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)
#> Classes 'tbl_df', 'tbl' and 'data.frame':    54 obs. of  6 variables:
#>  $ replication: num  1 1 1 1 1 1 1 1 1 1 ...
#>  $ block      : num  1 1 1 2 2 2 3 3 3 4 ...
#>  $ line       : num  1 1 1 3 3 3 4 4 4 2 ...
#>  $ tester     : num  11 12 13 11 12 13 11 12 13 11 ...
#>  $ check      : num  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 39.71542 63.26313 62.81656
#>     2 57.41419 55.69333 58.82389
#>     3 58.07933 45.48036 51.48648
#>     4 54.63878 51.24719 48.85824
#>     5 40.67837 46.95009 61.85992
#> 
#> $`Overall ANOVA`
#>                           Df     Sum Sq   Mean Sq F value Pr(>F)
#> Replication                2   40.56006  20.28003   0.195 0.8241
#> Blocks within Replication 10 1078.34500 107.83450   1.039 0.4425
#> Treatments                17 3998.28863 235.19345   2.265 0.0326
#> Crosses                   14 2439.10541 174.22182   1.678 0.1283
#> Checks                     2 1541.39151 770.69575   7.423 0.0031
#> Lines                      4  336.80619  84.20155   0.383 0.8151
#> Testers                    2  341.33346 170.66673   0.775 0.4924
#> Lines X Testers            8 1760.96576 220.12072   2.120 0.0740
#> Error                     24 2491.83072 103.82628      NA     NA
#> Total                     53  467.13426        NA      NA     NA
#> 
#> $`Coefficient of Variation`
#> [1] 19.27023
#> 
#> $`Genetic Variance`
#>     Genotypic Variance    Phenotypic Variance Environmental Variance 
#>               71.63781              175.46409              103.82628 
#> 
#> $`Genetic Variability `
#>    Phenotypic coefficient of Variation     Genotypic coefficient of Variation 
#>                             25.0511369                             16.0067978 
#> Environmental coefficient of Variation                                   <NA> 
#>                             19.2702331                              0.4082762 
#> 
#> $`Line x Tester ANOVA`
#>                 Df    Sum Sq   Mean Sq F value Pr(>F)
#> Lines            4  336.8062  84.20155   0.383 0.8151
#> Testers          2  341.3335 170.66673   0.775 0.4924
#> Lines X Testers  8 1760.9658 220.12072   2.120 0.0740
#> 
#> $`GCA lines`
#>      1      2      3      4      5 
#>  2.131  4.177 -1.452 -1.552 -3.304 
#> 
#> $`GCA testers`
#>     11     12     13 
#> -3.028 -0.607  3.635 
#> 
#> $`SCA crosses`
#>      Testers
#> Lines      11     12     13
#>     1 -12.521  8.605  3.916
#>     2   3.132 -1.010 -2.122
#>     3   9.426 -5.595 -3.831
#>     4   6.086  0.273 -6.358
#>     5  -6.123 -2.273  8.395
#> 
#> $`Proportional Contribution`
#>          Lines         Tester  Line x Tester 
#>       13.80860       13.99421       72.19720 
#> 
#> $`GV Singh & Chaudhary`
#>                  Cov H.S. (line)                Cov H.S. (tester) 
#>                       -15.102130                        -3.296933 
#>               Cov H.S. (average)               Cov F.S. (average) 
#>                        -1.622689                        19.249588 
#> F = 0, Adittive genetic variance F = 1, Adittive genetic variance 
#>                        -6.490754                        -3.245377 
#> F = 0, Variance due to Dominance F = 1, Variance due to Dominance 
#>                        77.529627                        38.764814 
#> 
#> $`Standard Errors`
#>      S.E. gca for line    S.E. gca for tester        S.E. sca effect 
#>               3.396506               2.630922               5.882921 
#>     S.E. (gi - gj)line   S.E. (gi - gj)tester S.E. (sij - skl)tester 
#>               4.803385               3.720686               8.319707 
#> 
#> $`Critical differance`
#>      C.D. gca for line    C.D. gca for tester        C.D. sca effect 
#>               7.010044               5.429957              12.141752 
#>     C.D. (gi - gj)line   C.D. (gi - gj)tester C.D. (sij - skl)tester 
#>               9.913699               7.679118              17.171031

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)
#> Classes 'tbl_df', 'tbl' and 'data.frame':    72 obs. of  5 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 ...
#>  $ check      : num  NA NA NA NA NA NA NA NA NA NA ...
#>  $ yield      : num  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 2579.5904   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