Basic terminology in comparative experiments modified versions of Bailey (2008)

Experimental structures as defined by Bailey (2008)

Unreplicated experiments

Treatment replications

Plan 1 Treatment allocation for nested unit structure

• Units: 2 pens with 3 cows each
• Observational units: 6 cows
• Treatments: 3 types of supplements
• Allotment: supplements cows

Are the treatment means of say,
and comparable?

How would you distribute the treatments?

Plan 2 Treatment allocation for nested unit structure

Systematic designs

Randomised designs

Factorial treatment structure 1

• Experimental units: 12 plots
• Observational units: 12 plots
• Observation: wheat yield
• Treatments: combination of:
  • Water: irrigated or rain-fed
  • Fertilizer: type A or type B
• Allotment:
  • Water plots
  • Fertilizer plots
• Assignment: random order

How many treatments are there?

Treatment	Replication
	3
	3
	3
	3

Treatment factor	Count
	6
	6
	6
	6

Factorial treatment structure 2

• Experimental units: 12 plots
• Observational units: 12 plots
• Observation: wheat yield
• Treatments: combination of:
  • Water: irrigated or rain-fed
  • Fertilizer: type A or type B
• Allotment:
  • Water and fertilizer plots
• Assignment: random order

Treatment	Replication
	3
	3
	3
	3

Treatment factor	Count
	6
	6
	6
	6

Factorial treatment structure, nested unit structure, and treatment constraint

A Completely Randomised Design (CRD)

B Randomised Complete Block Design (RCBD)

C Factorial Design

D Split-Plot Design

Design of experiments area appear to have the least collaboration

Top downloaded R-packages in the design of experiments

B agricolae::design.rcbd

Randomised complete block design for $t =3$ treatments with $2$ blocks

trt <- c("A", "B", "C")
agricolae::design.rcbd(trt = trt, r = 2)

## $parameters
## $parameters$design
## [1] "rcbd"
## 
## $parameters$trt
## [1] "A" "B" "C"
## 
## $parameters$r
## [1] 2
## 
## $parameters$serie
## [1] 2
## 
## $parameters$seed
## [1] 351889891
## 
## $parameters$kinds
## [1] "Super-Duper"
## 
## $parameters[[7]]
## [1] TRUE
## 
## 
## $sketch
##      [,1] [,2] [,3]
## [1,] "A"  "C"  "B" 
## [2,] "B"  "C"  "A" 
## 
## $book
##   plots block trt
## 1   101     1   A
## 2   102     1   C
## 3   103     1   B
## 4   201     2   B
## 5   202     2   C
## 6   203     2   A

AlgDesign::gen.factorial()

• First, a helper function to create the treatment (and replicate) combinations:

dat <- AlgDesign::gen.factorial(levels = 3, 
                                nVars = 3, 
                                center = FALSE, 
                                varNames = c("irrigation", 
                                             "fertilizer", 
                                             "variety"), 
                                factors = "all")
dat

##    irrigation fertilizer variety
## 1           1          1       1
## 2           2          1       1
## 3           3          1       1
## 4           1          2       1
## 5           2          2       1
## 6           3          2       1
## 7           1          3       1
## 8           2          3       1
## 9           3          3       1
## 10          1          1       2
## 11          2          1       2
## 12          3          1       2
## 13          1          2       2
## 14          2          2       2
## 15          3          2       2
## 16          1          3       2
## 17          2          3       2
## 18          3          3       2
## 19          1          1       3
## 20          2          1       3
## 21          3          1       3
## 22          1          2       3
## 23          2          2       3
## 24          3          2       3
## 25          1          3       3
## 26          2          3       3
## 27          3          3       3

AlgDesign::optFederov

• Optimum design with 14 trials using Federov's exchange algorithm

AlgDesign::optFederov(frml = ~ ., # assume additive effects
                      data = dat, 
                      nTrials = 14, 
                      criterion = "D")

## $D
## [1] 0.2343815
## 
## $A
## [1] 6.25
## 
## $Ge
## [1] 0.727
## 
## $Dea
## [1] 0.687
## 
## $design
##    irrigation fertilizer variety
## 2           2          1       1
## 3           3          1       1
## 4           1          2       1
## 5           2          2       1
## 7           1          3       1
## 9           3          3       1
## 10          1          1       2
## 13          1          2       2
## 15          3          2       2
## 17          2          3       2
## 19          1          1       3
## 23          2          2       3
## 24          3          2       3
## 25          1          3       3
## 
## $rows
##  [1]  2  3  4  5  7  9 10 13 15 17 19 23 24 25

AlgDesign::optBlock()

• An optimal design with 3 blocks of size 9.

