Computer and Biometric Services Unit International Center for Agricultural Research in the Dry Areas (ICARDA) P.O. Box 5466, Aleppo, Syria Online BioComputing Service ......... Date(D/M/Y) : 16 / 5 / 2017 Time : 12 hr 8 min (Program codes updated: 15 June 2017, Amman, Jordan) Summary of the analysis of the data from similar trials conducted in augmented designs in one-way blocks ..................................................................................................................... ..................... This includes i. Regression analyses of variance ii. REML produced predicted values of genotypes and standard errors assuming a) block and genotype effects fixed b) block and genotype effects random iii. REML produced standard error of differences of predicted values and t-values for LSD computation REFERENCE: W.T. Federer (1961). Augmented designs with one-way elimination of heterogeneity. Biometrics,17: 447-473 Singh, M, M. van Ginkel, A. Sarker, R. S. Malhotra, M. Imtiaz and S. Kumar (2012). Agricultural Research, 1: 285-294 ********** Notations ************************************ Blk = Block factor for blocks Geno = Genotype factor for check and test genotypes Chk_Test = Check genotypes versus test genotypes Chk_Test.Checks = Between check genotypes only Chk_Test.Tests = Between test genotypes only BLUE = Best linear unbiased estimate BLUP = Best linear unbiased predictor estimate GrandMn = Grand mean HeritAll = Broad-sense and plot-basis heritability based on all the genotypes (test and checks). SeHeritAll = Standard error of HeritAll HeritTest = Broad-sense and plot-basis heritability based on all the test genotypes alone. SeHeritTest = Standard error of HeritTest 1. Trials and parameters of the designs ................................................... No. of similar trials = 2 No. of incomplete blocks = 6 No. of genotypes/treatment = 7 No. of (replicated)checks = 4 No. of (unreplicated)tests = 3 No. of plots in each trial = 15 Variables analyzed : GYld, HSW .................................................................................... 2. Trial-wise summary ............................................................... ............................................................... Trial = 1 Variable = GYld 1.........Regression analysis of variance............... 1.1........Genotype as an unpartitioned factor ............... Regression analysis =================== Response variate: GYld Fitted terms: Constant + Blk + Geno Accumulated analysis of variance -------------------------------- Change d.f. s.s. m.s. v.r. F pr. + Blk 5 84.917 16.983 6.37 0.079 + Geno 6 46.417 7.736 2.90 0.205 Residual 3 8.000 2.667 Total 14 139.333 9.952 1.2........Genotype partitioned into: Checks vs. tests : Chk_Test between checks : Chk_Test.Checks between tests : Chk_Test.Tests Regression analysis =================== Response variate: GYld Fitted terms: Constant + Blk + Chk_Test + Chk_Test.Checks + Chk_Test.Tests Accumulated analysis of variance -------------------------------- Change d.f. s.s. m.s. v.r. F pr. + Blk 5 84.917 16.983 6.37 0.079 + Chk_Test 1 2.017 2.017 0.76 0.448 + Chk_Test.Checks 3 36.582 12.194 4.57 0.122 + Chk_Test.Tests 2 7.818 3.909 1.47 0.360 Residual 3 8.000 2.667 Total 14 139.333 9.952 2.........Mixed model fitting................ ......Block effects and genotype effects assumed fixed............ REML variance components analysis ================================= Response variate: GYld Fixed model: Constant + Blk + Geno Number of units: 15 Residual term has been added to model Sparse algorithm with AI optimisation Residual variance model ----------------------- Term Model(order) Parameter Estimate s.e. Residual Identity Sigma2 2.667 2.177 Tests for fixed effects ----------------------- Sequentially adding terms to fixed model Fixed term Wald statistic n.d.f. F statistic d.d.f. F pr Blk 31.84 5 6.37 3.0 0.079 Geno 17.41 6 2.90 3.0 0.205 Dropping individual terms from full fixed model Fixed term Wald statistic n.d.f. F statistic d.d.f. F pr Blk 16.00 5 3.20 3.0 0.184 Geno 17.41 6 2.90 3.0 0.205 * MESSAGE: denominator degrees of freedom for approximate F-tests are calculated using algebraic derivatives ignoring fixed/boundary/singular variance parameters. 2.1........ Predicted means and their standard errors ..... BLUE Standard error Geno 5 11.00 2.028 6 13.00 2.028 7 8.00 2.028 Geno 1 9.00 1.106 2 8.00 1.106 3 13.00 1.106 4 10.00 1.106 Av SE(Difference of two check entry means)...............: 1.633 Av SE(Difference of two test entries means)..............: 2.749 Av SE(Difference of a check entry and a test entry means): 2.309 3.........Mixed model fitting................ ......Block effects and genotype effects assumed random................... ...........Mixed model used: REML variance components analysis ================================= Response variate: GYld Fixed model: Constant Random model: Blk + Geno Number of units: 15 Residual term has been added to model Sparse algorithm with AI optimisation Estimated variance components ----------------------------- Random term component s.e. Blk 3.886 3.380 Geno 3.070 2.705 Residual variance model ----------------------- Term Model(order) Parameter Estimate s.e. Residual Identity Sigma2 2.395 1.681 3.1........ Predicted means and their standard errors ..... BLUP Standard error Geno 5 9.93 1.555 6 11.05 1.555 7 9.13 1.548 Geno 1 8.78 1.194 2 8.44 1.201 3 12.40 1.190 4 10.40 1.185 Av SE(Difference of two check entry means)...............: 1.251 Av SE(Difference of two test entries means)..............: 1.741 Av SE(Difference of a check entry and a test entry means): 1.545 3.2........ Heritability estimates in broad-sense and on plot-basis from ALL THE GENOTYPES and genetic gain (GG) at 5%, 10%, 20% selection intensity .........Heritability and genetic gains due to selection GrandMn HeritAll SeHeritAll 9.667 0.5618 0.3117 Selection intensity% Genetic Gain % 5% 28.02 10% 23.84 20% 19.02 3.3........ Heritability estimates in broad-sense and on plot-basis from only THE TEST GENOTYPES and genetic gain (GG) at 5%, 10%, 20% selection intensity ........Mixed model used: (Note Check vs Test and Checks effects terms assumed fixed) REML variance components analysis ================================= Response variate: GYld Fixed model: Constant + Chk_Test + Chk_Test.Checks Random model: Blk + Chk_Test.Tests Number of units: 15 Residual term has been added to model Sparse algorithm with AI optimisation Estimated variance components ----------------------------- Random term component s.e. Blk 2.248 2.855 Chk_Test.Tests 0.000 bound Residual variance model ----------------------- Term Model(order) Parameter Estimate s.e. Residual Identity Sigma2 3.261 2.066 .........Heritability and genetic gains due to selection HeritTest SeHeritTest 3.1607E-08 0 Selection intensity% Genetic Gain % 5% 0.000001218 10% 0.000001036 20% 0.0000008265 ............................................................... Trial = 1 Variable = HSW 1.........Regression analysis of variance............... 1.1........Genotype as an unpartitioned factor ............... Regression analysis =================== Response variate: HSW Fitted terms: Constant + Blk + Geno Accumulated analysis of variance -------------------------------- Change d.f. s.s. m.s. v.r. F pr. + Blk 5 92.083 18.417 4.95 0.109 + Geno 6 41.669 6.945 1.87 0.325 Residual 3 11.158 3.719 Total 14 144.909 10.351 1.2........Genotype partitioned into: Checks vs. tests : Chk_Test between checks : Chk_Test.Checks between tests : Chk_Test.Tests Regression analysis =================== Response variate: HSW Fitted terms: Constant + Blk + Chk_Test + Chk_Test.Checks + Chk_Test.Tests Accumulated analysis of variance -------------------------------- Change d.f. s.s. m.s. v.r. F pr. + Blk 5 92.083 18.417 4.95 0.109 + Chk_Test 1 4.161 4.161 1.12 0.368 + Chk_Test.Checks 3 29.581 9.860 2.65 0.222 + Chk_Test.Tests 2 7.928 3.964 1.07 0.447 Residual 3 11.157 3.719 Total 14 144.909 10.351 2.........Mixed model fitting................ ......Block effects and genotype effects assumed fixed............ REML variance components analysis ================================= Response variate: HSW Fixed model: Constant + Blk + Geno Number of units: 15 Residual term has been added to model Sparse algorithm with AI optimisation Residual variance model ----------------------- Term Model(order) Parameter Estimate s.e. Residual Identity Sigma2 3.719 3.037 Tests for fixed effects ----------------------- Sequentially adding terms to fixed model Fixed term Wald statistic n.d.f. F statistic d.d.f. F pr Blk 24.76 5 4.95 3.0 0.109 Geno 11.20 6 1.87 3.0 0.325 Dropping individual terms from full fixed model Fixed term Wald statistic n.d.f. F statistic d.d.f. F pr Blk 11.05 5 2.21 3.0 0.273 Geno 11.20 6 1.87 3.0 0.325 * MESSAGE: denominator degrees of freedom for approximate F-tests are calculated using algebraic derivatives ignoring fixed/boundary/singular variance parameters. 