Sisvar is a statistical analysis system, first released in 1996 although its development began in 1994. The first version was done in the programming language Pascal and compiled with Borland Turbo Pascal 3. Sisvar was developed to achieve some specific goals. The first objective was to obtain software that could be used directly on the statistical experimental course of the Department of Exact Science at the Federal University of Lavras. The second objective was to initiate the development of a genuinely Brazilian free software program that met the demands and peculiarities of research conducted in the country. The third goal was to present statistical analysis software for the Brazilian scientific community that would allow research results to be analyzed efficiently and reliably. All of the initial goals were achieved. Sisvar gained acceptance by the scientific community because it provides reliable, accurate, precise, simple and robust results, and allows users a greater degree of interactivity.

This paper presents a special capability of Sisvar to deal with fixed effect models with several restriction in the randomization procedure. These restrictions lead to models with fixed treatment effects, but with several random errors. One way do deal with models of this kind is to perform a mixed model analysis, considering only the error effects in the model as random effects and with different covariance structure for the error terms. Another way is to perform a analysis of variance with several error. These kind of analysis, when the data are balanced, can be done by using Sisvar. The software lead a exact $F$ test for the fixed effects and allow the user to applied multiple comparison procedures or regression analysis for the levels of the fixed effect factors, regarding they are single effects, interaction effects or hierarchical effects. Sisvar is an interesting statistical computer system for using in balanced agricultural and industrial data sets.

Sisvar is a statistical analysis system with a large usage by the scientific community to produce statistical analyses and to produce scientific results and conclusions. The large use of the statistical procedures of Sisvar by the scientific community is due to it being accurate, precise, simple and robust. With many options of analysis, Sisvar has a not so largely used analysis that is the multiple comparison procedures using bootstrap approaches. This paper aims to review this subject and to show some advantages of using Sisvar to perform such analysis to compare treatments means. Tests like Dunnett, Tukey, Student-Newman-Keuls and Scott-Knott are performed alternatively by bootstrap methods and show greater power and better controls of experimentwise type I error rates under non-normal, asymmetric, platykurtic or leptokurtic distributions.

Key message We compare genomic selection methods that use correlated traits to help predict biomass yield in sorghum, and find that trait-assisted genomic selection performs best. Abstract Genomic selection (GS) is usually performed on a single trait, but correlated traits can also help predict a focal trait through indirect or multi-trait GS. In this study, we use a pre-breeding population of biomass sorghum to compare strategies that use correlated traits to improve prediction of biomass yield, the focal trait. Correlated traits include moisture, plant height measured at monthly intervals between planting and harvest, and the area under the growth progress curve. In addition to single- and multi-trait direct and indirect GS, we test a new strategy called trait-assisted GS, in which correlated traits are used along with marker data in the validation population to predict a focal trait. Single-trait GS for biomass yield had a prediction accuracy of 0.40. Indirect GS performed best using area under the growth progress curve to predict biomass yield, with a prediction accuracy of 0.37, and did not differ from indirect multi-trait GS that also used moisture information. Multi-trait GS and single-trait GS yielded similar results, indicating that correlated traits did not improve prediction of biomass yield in a standard GS scenario. However, trait-assisted GS increased prediction accuracy by up to \(50\%\) when using plant height in both the training and validation populations to help predict yield in the validation population. Coincidence between selected genotypes in phenotypic and genomic selection was also highest in trait-assisted GS. Overall, these results suggest that trait-assisted GS can be an efficient strategy when correlated traits are obtained earlier or more inexpensively than a focal trait.

We propose a multivariate extension of the univariate chi-squared normality test. Using a known result for the distribution of quadratic forms in normal variables, we show that the proposed test statistic has an approximated chi-squared distribution under the null hypothesis of multivariate normality. As in the univariate case, the new test statistic is based on a comparison of observed and expected frequencies for specified events in sample space. In the univariate case, these events are the standard class intervals, but in the multivariate extension we propose these become hyper-ellipsoidal annuli in multivariate sample space. We assess the performance of the new test using Monte Carlo simulation. Keeping the type I error rate fixed, we show that the new test has power that compares favourably with other standard normality tests, though no uniformly most powerful test has been found. We recommend the new test due to its competitive advantages.