R/example2.R

In RNED/agriTutorial: Tutorial Analysis of Some Agricultural Experiments

#' @name example2
#' @title  EXAMPLE 2: Lack-of-fit and marginality for a single quantitative treatment factor
#' @description
#' Petersen (1994, p. 125) describes an experiment conducted to assess the effects
#' of five different quantities of N-fertiliser (0, 35, 70, 105 and 140 kg N/ha) on root dry
#' matter yield of sugar beet (t/ha) with three complete replications laid out in three
#' randomized complete blocks. One objective of this experiment was to determine the amount
#' of fertilizer for maximizing yield.
#'
#' @details
#'
#' The first stage of the analysis is the calculation of raw polynomial powers of N using the poly() function.
#' The N rates are re-scaled by division by 100 to improve numerical stability.
#'
#' The second stage fits a full polynomial analysis of variance based on polynomial contrasts
#' fitted in sequence from the lowest to the highest. This is equivalent to the analysis shown in Tables 4 and 5
#' of Piepho and Edmondson except that a complete partition into single degree of freedom polynomial contrasts is
#' shown here compared with the pooled 'lack of fit' term shown in Tables 4 and 5.
#'
#' The third stage fits a quadratic regression model with linear and quadratic terms only.
#' This model provides the model coefficients, standard errors and the confidence intervals
#' shown in Table 6 of Piepho and Edmondson. A set of diagnostic plots are fitted for
#' the fitted quadratic regression model to check the validity of the model assumptions.
#'
#' Finally, a smoothed quadratic graph of the yield versus the N rate is plotted to show the
#' goodness of fit of the quadratic regression model. This plot corresponds to plot Fig 3 in
#' Piepho and Edmondson.
#'
#' \code{\link[agriTutorial]{agriTutorial}} : back to home page\cr
#'
#' @references
#' Petersen, R.G. (1994). Agricultural field experiments. Design and analysis. New York: Marcel Dekker.
#'
#' Piepho, H. P. & Edmondson R. N. (accepted). A tutorial on the statistical analysis of factorial experiments with qualitative and quantitative
#' treatment factor levels.Journal of Agronomy and Crop Science. Accepted.
#'
#' @examples
#'
#' ## Copy and paste the following code into a R console or GUI:
#' ## ggplot2 MUST be installed
#'
#' \dontrun{
#'
#' ## *************************************************************************************
#' ##                            Preliminaries
#' ##**************************************************************************************
#'
#' ## sink("F:\\tutorial2\\OutputsR\\outExample2.txt") #sink file for outputs
#' ## pdf("F:\\tutorial2\\OutputsR\\outExample2_Fig_S2.pdf") #opens a graphical pdf output file
#' options(contrasts=c('contr.treatment','contr.poly'))
#' require(ggplot2)
#' data(beet)
#' ## write.table(beet, "c:/beet.txt", sep="\t") # export data to a text file
#' ## write.xlsx(beet, "c:/beet.xlsx") # export data to a spread sheet
#'
#' ## *************************************************************************************
#' ##         Polynomial analysis and graphical plots of factorial treatment effects
#' ##**************************************************************************************
#'
#' N=poly((beet$nrate/100), degree=4, raw=TRUE)
#' colnames(N)=c("Linear_N","Quadratic_N","Cubic_N","Quartic_N")
#' beet=cbind(beet,N)
#'
#' ## Tables 4 & 5: Full polynomial analysis of variance based on raw polynomials
#' anova(lm(yield ~ Replicate +  Linear_N + Quadratic_N + Cubic_N + Quartic_N , data=beet))
#'
#' ##  Table 6: showing quadratic model coefficients with standard errors and confidence intervals
#' quadratic = lm(yield ~ Replicate +  Linear_N + Quadratic_N, data=beet)
#' summary(quadratic)
#' confint(quadratic, level=0.95)
#'
#' par(mfrow=c(2,2),oma=c(0,0,2,0))
#' plot(quadratic,sub.caption=NA)
#' title(main="Diagnostic plots for quadratic nitrogen effects model", outer=TRUE)
#'
#' ggplot(beet, aes(x=nrate, y=yield)) +
#' ggtitle("Fig 3 Yield versus N for sugar beet with 95% confidence band")+
#' geom_point(shape=1)+
#' stat_summary(fun.y = mean, geom="point")+
#' geom_smooth(method=lm, formula=y ~ poly(x, 2))+
#' theme_bw()
#'
#' ## *************************************************************************************
#' ##                                  Closure
#' ##**************************************************************************************
#'
#' ## dev.off()
#' ## sink() #closes sink file
#' }
#'
#' @importFrom ggplot2 ggplot
#'
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