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ltcchk: Analysing Line x Tester data containing crosses and checks.

Nandan Patil

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.

Example: Analyzing Line x Tester data (crosses and checks) laid out in 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

Example: Analyzing Line x Tester data (crosses and checks) laid out in RCBD.

# 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

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
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