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Griffing's analysis from a table of cross means

Source: R/GriffingMeans.R
GriffingMeans.Rd

GriffingMeans() performs Griffing's (1956) combining-ability analysis when only the cross means and the error mean square are available, as in published examples: the cross means come from data (one row per cross) and the error from the experiment's analysis of variance. The analysis is that of Griffing.

Usage

GriffingMeans(y, Cross1, Cross2, data, Method, Model, ErrorMS, ErrorDf)

Arguments

y

column of data with the cross means (bare name, string or vector).

Cross1, Cross2

columns of data with the two parents of each cross.

data

a data frame with one row per cross (and per parent in Methods 1 and 2).

Method, Model

as in Griffing.

ErrorMS

error mean square on the basis of a cross mean (see Details).

ErrorDf

degrees of freedom of ErrorMS.

Value

An object of class c("da_griffing", "da_result", "list") with the components of Griffing except RCBD (there are no plot data).

Details

Error. ErrorMS is the error mean square on the basis of a cross mean, Griffing's \(M'_e = M_e/(bc)\) for \(b\) blocks and \(c\) plants per plot: for Model 1 the within-plot (or plot) error divided by the number of observations per mean, for Model 2 the variety by block mean square divided by the same number (Griffing 1956, Tables 8 and 12). ErrorDf is its degrees of freedom. All other quantities, formulas and components are as documented in Griffing.

References

Griffing, B. (1956). Concept of general and specific combining ability in relation to diallel crossing systems. Australian Journal of Biological Sciences, 9(4), 463–493. doi:10.1071/BI9560463

See also

Griffing, Griffing56

Other DiallelAnalysisR analyses: GardnerEberhart(), Griffing(), GriffingEnv(), Hayman(), Heterosis(), LineTester(), NCDesign(), PartialDiallel()

Author

Muhammad Yaseen (myaseen208@gmail.com)

Examples

#-------------------------------------------------------------
## Griffing's (1956) example: Method 4, Model 1, total yield
#-------------------------------------------------------------
g56 <-
  GriffingMeans(
      y       = TotalYield
    , Cross1  = Cross1
    , Cross2  = Cross2
    , data    = Griffing56
    , Method  = 4
    , Model   = 1
    , ErrorMS = 1642.48 / 78
    , ErrorDf = 2558
    )
g56$ANOVA
#>         Df Sum Sq Mean Sq F value    Pr(>F)    
#> gca      8  18606 2325.75  110.45 < 2.2e-16 ***
#> sca     27   9165  339.44   16.12 < 2.2e-16 ***
#> Error 2558  53865   21.06                      
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
round(x = g56$GCA, digits = 2)
#>      1      2      3      4      5      6      7      8      9 
#>   9.35 -20.65 -10.16 -22.55  -1.51  -1.89  28.12  -6.93  26.22 

#-------------------------------------------------------------
## The same data with Model 2 (variety x block error)
#-------------------------------------------------------------
g56r <-
  GriffingMeans(
      y       = TotalYield
    , Cross1  = Cross1
    , Cross2  = Cross2
    , data    = Griffing56
    , Method  = 4
    , Model   = 2
    , ErrorMS = 11803.61 / 78
    , ErrorDf = 175
    )
g56r$Genetic.Components
#>          Components
#> gca      283.758320
#> sca      188.110608
#> Error    151.328333
#> Additive 567.516640
#> Dominant 188.110608
#> gca/sca    1.508465