The function ltcchk conducts Line x Tester analysis when
the data contains crosses and checks. The experimental design may be
RCBD or Alpha lattice design.
# Load the package
library(gpbStat)
#Load the dataset
data(alphaltcchk)
# View the structure of dataframe.
str(alphaltcchk)
#> 'data.frame': 54 obs. of 6 variables:
#> $ replication: chr "r1" "r1" "r1" "r1" ...
#> $ block : chr "b2" "b4" "b2" "b6" ...
#> $ line : int 1 2 3 4 5 1 2 3 4 5 ...
#> $ tester : int 11 11 11 11 11 12 12 12 12 12 ...
#> $ check : int NA NA NA NA NA NA NA NA NA NA ...
#> $ yield : num 41.7 66 71.6 53.8 54.9 ...
# Conduct Line x Tester analysis
result = ltcchk(alphaltcchk, replication, line, tester, check, yield, block)
#>
#> Analysis of Line x Tester: yield
# View the output
result
#> $Means
#> Testers
#> Lines 11 12 13
#> 1 55.11815 56.00024 48.86192
#> 2 46.10276 47.18926 51.60208
#> 3 57.17833 63.38786 39.82822
#> 4 51.82018 53.52738 44.06331
#> 5 45.08720 59.65115 58.72662
#>
#> $`Overall ANOVA`
#> Df Sum Sq Mean Sq F value Pr(>F)
#> Replication 2 40.56006 20.28003 0.112 0.8946
#> Blocks within Replication 15 1605.96516 107.06434 0.591 0.8474
#> Treatments 17 2522.99574 148.41151 0.820 0.6571
#> Crosses 14 1845.00871 131.78634 0.728 0.7244
#> Checks 2 407.62289 203.81144 1.126 0.3450
#> Lines 4 256.94867 64.23717 0.439 0.7777
#> Testers 2 418.43308 209.21654 1.431 0.2943
#> Lines X Testers 8 1169.62696 146.20337 0.808 0.6039
#> Error 19 3439.50344 181.02650 NA NA
#> Total 53 456.78239 NA NA NA
#>
#> $`Coefficient of Variation`
#> [1] 25.44511
#>
#> $`Genetic Variance`
#> Genotypic Variance Phenotypic Variance Environmental Variance
#> 42.71049 223.73699 181.02650
#>
#> $`Genetic Variability `
#> Phenotypic coefficient of Variation Genotypic coefficient of Variation
#> 28.287998 12.359492
#> Environmental coefficient of Variation <NA>
#> 25.445114 0.190896
#>
#> $`Line x Tester ANOVA`
#> Df Sum Sq Mean Sq F value Pr(>F)
#> Lines 4 256.9487 64.23717 0.439 0.7777
#> Testers 2 418.4331 209.21654 1.431 0.2943
#> Lines X Testers 8 1169.6270 146.20337 0.808 0.6039
#>
#> $`GCA lines`
#> 1 2 3 4 5
#> 1.450 -3.578 1.588 -2.073 2.612
#>
#> $`GCA testers`
#> 11 12 13
#> -0.815 4.075 -3.260
#>
#> $`SCA crosses`
#> Testers
#> Lines 11 12 13
#> 1 2.606 -1.401 -1.205
#> 2 -1.380 -5.184 6.564
#> 3 4.529 5.848 -10.377
#> 4 2.832 -0.351 -2.480
#> 5 -8.586 1.088 7.498
#>
#> $`Proportional Contribution`
#> Lines Tester Line x Tester
#> 13.92669 22.67919 63.39412
#>
#> $`GV Singh & Chaudhary`
#> Cov H.S. (line) Cov H.S. (tester)
#> -9.1073559 4.2008782
#> Cov H.S. (average) Cov F.S. (average)
#> -0.5096931 -13.3738060
#> F = 0, Adittive genetic variance F = 1, Adittive genetic variance
#> -2.0387724 -1.0193862
#> F = 0, Variance due to Dominance F = 1, Variance due to Dominance
#> -23.2154182 -11.6077091
#>
#> $`Standard Errors`
#> S.E. gca for line S.E. gca for tester S.E. sca effect
#> 4.484870 3.473965 7.768022
#> S.E. (gi - gj)line S.E. (gi - gj)tester S.E. (sij - skl)tester
#> 6.342563 4.912928 10.985642
#>
#> $`Critical differance`
#> C.D. gca for line C.D. gca for tester C.D. sca effect
#> 9.386940 7.271092 16.258657
#> C.D. (gi - gj)line C.D. (gi - gj)tester C.D. (sij - skl)tester
#> 13.275138 10.282877 22.993213# Load the package
library(gpbStat)
#Load the dataset
data("rcbdltcchk")
# View the structure of dataframe.
str(rcbdltcchk)
#> tibble [72 × 5] (S3: tbl_df/tbl/data.frame)
#> $ replication: num [1:72] 1 2 3 4 1 2 3 4 1 2 ...
