#' @title Example 5.1 from Experimental Design and Analysis for Tree Improvement
#' @name Exam5.1
#' @description Exam5.1 presents the height of 27 seedlots from 4 sites.
#' @author
#' \enumerate{
#' \item Muhammad Yaseen (\email{myaseen208@@gmail.com})
#' \item Sami Ullah (\email{samiullahuos@@gmail.com})
#' }
#'
#' @references
#' \enumerate{
#' \item E.R. Williams, C.E. Harwood and A.C. Matheson (2023). \emph{Experimental Design and Analysis for Tree Improvement}.
#' CSIRO Publishing (\href{https://www.publish.csiro.au/book/3145/}{https://www.publish.csiro.au/book/3145/}).
#' }
#'
#' @seealso
#' \code{\link{DataExam5.1}}
#'
#' @importFrom car Anova
#' @import dae
#' @import dplyr
#' @importFrom emmeans emmeans emmip
#' @import ggplot2
#' @importFrom lmerTest lmer
#' @importFrom magrittr %>%
#' @import predictmeans
#' @importFrom stats lm anova model.tables
#' @importFrom supernova supernova
#'
#' @examples
#' library(car)
#' library(dae)
#' library(dplyr)
#' library(emmeans)
#' library(ggplot2)
#' library(lmerTest)
#' library(magrittr)
#' library(predictmeans)
#' library(supernova)
#'
#' data(DataExam5.1)
#'
#' # Pg.68
#' fm5.4 <- lm(formula = Ht ~ Site*SeedLot, data = DataExam5.1)
#'
#' # Pg. 73
#' anova(fm5.4)
#' # Pg. 73
#' emmeans(object = fm5.4, specs = ~ Site)
#' emmeans(object = fm5.4, specs = ~ SeedLot)
#'
#' ANOVAfm5.4 <- anova(fm5.4)
#'
#' ANOVAfm5.4[4, 1:3] <- c(208, 208*1040, 1040)
#' ANOVAfm5.4[3, 4] <- ANOVAfm5.4[3, 3]/ANOVAfm5.4[4, 3]
#' ANOVAfm5.4[3, 5] <- pf(
#' q = ANOVAfm5.4[3, 4]
#' , df1 = ANOVAfm5.4[3, 1]
#' , df2 = ANOVAfm5.4[4, 1]
#' , lower.tail = FALSE
#' )
#' # Pg. 73
#' ANOVAfm5.4
#'
#' # Pg. 80
#' DataExam5.1 %>%
#' filter(SeedLot %in% c("13653", "13871")) %>%
#' ggplot(
#' data = .
#' , mapping = aes(x = SiteMean, y = Ht, color = SeedLot, shape = SeedLot)
#' ) +
#' geom_point() +
#' geom_smooth(method = lm, se = FALSE, fullrange = TRUE)+
#' theme_classic() +
#' labs(
#' x = "SiteMean"
#' , y = "SeedLot Mean"
#' )
#'
#'
#'
#' Tab5.10 <-
#' DataExam5.1 %>%
#' summarise(Mean = mean(Ht), .by = SeedLot) %>%
#' left_join(
#' DataExam5.1 %>%
#' nest_by(SeedLot) %>%
#' mutate(fm1 = list(lm(Ht ~ SiteMean, data = data))) %>%
#' summarise(Slope = coef(fm1)[2])
#' , by = "SeedLot"
#' )
#'
#' # Pg. 81
#' Tab5.10
#'
#' ggplot(data = Tab5.10, mapping = aes(x = Mean, y = Slope))+
#' geom_point(size = 2) +
#' theme_bw() +
#' labs(
#' x = "SeedLot Mean"
#' , y = "Regression Coefficient"
#' )
#'
#' DevSS1 <-
#' DataExam5.1 %>%
#' nest_by(SeedLot) %>%
#' mutate(fm1 = list(lm(Ht ~ SiteMean, data = data))) %>%
#' summarise(SSE = anova(fm1)[2, 2]) %>%
#' ungroup() %>%
#' summarise(Dev = sum(SSE)) %>%
#' as.numeric()
#'
#' ANOVAfm5.4[2, 2]
#'
#' length(levels(DataExam5.1$SeedLot))
#'
#' ANOVAfm5.4.1 <-
#' rbind(
#' ANOVAfm5.4[1:3, ]
#' , c(
#' ANOVAfm5.4[2, 1]
#' , ANOVAfm5.4[3, 2] - DevSS1
#' , (ANOVAfm5.4[3, 2] - DevSS1)/ANOVAfm5.4[2, 1]
#' , NA
#' , NA
#' )
#' , c(
#' ANOVAfm5.4[3, 1]-ANOVAfm5.4[2, 1]
#' , DevSS1
#' , DevSS1/(ANOVAfm5.4[3, 1]-ANOVAfm5.4[2, 1])
#' , DevSS1/(ANOVAfm5.4[3, 1]-ANOVAfm5.4[2, 1])/ANOVAfm5.4[4, 3]
#' , pf(
#' q = DevSS1/(ANOVAfm5.4[3, 1]-ANOVAfm5.4[2, 1])/ANOVAfm5.4[4, 3]
#' , df1 = ANOVAfm5.4[3, 1]-ANOVAfm5.4[2, 1]
#' , df2 = ANOVAfm5.4[4, 1]
#' , lower.tail = FALSE
#' )
#' )
#' , ANOVAfm5.4[4, ]
#' )
#' rownames(ANOVAfm5.4.1) <-
#' c("Site", "SeedLot", "Site:SeedLot", " regressions", " deviations", "Residuals")
#' # Pg. 82
#' ANOVAfm5.4.1
#'
NULL
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