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Example 4.4 from Experimental Design and Analysis for Tree Improvement

Source: R/Exam4.4.R
Exam4.4.Rd

Exam4.4 presents the height means for 4 seedlots under factorial arrangement for two levels of Fertilizer and two levels of Irrigation.

References

  1. E.R. Williams, C.E. Harwood and A.C. Matheson (2023). Experimental Design and Analysis for Tree Improvement. CSIRO Publishing (https://www.publish.csiro.au/book/3145/).

See also

DataExam4.4

Author

  1. Muhammad Yaseen (myaseen208@gmail.com)

  2. Sami Ullah (samiullahuos@gmail.com)

Examples

library(car)
library(dae)
library(dplyr)
library(emmeans)
library(ggplot2)
library(lmerTest)
library(magrittr)
library(predictmeans)

data(DataExam4.4)

# Pg. 58
fm4.6    <-
  aov(
      formula = height ~ repl + irrig*fert*seedlot +
                         Error(repl/irrig:fert)
    , data    = DataExam4.4
    )
#> Warning: Error() model is singular

# Pg. 61
 summary(fm4.6)
#> 
#> Error: repl
#>      Df Sum Sq Mean Sq
#> repl  1 0.7564  0.7564
#> 
#> Error: repl:irrig:fert
#>            Df Sum Sq Mean Sq F value Pr(>F)    
#> irrig       1    0.1     0.1   0.154  0.721    
#> fert        1  590.6   590.6 841.110  9e-05 ***
#> irrig:fert  1    0.0     0.0   0.010  0.926    
#> Residuals   3    2.1     0.7                   
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Error: Within
#>                    Df Sum Sq Mean Sq F value  Pr(>F)    
#> seedlot             3  39.65  13.218  19.680 6.3e-05 ***
#> irrig:seedlot       3   1.11   0.370   0.551  0.6572    
#> fert:seedlot        3   9.95   3.317   4.938  0.0185 *  
#> irrig:fert:seedlot  3   1.74   0.579   0.862  0.4874    
#> Residuals          12   8.06   0.672                    
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

# Pg. 61
model.tables(x = fm4.6, type = "means")
#> Tables of means
#> Grand mean
#>          
#> 10.00437 
#> 
#>  repl 
#> repl
#>      1      2 
#> 10.158  9.851 
#> 
#>  irrig 
#> irrig
#>   none   plus 
#>  9.946 10.062 
#> 
#>  fert 
#> fert
#>   none   plus 
#>  5.708 14.301 
#> 
#>  seedlot 
#> seedlot
#>  Bulahdelah    Coffs SO Pomona pltn    Atherton 
#>      10.178      11.404      10.149       8.287 
#> 
#>  irrig:fert 
#>       fert
#> irrig  none   plus  
#>   none  5.635 14.257
#>   plus  5.781 14.344
#> 
#>  irrig:seedlot 
#>       seedlot
#> irrig  Bulahdelah Coffs SO Pomona pltn Atherton
#>   none 10.060     11.647   10.055       8.022  
#>   plus 10.295     11.160   10.242       8.552  
#> 
#>  fert:seedlot 
#>       seedlot
#> fert   Bulahdelah Coffs SO Pomona pltn Atherton
#>   none  5.687      6.790    5.410       4.945  
#>   plus 14.667     16.017   14.887      11.630  
#> 
#>  irrig:fert:seedlot 
#> , , seedlot = Bulahdelah
#> 
#>       fert
#> irrig  none   plus  
#>   none  5.275 14.845
#>   plus  6.100 14.490
#> 
#> , , seedlot = Coffs SO
#> 
#>       fert
#> irrig  none   plus  
#>   none  7.125 16.170
#>   plus  6.455 15.865
#> 
#> , , seedlot = Pomona pltn
#> 
#>       fert
#> irrig  none   plus  
#>   none  5.625 14.485
#>   plus  5.195 15.290
#> 
#> , , seedlot = Atherton
#> 
#>       fert
#> irrig  none   plus  
#>   none  4.515 11.530
#>   plus  5.375 11.730
#> 

# Pg. 61
emmeans(object = fm4.6, specs = ~ irrig)
#> Note: re-fitting model with sum-to-zero contrasts
#> Warning: Error() model is singular
#> NOTE: Results may be misleading due to involvement in interactions
#>  irrig emmean  SE  df asymp.LCL asymp.UCL
#>  none    9.95 NaN NaN       NaN       NaN
#>  plus   10.06 NaN NaN       NaN       NaN
#> 
#> Results are averaged over the levels of: repl, fert, seedlot 
#> Warning: EMMs are biased unless design is perfectly balanced 
#> Confidence level used: 0.95 
emmip(object = fm4.6, formula  = ~ irrig) +
    theme_classic()
#> Note: re-fitting model with sum-to-zero contrasts
#> Warning: Error() model is singular
#> NOTE: Results may be misleading due to involvement in interactions