2.1........ Predicted means and their standard errors ..... BLUE Standard error Geno 5 22.49 2.395 6 24.49 2.395 7 19.45 2.395 Geno 1 19.97 1.306 2 19.20 1.306 3 23.50 1.306 4 21.72 1.306 Av SE(Difference of two check entry means)...............: 1.929 Av SE(Difference of two test entries means)..............: 3.246 Av SE(Difference of a check entry and a test entry means): 2.727 3.........Mixed model fitting................ ......Block effects and genotype effects assumed random................... ...........Mixed model used: REML variance components analysis ================================= Response variate: HSW Fixed model: Constant Random model: Blk + Geno Number of units: 15 Residual term has been added to model Sparse algorithm with AI optimisation Estimated variance components ----------------------------- Random term component s.e. Blk 3.712 3.357 Geno 2.705 2.614 Residual variance model ----------------------- Term Model(order) Parameter Estimate s.e. Residual Identity Sigma2 2.880 1.870 3.1........ Predicted means and their standard errors ..... BLUP Standard error Geno 5 21.12 1.563 6 22.09 1.563 7 20.54 1.555 Geno 1 19.92 1.218 2 19.60 1.226 3 23.01 1.213 4 21.95 1.207 Av SE(Difference of two check entry means)...............: 1.304 Av SE(Difference of two test entries means)..............: 1.751 Av SE(Difference of a check entry and a test entry means): 1.571 3.2........ Heritability estimates in broad-sense and on plot-basis from ALL THE GENOTYPES and genetic gain (GG) at 5%, 10%, 20% selection intensity .........Heritability and genetic gains due to selection GrandMn HeritAll SeHeritAll 20.77 0.4843 0.3235 Selection intensity% Genetic Gain % 5% 11.36 10% 9.669 20% 7.712 3.3........ Heritability estimates in broad-sense and on plot-basis from only THE TEST GENOTYPES and genetic gain (GG) at 5%, 10%, 20% selection intensity ........Mixed model used: (Note Check vs Test and Checks effects terms assumed fixed) REML variance components analysis ================================= Response variate: HSW Fixed model: Constant + Chk_Test + Chk_Test.Checks Random model: Blk + Chk_Test.Tests Number of units: 15 Residual term has been added to model Sparse algorithm with AI optimisation Estimated variance components ----------------------------- Random term component s.e. Blk 1.746 2.731 Chk_Test.Tests 0.000 bound Residual variance model ----------------------- Term Model(order) Parameter Estimate s.e. Residual Identity Sigma2 3.842 2.386 .........Heritability and genetic gains due to selection HeritTest SeHeritTest 0.0000003947 0 Selection intensity% Genetic Gain % 5% 0.000007683 10% 0.000006537 20% 0.000005214 ............................................................... ............................................................... ............................................................... Trial = 2 Variable = GYld 1.........Regression analysis of variance............... 1.1........Genotype as an unpartitioned factor ............... Regression analysis =================== Response variate: GYld Fitted terms: Constant + Blk + Geno Accumulated analysis of variance -------------------------------- Change d.f. s.s. m.s. v.r. F pr. + Blk 5 84.917 16.983 6.37 0.079 + Geno 6 46.417 7.736 2.90 0.205 Residual 3 8.000 2.667 Total 14 139.333 9.952 1.2........Genotype partitioned into: Checks vs. tests : Chk_Test between checks : Chk_Test.Checks between tests : Chk_Test.Tests Regression analysis =================== Response variate: GYld Fitted terms: Constant + Blk + Chk_Test + Chk_Test.Checks + Chk_Test.Tests Accumulated analysis of variance -------------------------------- Change d.f. s.s. m.s. v.r. F pr. + Blk 5 84.917 16.983 6.37 0.079 + Chk_Test 1 2.017 2.017 0.76 0.448 + Chk_Test.Checks 3 36.582 12.194 4.57 0.122 + Chk_Test.Tests 2 7.818 3.909 1.47 0.360 Residual 3 8.000 2.667 Total 14 139.333 9.952 2.........Mixed model fitting................ ......Block effects and genotype effects assumed fixed............ REML variance components analysis ================================= Response variate: GYld Fixed model: Constant + Blk + Geno Number of units: 15 Residual term has been added to model Sparse algorithm with AI optimisation Residual variance model ----------------------- Term Model(order) Parameter Estimate s.e. Residual Identity Sigma2 2.667 2.177 Tests for fixed effects ----------------------- Sequentially adding terms to fixed model Fixed term Wald statistic n.d.f. F statistic d.d.f. F pr Blk 31.84 5 6.37 3.0 0.079 Geno 17.41 6 2.90 3.0 0.205 Dropping individual terms from full fixed model Fixed term Wald statistic n.d.f. F statistic d.d.f. F pr Blk 16.00 5 3.20 3.0 0.184 Geno 17.41 6 2.90 3.0 0.205 * MESSAGE: denominator degrees of freedom for approximate F-tests are calculated using algebraic derivatives ignoring fixed/boundary/singular variance parameters. 2.1........ Predicted means and their standard errors ..... BLUE Standard error Geno 5 11.00 2.028 6 13.00 2.028 7 8.00 2.028 Geno 1 9.00 1.106 2 8.00 1.106 3 13.00 1.106 4 10.00 1.106 Av SE(Difference of two check entry means)...............: 1.633 Av SE(Difference of two test entries means)..............: 2.749 Av SE(Difference of a check entry and a test entry means): 2.309 3.........Mixed model fitting................ ......Block effects and genotype effects assumed random................... ...........Mixed model used: REML variance components analysis ================================= Response variate: GYld Fixed model: Constant Random model: Blk + Geno Number of units: 15 Residual term has been added to model Sparse algorithm with AI optimisation Estimated variance components ----------------------------- Random term component s.e. Blk 3.886 3.380 Geno 3.070 2.705 Residual variance model ----------------------- Term Model(order) Parameter Estimate s.e. Residual Identity Sigma2 2.395 1.681 3.1........ Predicted means and their standard errors ..... BLUP Standard error Geno 5 9.93 1.555 6 11.05 1.555 7 9.13 1.548 Geno 1 8.78 1.194 2 8.44 1.201 3 12.40 1.190 4 10.40 1.185 Av SE(Difference of two check entry means)...............: 1.251 Av SE(Difference of two test entries means)..............: 1.741 Av SE(Difference of a check entry and a test entry means): 1.545 3.2........ Heritability estimates in broad-sense and on plot-basis from ALL THE GENOTYPES and genetic gain (GG) at 5%, 10%, 20% selection intensity .........Heritability and genetic gains due to selection GrandMn HeritAll SeHeritAll 9.667 0.5618 0.3117 Selection intensity% Genetic Gain % 5% 28.02 10% 23.84 20% 19.02 3.3........ Heritability estimates in broad-sense and on plot-basis from only THE TEST GENOTYPES and genetic gain (GG) at 5%, 10%, 20% selection intensity ........Mixed model used: (Note Check vs Test and Checks effects terms assumed fixed) REML variance components analysis ================================= Response variate: GYld Fixed model: Constant + Chk_Test + Chk_Test.Checks Random model: Blk + Chk_Test.Tests Number of units: 15 Residual term has been added to model Sparse algorithm with AI optimisation Estimated variance components ----------------------------- Random term component s.e. Blk 2.248 2.855 Chk_Test.Tests 0.000 bound Residual variance model ----------------------- Term Model(order) Parameter Estimate s.e. Residual Identity Sigma2 3.261 2.066 .........Heritability and genetic gains due to selection HeritTest SeHeritTest 3.1607E-08 0 Selection intensity% Genetic Gain % 5% 0.000001218 10% 0.000001036 20% 0.0000008265 ............................................................... Trial = 2 Variable = HSW 1.........Regression analysis of variance............... 