quark partners in proton-proton collisions at root s=13 TeV

A combination of searches for top squark pair production using proton-proton collision data at a center-of-mass energy of 13 TeV at the CERN LHC, corresponding to an integrated luminosity of 137 fb(-1) collected by the CMS experiment, is presented. Signatures with at least 2 jets and large missing transverse momentum are categorized into events with 0, 1, or 2 leptons. New results for regions of parameter space where the kinematical properties of top squark pair production and top quark pair production are very similar are presented. Depending on themodel, the combined result excludes a top squarkmass up to 1325 GeV for amassless neutralino, and a neutralinomass up to 700 GeV for a top squarkmass of 1150 GeV. Top squarks with masses from 145 to 295 GeV, for neutralino masses from 0 to 100 GeV, with a mass difference between the top squark and the neutralino in a window of 30 GeV around the mass of the top quark, are excluded for the first time with CMS data. The results of theses searches are also interpreted in an alternative signal model of dark matter production via a spin-0 mediator in association with a top quark pair. Upper limits are set on the cross section for mediator particle masses of up to 420 GeV