The function ltc conducts Line x Tester analysis when the data contains only crosses. The experimental design may be RCBD or Alpha lattice design.
# Load the package
library(gpbStat)
#Load the dataset
data("alphaltc")
# View the structure of dataframe.
str(alphaltc)
#> 'data.frame': 60 obs. of 5 variables:
#> $ replication: chr "r1" "r1" "r1" "r1" ...
#> $ block : chr "b1" "b1" "b1" "b2" ...
#> $ line : int 5 1 4 4 1 2 2 5 3 1 ...
#> $ tester : int 7 8 8 6 7 7 6 6 8 6 ...
#> $ yield : num 47.3 109.4 36.3 36.2 70.7 ...
# Conduct Line x Tester analysis
result = ltc(alphaltc, replication, line, tester, yield, block)
#>
#> Analysis of Line x Tester: yield
# View the output
result
#> $Means
#> Testers
#> Lines 6 7 8
#> 1 86.47500 88.95833 89.55000
#> 2 88.64667 55.48000 50.12667
#> 3 51.19917 53.28417 36.91583
#> 4 33.47500 34.29833 50.78417
#> 5 45.30417 42.14500 49.98000
#>
#> $`Overall ANOVA`
#> Df Sum Sq Mean Sq F value Pr(>F)
#> Replication 3 1586.4934 528.8311 3.1440495 4.213104e-02
#> Crosses 14 23862.0199 1704.4300 10.1333150 3.161969e-07
#> Blocks within Replication 16 2555.9198 159.7450 0.9497288 5.307851e-01
#> Lines 4 18835.3119 4708.8280 24.8833344 6.536498e-11
#> Testers 2 463.1458 231.5729 1.2237239 3.037332e-01
#> Lines X Testers 8 4563.5622 570.4453 3.0144615 8.508293e-03
#> Error 26 4373.2165 168.2006 NA NA
#> Total 59 2561.2067 NA NA NA
#>
#> $`Coefficient of Variation`
#> [1] 22.70992
#>
#> $`Genetic Variance`
#> Genotypic Variance Phenotypic Variance Environmental Variance
#> 293.8997 462.1004 168.2006
#>
#> $`Genetic Variability `
#> Phenotypic coefficient of Variation Genotypic coefficient of Variation
#> 37.6417608 30.0193557
#> Environmental coefficient of Variation <NA>
#> 22.7099195 0.6360084
#>
#> $`Line x Tester ANOVA`
#> Df Sum Sq Mean Sq F value Pr(>F)
#> Lines 4 18835.3119 4708.8280 24.883334 6.536498e-11
#> Testers 2 463.1458 231.5729 1.223724 3.037332e-01
#> Lines X Testers 8 4563.5622 570.4453 3.014461 8.508293e-03
#> Error 26 4373.2165 168.2006 NA NA
#>
#> $`GCA lines`
#> 1 2 3 4 5
#> 31.220 7.643 -9.975 -17.589 -11.298
#>
#> $`GCA testers`
#> 6 7 8
#> 3.912 -2.275 -1.637
#>
#> $`SCA crosses`
#> Testers
#> Lines 6 7 8
#> 1 -5.765 2.906 2.859
#> 2 19.984 -6.996 -12.988
#> 3 0.154 8.426 -8.580
#> 4 -9.956 -2.946 12.902
#> 5 -4.417 -1.390 5.807
#>
#> $`Proportional Contribution`
#> Lines Tester Line x Tester
#> 78.934273 1.940933 19.124794
#>
#> $`GV Singh & Chaudhary`
#> Cov H.S. (line) Cov H.S. (tester)
#> 344.86523 -16.94362
#> Cov H.S. (average) Cov F.S. (average)
#> 30.06778 262.35565
#> F = 0, Adittive genetic variance F = 1, Adittive genetic variance
#> 120.27111 60.13555
#> F = 0, Variance due to Dominance F = 1, Variance due to Dominance
#> 201.12232 15.84306
#>
#> $`Standard Errors`
#> S.E. gca for line S.E. gca for tester S.E. sca effect
#> 3.743891 2.900005 6.484609
#> S.E. (gi - gj)line S.E. (gi - gj)tester S.E. (sij - skl)tester
#> 5.294661 4.101227 9.170622
#>
#> $`Critical differance`
#> C.D. gca for line C.D. gca for tester C.D. sca effect
#> 7.695678 5.961047 13.329305
#> C.D. (gi - gj)line C.D. (gi - gj)tester C.D. (sij - skl)tester
#> 10.883332 8.430193 18.850484# Load the package
library(gpbStat)
#Load the dataset
data("rcbdltc")
# View the structure of dataframe.
str(rcbdltc)
#> Classes 'tbl_df', 'tbl' and 'data.frame': 60 obs. of 4 variables:
#> $ replication: num 1 2 3 4 1 2 3 4 1 2 ...
#> $ line : num 1 1 1 1 1 1 1 1 1 1 ...
#> $ tester : num 6 6 6 6 7 7 7 7 8 8 ...
#> $ yield : num 74.4 70.9 60.9 68 91.8 ...
# Conduct Line x Tester analysis
result1 = ltc(rcbdltc, replication, line, tester, yield)
#>
#> Analysis of Line x Tester: 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 3 148.436 49.47866 0.509612 6.778194e-01
#> Crosses 14 26199.654 1871.40388 19.274772 6.737492e-14
#> Lines 4 10318.361 2579.59035 27.466791 1.421271e-11
#> Testers 2 1718.926 859.46289 9.151332 4.626865e-04
#> Lines X Testers 8 14162.367 1770.29589 18.849639 4.973396e-12
#> Error 42 4077.815 97.09084 NA NA
#> Total 59 30425.906 NA NA NA
#>
#> $`Coefficient of Variation`
#> [1] 11.42608
#>
#> $`Genetic Variance`
#> Genotypic Variance Phenotypic Variance Environmental Variance
#> 455.48131 552.57215 97.09084
#>
#> $`Genetic Variability `
#> Phenotypic coefficient of Variation Genotypic coefficient of Variation
#> 27.2585365 24.7481829
#> Environmental coefficient of Variation <NA>
#> 11.4260778 0.8242929
#>
#> $`Line x Tester ANOVA`
#> Df Sum Sq Mean Sq F value Pr(>F)
#> Lines 4 10318.361 2579.59035 27.466791 1.421271e-11
#> Testers 2 1718.926 859.46289 9.151332 4.626865e-04
#> Lines X Testers 8 14162.367 1770.29589 18.849639 4.973396e-12
#> Error 42 4077.815 97.09084 NA NA
#>
#> $`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 408.052454
#> 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
#> 836.602526 418.301263
#>
#> $`Standard Errors`
#> S.E. gca for line S.E. gca for tester S.E. sca effect
#> 2.844451 2.203303 4.926734
#> S.E. (gi - gj)line S.E. (gi - gj)tester S.E. (sij - skl)tester
#> 4.022662 3.115940 6.967454
#>
#> $`Critical differance`
#> C.D. gca for line C.D. gca for tester C.D. sca effect
#> 5.740335 4.446445 9.942552
#> C.D. (gi - gj)line C.D. (gi - gj)tester C.D. (sij - skl)tester
#> 8.118060 6.288222 14.060892