1.1........Genotype as an unpartitioned factor ............... Regression analysis =================== Response variate: HSW Fitted terms: Constant + Blk + Geno Accumulated analysis of variance -------------------------------- Change d.f. s.s. m.s. v.r. F pr. + Blk 5 93.8982 18.7796 24.74 0.012 + Geno 6 67.7617 11.2936 14.88 0.025 Residual 3 2.2775 0.7592 Total 14 163.9373 11.7098 1.2........Genotype partitioned into: Checks vs. tests : Chk_Test between checks : Chk_Test.Checks between tests : Chk_Test.Tests Regression analysis =================== Response variate: HSW Fitted terms: Constant + Blk + Chk_Test + Chk_Test.Checks + Chk_Test.Tests Accumulated analysis of variance -------------------------------- Change d.f. s.s. m.s. v.r. F pr. + Blk 5 93.8982 18.7796 24.74 0.012 + Chk_Test 1 2.1282 2.1282 2.80 0.193 + Chk_Test.Checks 3 50.1083 16.7028 22.00 0.015 + Chk_Test.Tests 2 15.5252 7.7626 10.23 0.046 Residual 3 2.2775 0.7592 Total 14 163.9373 11.7098 2.........Mixed model fitting................ ......Block effects and genotype effects assumed fixed............ REML variance components analysis ================================= Response variate: HSW Fixed model: Constant + Blk + Geno Number of units: 15 Residual term has been added to model Sparse algorithm with AI optimisation Residual variance model ----------------------- Term Model(order) Parameter Estimate s.e. Residual Identity Sigma2 0.759 0.6199 Tests for fixed effects ----------------------- Sequentially adding terms to fixed model Fixed term Wald statistic n.d.f. F statistic d.d.f. F pr Blk 123.69 5 24.74 3.0 0.012 Geno 89.26 6 14.88 3.0 0.025 Dropping individual terms from full fixed model Fixed term Wald statistic n.d.f. F statistic d.d.f. F pr Blk 64.64 5 12.93 3.0 0.030 Geno 89.26 6 14.88 3.0 0.025 * MESSAGE: denominator degrees of freedom for approximate F-tests are calculated using algebraic derivatives ignoring fixed/boundary/singular variance parameters. 2.1........ Predicted means and their standard errors ..... BLUE Standard error Geno 5 21.26 1.082 6 25.36 1.082 7 18.89 1.082 Geno 1 20.52 0.5899 2 18.60 0.5899 3 24.78 0.5899 4 21.60 0.5899 Av SE(Difference of two check entry means)...............: 0.8713 Av SE(Difference of two test entries means)..............: 1.467 Av SE(Difference of a check entry and a test entry means): 1.232 3.........Mixed model fitting................ ......Block effects and genotype effects assumed random................... ...........Mixed model used: REML variance components analysis ================================= Response variate: HSW Fixed model: Constant Random model: Blk + Geno Number of units: 15 Residual term has been added to model Sparse algorithm with AI optimisation Estimated variance components ----------------------------- Random term component s.e. Blk 5.6649 3.9452 Geno 6.0766 3.9215 Residual variance model ----------------------- Term Model(order) Parameter Estimate s.e. Residual Identity Sigma2 0.815 0.6786 3.1........ Predicted means and their standard errors ..... BLUP Standard error Geno 5 20.92 1.407 6 24.53 1.407 7 19.45 1.406 Geno 1 20.35 1.134 2 18.76 1.136 3 24.67 1.134 4 21.73 1.133 Av SE(Difference of two check entry means)...............: 0.8570 Av SE(Difference of two test entries means)..............: 1.369 Av SE(Difference of a check entry and a test entry means): 1.167 3.2........ Heritability estimates in broad-sense and on plot-basis from ALL THE GENOTYPES and genetic gain (GG) at 5%, 10%, 20% selection intensity .........Heritability and genetic gains due to selection GrandMn HeritAll SeHeritAll 21.09 0.8817 0.1175 Selection intensity% Genetic Gain % 5% 22.64 10% 19.26 20% 15.37 3.3........ Heritability estimates in broad-sense and on plot-basis from only THE TEST GENOTYPES and genetic gain (GG) at 5%, 10%, 20% selection intensity ........Mixed model used: (Note Check vs Test and Checks effects terms assumed fixed) REML variance components analysis ================================= Response variate: HSW Fixed model: Constant + Chk_Test + Chk_Test.Checks Random model: Blk + Chk_Test.Tests Number of units: 15 Residual term has been added to model Sparse algorithm with AI optimisation Estimated variance components ----------------------------- Random term component s.e. Blk 5.6259 3.9608 Chk_Test.Tests 8.0901 9.3853 Residual variance model ----------------------- Term Model(order) Parameter Estimate s.e. Residual Identity Sigma2 0.848 0.7281 .........Heritability and genetic gains due to selection HeritTest SeHeritTest 0.9052 0.1332 Selection intensity% Genetic Gain % 5% 26.47 10% 22.52 20% 17.96 ............................................................... ...............................................................