#> $ line : num [1:72] 1 1 1 1 1 1 1 1 1 1 ...
#> $ tester : num [1:72] 6 6 6 6 7 7 7 7 8 8 ...
#> $ check : num [1:72] NA NA NA NA NA NA NA NA NA NA ...
#> $ yield : num [1:72] 74.4 70.9 60.9 68 91.8 ...
# Conduct Line x Tester analysis
result1 = ltcchk(rcbdltcchk, replication, line, tester, check, yield)
#>
#> Analysis of Line x Tester with crosses and checks: yield
# View the output
result1
#> $Means
#> Testers
#> Lines 6 7 8
#> 1 68.550 107.640 52.640
#> 2 73.265 97.640 85.650
#> 3 100.885 111.540 117.735
#> 4 105.795 64.450 46.855
#> 5 84.150 81.935 94.820
#>
#> $`Overall ANOVA`
#> Df Sum Sq Mean Sq F value Pr(>F)
#> Replication 3 181.4450 60.48168 0.750 0.5274
#> Treatments 17 26842.2856 1578.95798 19.583 0.0000
#> Crosses 14 26199.6543 1871.40388 23.211 0.0000
#> Checks 2 551.0746 275.53731 3.417 0.0405
#> Lines 4 10318.3614 2579.59035 1.457 0.3009
#> Testers 2 1718.9258 859.46289 0.485 0.6327
#> Lines X Testers 8 14162.3672 1770.29589 21.956 0.0000
#> Error 51 4111.9998 80.62745 NA NA
#> Total 71 31135.7305 NA NA NA
#>
#> $`Coefficient of Variation`
#> [1] 10.47362
#>
#> $`Genetic Variance`
#> Genotypic Variance Phenotypic Variance Environmental Variance
#> 379.61908 460.24652 80.62745
#>
#> $`Genetic Variability `
#> Phenotypic coefficient of Variation Genotypic coefficient of Variation
#> 25.0236394 22.7263258
#> Environmental coefficient of Variation <NA>
#> 10.4736166 0.8248168
#>
#> $`Line x Tester ANOVA`
#> Df Sum Sq Mean Sq F value Pr(>F)
#> Lines 4 10318.361 2579.5903 1.457 0.3009
#> Testers 2 1718.926 859.4629 0.485 0.6327
#> Lines X Testers 8 14162.367 1770.2959 21.956 0.0000
#>
#> $`GCA lines`
#> 1 2 3 4 5
#> -9.960 -0.718 23.817 -13.870 0.732
#>
#> $`GCA testers`
#> 6 7 8
#> 0.292 6.404 -6.697
#>
#> $`SCA crosses`
#> Testers
#> Lines 6 7 8
#> 1 -8.019 24.959 -16.940
#> 2 -12.546 5.717 6.828
#> 3 -9.461 -4.918 14.378
#> 4 33.136 -14.321 -18.815
#> 5 -3.111 -11.438 14.548
#>
#> $`Proportional Contribution`
#> Lines Tester Line x Tester
#> 39.383578 6.560872 54.055550
#>
#> $`GV Singh & Chaudhary`
#> Cov H.S. (line) Cov H.S. (tester)
#> 67.441205 -45.541650
#> Cov H.S. (average) Cov F.S. (average)
#> 2.680894 412.168303
#> F = 0, Adittive genetic variance F = 1, Adittive genetic variance
#> 10.723574 5.361787
#> F = 0, Variance due to Dominance F = 1, Variance due to Dominance
#> 844.834223 422.417112
#>
#> $`Standard Errors`
#> S.E. gca for line S.E. gca for tester S.E. sca effect
#> 2.592095 2.007828 4.489639
#> S.E. (gi - gj)line S.E. (gi - gj)tester S.E. (sij - skl)tester
#> 3.665775 2.839497 6.349309
#>
#> $`Critical differance`
#> C.D. gca for line C.D. gca for tester C.D. sca effect
#> 5.203847 4.030882 9.013327
#> C.D. (gi - gj)line C.D. (gi - gj)tester C.D. (sij - skl)tester
#> 7.359351 5.700529 12.746770