Example 8.1.2 from Experimental Design & Analysis for Tree Improvement

Exam8.1.2 presents the Analysis of Nested Seedlot Structure of Diameter at breast height (Dbh) of 60 SeedLots under layout of row column design with 6 rows and 10 columns in 18 countries and 59 provinces of 18 selected countries given in Example 8.1.

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

DataExam8.1

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(DataExam8.1)

# Pg. 167
fm8.11 <-
  aov(
       formula = dbh ~ country + country:prov
     , data    = DataExam8.1
      )

  b <- anova(fm8.11)
  Res <- length(b[["Sum Sq"]])
  df  <- 119
  MSS <- 0.1951

  b[["Df"]][Res] <- df
  b[["Sum Sq"]][Res] <- MSS*df
  b[["Mean Sq"]][Res] <- b[["Sum Sq"]][Res]/b[["Df"]][Res]

  b[["F value"]][1:Res-1] <-
            b[["Mean Sq"]][1:Res-1]/b[["Mean Sq"]][Res]

  b[["Pr(>F)"]][Res-1] <-
     df(
       b[["F value"]][Res-1]
     , b[["Df"]][Res-1]
     , b[["Df"]][Res]
     )
  b
#> Analysis of Variance Table
#> 
#> Response: dbh
#>               Df Sum Sq Mean Sq F value        Pr(>F)    
#> country       17 54.619  3.2129  16.468 0.00000001235 ***
#> country:prov  41 18.606  0.4538   2.326      0.001502 ** 
#> Residuals    119 23.217  0.1951                          
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

 emmeans(fm8.11, specs = "country")
#> NOTE: A nesting structure was detected in the fitted model:
#>     prov %in% country
#> NOTE: Results may be misleading due to involvement in interactions
#>  country     emmean    SE  df lower.CL upper.CL
#>  India         3.57 0.165 177     3.25     3.90
#>  Vietnam       3.28 0.181 177     2.92     3.63
#>  Egypt         2.50 0.233 177     2.04     2.96
#>  Kenya         3.49 0.143 177     3.21     3.77
#>  Fiji          2.61 0.233 177     2.15     3.07
#>  Thailand      3.84 0.202 177     3.44     4.24
#>  Malaysia      4.03 0.135 177     3.77     4.30
#>  Philippines   3.61 0.233 177     3.15     4.07
#>  Australia     2.63 0.202 177     2.23     3.03
#>  PNG           3.65 0.404 177     2.85     4.45
#>  Solomon Is.   3.70 0.285 177     3.14     4.26
#>  Mauritius     3.12 0.404 177     2.33     3.92
#>  Sri Lanka     3.24 0.233 177     2.78     3.70
#>  Guam          2.34 0.404 177     1.55     3.14
#>  China         3.69 0.233 177     3.23     4.15
#>  Puerto Rico   3.35 0.404 177     2.55     4.14
#>  Vanuatu       2.76 0.404 177     1.97     3.56
#>  Benin         3.34 0.404 177     2.55     4.14
#> 
#> Results are averaged over the levels of: prov 
#> Confidence level used: 0.95