diets <- c("Control", "High-sugar", "High-fat")
# Completely Randomised Design
agricolae::design.crd(trt = diets, r = 10)
# Randomised Complete Block Design
agricolae::design.rcbd(trt = diets, r = 10)
exercise <- c("Yes", "No")
# Factorial design
agricolae::design.ab(trt = c(length(diets), length(exercise)), r = 10)
# Split-plot design
agricolae::design.split(trt1 = diets, trt2 = exercise, r = 10) The Originator of an Experiment
The “domain expert” drives the experimental objective and has the intricate knowledge about the subject area
Stick person images by OpenClipart-Vectors from Pixabay
The Designer of the Experiment
Let there be an experimental design!
The “statistican” creates the experimental design layout after taking into account the statistical and practical constraints.
The Executor of the Experiment
The “technician” carries out the experiment and collects the data.
The Digester of the Experiment
The “analyst” analyses the data after the data is collected.
The actors are purely illustrative
Roles may be fuzzy
In practice:
- multiple people can take on each role,
- one person can take on multiple roles, and/or
- a person in the role may not specialise in that role.
Hypothesis:
- increasing plant diversity leads to increasing soil microbial biomass and enzyme activity,
- higher temperature decreases soil microbial biomassand enzyme activity, and
- higher plant diversity buffers effects of elevated temperature on soil microbialbiomass and enzyme activity.
🌾 
MATERIALS AND METHODS
Experimental design
The present study took place in the BAC experiment site established at the Cedar Creek Ecosystem Science Reserve, Minnesota, USA. The site occurs on a glacial outwash plain with sandy soils. Mean temperature during the growing season (April–September) was 15.98°C in 2011 and 17.18°C in 2012. Precipitation during the growing season was 721 mm in 2011. The growing season in 2012 was considerably drier, with 545 mm rainfall.
Experimental plots (9Ă—9 m) were planted in 1994 and 1995 with different plant communities spanning a plant diversity gradient of one, four, and 16 species, which were randomly chosen from the species listed below (Tilman et al. 2001). The grassland prairie species belonged to one of five plant functional groups: C3 grasses (Agropyron smithii Tydb., Elymus canadensis L., Koeleria cristata (Ledeb.) Schult., Poa pratensis L.), C4 grasses (Andropogon gerardii Vitman., Panicum virgatum L., Schizachyrium scoparium (Michx.) Nash, Sorghas-trum nutans (L.) Nash), legumes (Amorpha canescens Pursh., Lespedeza capitata Michx., Lupinus perennis L., Petalostemum purpureum (Vent.) Rydb., Petalostemum villosum Spreng.), nonlegume forbs (Achillea millefolium L., Asclepias tuberosa L., Liatris aspera Michx., Monarda fistulosa L., Soldidago rigida L.), and woody species (Quercus ellipsoidalis E. J. Hill, Quercus macro-carpa Michx.). The individuals of those two woody species (Quercus spp.), which were small in size and rare because of low survival, were removed from all plots in which they occurred in 2010.
In addition to the manipulation of plant diversity,the plots were divided into three subplots (2.5×3.0 m). Heat treatments were applied from March to November each year, beginning in 2009, using infrared lamps 1.8 m above ground emitting 600 W (which caused a 1.5°C increase in soil temperature for vegetation-freesoils) and 1200 W (which caused a 3°C increase; Valpine and Harte 2001, Kimball 2005, Whittingtonet al. 2013) to increase the surface soil temperature of each subplot (see Plate 1). To account for possible shading effects, metal flanges and frames were hungover control subplots. An average across all vegetated plots, temperature manipulations elevated soil temperature at 1 cm depth by 1.18°C in the low warming (+1.5°C) treatment and by 2.69°C in the high warming (+3°C) treatment, and at 10 cm depth temperature by 1.00°C in the low warming (+1.5°C) treatment and by 2.16°C in the high warming (+3°C) treatment.
