A factorial experiment was conducted to evaluate the efficacy of three herbicides (Herbicide) across nine different populations of black-grass (Population). Herbicides A and C belong to the same chemical group (Type 1), while herbicide B represents a different group (Type 2). The experiment followed a randomized complete block design with five replicates (Rep), each comprising 27 pots (dummy factor DPot). Six plants were grown per pot, and their combined fresh weight (Fwt, in grams) was measured at the conclusion of the study. The dataset allows investigation of differences in herbicide efficacy both between and within herbicide groups, as well as variation in response among different black-grass populations.
Format
A data frame with 7 variables: ID, Rep, DPot, Population, Type, Herbicide, Fwt.
- ID
Factor. Unique identifier for each pot (experimental unit).
- Rep
Factor. Block number in the randomized complete block design corresponding to replicate (1–5).
- DPot
Factor. Dummy variable indicating the pot number within each block.
- Population
Factor. Identifier for the black-grass population (e.g., "P1"–"P9").
- Type
Factor. Chemical group of the applied herbicide (1: group for Herbicides A and C, 2: group for Herbicide B).
- Herbicide
Factor. Applied herbicide treatment ("A", "B", or "C").
- Fwt
Numeric. Total fresh weight (in grams) of six black-grass plants grown in the pot.
Source
Welham, S. J., Gezan, S. A., Clark, S. J., and Mead, A. (2015) Statistical Methods in Biology: Design and analysis of experiments and regression
R. Hull, Rothamsted Research.
Examples
aov(sqrt(Fwt) ~ Herbicide * Population + Error(Rep/DPot), data = herbicide)
#>
#> Call:
#> aov(formula = sqrt(Fwt) ~ Herbicide * Population + Error(Rep/DPot),
#> data = herbicide)
#>
#> Grand Mean: 1.653736
#>
#> Stratum 1: Rep
#>
#> Terms:
#> Residuals
#> Sum of Squares 1.311058
#> Deg. of Freedom 4
#>
#> Residual standard error: 0.5725072
#>
#> Stratum 2: Rep:DPot
#>
#> Terms:
#> Herbicide Population Herbicide:Population Residuals
#> Sum of Squares 15.72075 3.50803 13.94369 12.76256
#> Deg. of Freedom 2 8 16 104
#>
#> Residual standard error: 0.3503098
#> Estimated effects may be unbalanced