agriTutorial: Tutorial Analysis of Agricultural Experiments
In RNED/agriTutorial: Tutorial Analysis of Some Agricultural Experiments

The agri.tutorial package provides example software for the analysis of five agricultural example data sets in the paper: 'A tutorial on the statistical analysis of factorial experiments with qualitative and quantitative treatment factor levels' by Piepho and Edmondson (in press).

Code

The example code reproduces the statistical analyses of the agricultural data sets discussed in Piepho and Edmondson and also produces some graphical methods of data analysis. The data for each analysis is provided as a data frame which is loaded automatically whenever the package is loaded. The example code for each analysis is provided as a set of examples which can be executed by pasting the example code into any suitable R console terminal window. Provided that all the required packages (including agriTutorial) have been loaded,the output should then reproduce the example analyses given by Piepho and Edmondson.

All printed output should appear appear in the gui or terminal window but can be diverted to a suitable text file by using a sink file command, if required. Graphical output should appear in the gui graphics window but can be diverted to a suitable pdf file by using a pdf file command, if required. Data and output can be exported directly to a text file or spread sheet file by using the write.table or write.xlsx functions, if required.

The lines of code for opening or closing .txt files or .pdf files or for exporting data sets are preceded by a hash symbol to suppress the command but these lines can be activated by deleting the hash symbol. The "dontrun" tags are required for package testing at CRAN and and can be ignored here.

The example code demonstrates some basic modern methodology for the analysis of data from designed experiments but there are many other packages available and it is straightforward to extend the example code by adding functionality from other packages. One source of package information is the set of package 'views' available at: https://cran.rstudio.com/web/views/.

Polynomials
The polynomials used in this tutorial are either raw polynomials or orthogonal polynomials. A raw polynomial is a numeric vector raised to the power of the required polynomial whereas an orthogonal polynomial is a linear combination of raw polynomials of degree equal to or less than the degree of the required polynomial. Raw polynomial coefficients are the actual required polynomial model coefficients whereas orthogonal polynomial coefficients are linear combinations of the required polynomial model coefficients. Raw polynomial coefficients have a direct interpretation as polynomial model coeffcients but can be numerically unstable for higher-degree polynomials whereas orthogonal polynomial coefficients are numerically stable but can be difficult to interpret. Raw polynomials are the polynomials of choice for most analyses but sometimes orthogonal polynomials can be useful when, for example, fitting higher-degree polynomials in a long series of repeated measures (see example 4).

Functional marginality
Any polynomial expansion of an unknown function must include all polynomial terms up to and including the degree of the expansion.This is the property of functional marginality and applies to any response surface design including designs with polynomial interaction effects (Nelder, 2000). In this tutorial, all polynomial models and response surface designs will be assumed to conform with the requirements of functional marginality.

Packages
The example code depends on a number of R packages which must be installed on the user machine before the example code can be properly executed. The required packages are lmerTest, lsmeans, pbkrtest, lattice, nlme and ggplot2, all of which should install automatically. If, for any reason, packages need to be installed by hand, this can be done by using the install.packages(—package name—) command from an R interface.

NB. It is important to keep packages updated using the update.packages() command.

Examples:

example1 : split-plot design with one quantitative and one qualitative treatment factor
example2 : block design with one qualitative treatment factor
example3 : response surface design with two quantitative treatment factors
example4 : repeated measures design with one quantitative treatment factor
example5 : block design with transformed quantitative treatment levels

Piepho, H. P, and 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.

Nelder, J. A. (2000). Functional marginality and response-surface fitting. Journal of Applied Statistics, 26, 109-122.

RNED/agriTutorial documentation built on May 28, 2019, 2:26 p.m.