Soil samples of three subplots in each of 27 experimental plots were taken; due to technical difficulties we could only analyze 66 samples out of 81 existing subplots (monoculture, 10 replicates in ambient +0°C treatment, eight replicates in +1.5°C treatment, nine replicates in +3°C treatment; four species mixture, six replicates in ambient +0°C treatment, six replicates in +1.5°C treatment, seven replicates in +3°C treatment; 16 species mixture, six replicates in ambient +0°C treatment, six replicates in +1.5°C treatment, eight replicates in +3°C treatment). The BAC plots are a representative subset of the plots in the biodiversity experiment E120 at Cedar Creek, which were assembled as random draws of a given number of species from the species pool (Zak et al. 2003). Given low heterogeneity of soil abiotic conditions at the start of the experiment, the experiment was not blocked.
🌾
MATERIALS AND METHODS
Experimental design (condensed version)
- Experimental plots were planted with different plant communities spanning a plant diversity gradient of one, four, and 16 species, which were randomly chosen from the species listed (5 plant functional groups – 19 species in total)
- Plots were divided into three subplots
- Heat treatments were applied to subplots emitting 600 W which caused a 1.5°C increase in soil temperature for vegetation-free soils) and 1200 W (which caused a 3°C increase) (control with 0°C included)
- Soil samples of three subplots in each of 27 experimental plots were taken
- Given low heterogeneity of soil abiotic conditions at the start of the experiment, the experiment was not blocked.
This is in fact a split-plot design!
library(edibble)
des1 <- design("Steinauer et al. 2015") %>%
set_units(plot = 27,
subplot = nested_in(plot, 3)) %>%
set_trts(
nspecies = c(1, 4, 16),
temperature = c("0°C", "1.5°C", "3°C")) %>%
allot_trts( nspecies ~ plot,
temperature ~ subplot) %>%
assign_trts("random") %>%
serve_table()
des1# Steinauer et al. 2015
# An edibble: 81 x 4
plot subplot nspecies temperature
<unit(27)> <unit(81)> <trt(3)> <trt(3)>
1 plot1 subplot1 4 1.5°C
2 plot1 subplot2 4 3°C
3 plot1 subplot3 4 0°C
4 plot2 subplot4 16 3°C
5 plot2 subplot5 16 1.5°C
6 plot2 subplot6 16 0°C
7 plot3 subplot7 1 3°C
8 plot3 subplot8 1 1.5°C
9 plot3 subplot9 1 0°C
10 plot4 subplot10 1 1.5°C
# … with 71 more rowsDownstream Benefit #1 Easy-and-quick visualisation
Downstream Benefit #2 Cutomise visualisation
library(deggust)
autoplot(des1, aspect_ratio = 3/2) +
# the result is a ggplot object --
# add ggplot functions on top
# as you like to customise the plot!
theme(
legend.position = "bottom",
text = element_text(size = 18),
plot.background =
element_rect(color = "black",
linetype = "dashed",
fill = "wheat"),
plot.margin = margin(20, 20, 20, 20),
plot.subtitle =
element_text(margin = margin(0, 0, 10, 0))) +
scale_fill_brewer(palette = "Reds")
Specifying unbalanced designs
MATERIALS AND METHODS
Experimental design (condensed version)
- Experimental plots were planted with different plant communities spanning a plant diversity gradient of one, four, and 16 species, which were randomly chosen from the species listed (5 plant functional groups – 19 species in total)
des2 <- design("Steinauer et al. 2015 Part II") %>%
set_units(plot = 27,
plant = nested_in(plot, 1:9 ~ 1,
10:18 ~ 4,
19:27 ~ 16)) %>%
set_trts(species = 19) %>%
allot_trts(species ~ plant) %>%
assign_trts("random") %>%
serve_table()
options(deggust.nfill_max = 3)
autoplot(des2) + facet_wrap(~plot, nrow = 2)
- Experiments are human endeavours.
- Our understanding is fuzzy but certain frameworks can shed clarity.
- Remember the “garbage-in garbage-out” principle.
- Slides at emitanaka.org/slides/Ihaka2022/
-
install.packages(“edibble”)
remotes::install_github(“emitanaka/deggust”) - emitanaka.org/edibble-book (WIP)
- Paper about experimental design R-packages at arxiv.org/abs/2206.07532
- emi.tanaka@monash.edu