AlgDesign::optBlock(frml = ~ ., # assume additive effects
                    withinData = dat, 
                    blocksizes = rep(9, 3),
                    criterion = "D")

## $D
## [1] 0.1924501
## 
## $diagonality
## [1] 0.866
## 
## $Blocks
## $Blocks$B1
##    irrigation fertilizer variety
## 2           2          1       1
## 5           2          2       1
## 8           2          3       1
## 12          3          1       2
## 15          3          2       2
## 16          1          3       2
## 21          3          1       3
## 22          1          2       3
## 25          1          3       3
## 
## $Blocks$B2
##    irrigation fertilizer variety
## 1           1          1       1
## 6           3          2       1
## 9           3          3       1
## 10          1          1       2
## 13          1          2       2
## 18          3          3       2
## 20          2          1       3
## 23          2          2       3
## 26          2          3       3
## 
## $Blocks$B3
##    irrigation fertilizer variety
## 3           3          1       1
## 4           1          2       1
## 7           1          3       1
## 11          2          1       2
## 14          2          2       2
## 17          2          3       2
## 19          1          1       3
## 24          3          2       3
## 27          3          3       3
## 
## 
## $design
##    irrigation fertilizer variety
## 2           2          1       1
## 5           2          2       1
## 8           2          3       1
## 12          3          1       2
## 15          3          2       2
## 16          1          3       2
## 21          3          1       3
## 22          1          2       3
## 25          1          3       3
## 1           1          1       1
## 6           3          2       1
## 9           3          3       1
## 10          1          1       2
## 13          1          2       2
## 18          3          3       2
## 20          2          1       3
## 23          2          2       3
## 26          2          3       3
## 3           3          1       1
## 4           1          2       1
## 7           1          3       1
## 11          2          1       2
## 14          2          2       2
## 17          2          3       2
## 19          1          1       3
## 24          3          2       3
## 27          3          3       3
## 
## $rows
##  [1]  2  5  8 12 15 16 21 22 25  1  6  9 10 13 18 20 23 26  3  4  7 11 14 17 19 24 27

Drawing faces 1 Specific instructions for the computer

Drawing a happy face

library(grid)
# face shape
grid.circle(x = 0.5, y = 0.5, r = 0.5)
# eyes
grid.circle(x = c(0.35, 0.65),
            y = c(0.6, 0.6),
            r = 0.05,
            gp = gpar(fill = "black"))
# mouth
grid.curve(x1 = 0.4, y1 = 0.4,
           x2 = 0.6, y2 = 0.4,
           square = FALSE)

Drawing faces 1 Specific instructions for the computer

Drawing a sad face

library(grid)
# face shape
grid.circle(x = 0.5, y = 0.5, r = 0.5)
# eyes
grid.circle(x = c(0.35, 0.65),
            y = c(0.6, 0.6),
            r = 0.05,
            gp = gpar(fill = "black"))
# mouth
grid.curve(x1 = 0.4, y1 = 0.4,
           x2 = 0.6, y2 = 0.4,
           square = FALSE,
           curvature = -1)

Drawing faces 2 Functional instructions for the computer

Use functions to draw faces

face1 <- function() {
  grid::grid.circle(x = 0.5, y = 0.5, r = 0.5)
  grid::grid.circle(x = c(0.35, 0.65),
                    y = c(0.6, 0.6),
                    r = 0.05,
                    gp = gpar(fill = "black"))
  grid::grid.curve(x1 = 0.4, y1 = 0.4,
                   x2 = 0.6, y2 = 0.4,
                   square = FALSE)
}
face2 <- function() {
  grid::grid.circle(x = 0.5, y = 0.5, r = 0.5)
  grid::grid.circle(x = c(0.35, 0.65),
                    y = c(0.6, 0.6),
                    r = 0.05,
                    gp = gpar(fill = "black"))
  grid::grid.curve(x1 = 0.4, y1 = 0.4,
                   x2 = 0.6, y2 = 0.4,
                   square = FALSE,
                   curvature = -1)
}

face1()

face1()

face2()

face2()

face1()

face1()

Drawing faces 3 Human-centered design

Adapt computational systems for human use with syntactic sugar

face1()

face2()

face3()

Alternative function names:

face_happy()

face_sad()

face_angry()

Now what do you expect for the output?

• Functions are named after emotions
• Emotion is a surrogate for describing the entire face

Drawing faces 4 Rethinking function arguments as facial parts

Let's reframe how we think

Drawing faces 4 Rethinking function arguments as facial parts

Let's reframe how we think

https://github.com/emitanaka/portrait

library(portrait)

Drawing faces 4 Rethinking function arguments as facial parts

Let's reframe how we think

https://github.com/emitanaka/portrait

library(portrait)

face(eyes = "googly",
     mouth = "smile",
     shape = "round")

face(eyes = "round",
     mouth = "sad",
     shape = "oval")

• We can easily make large number of faces with a single function
• It makes users think about faces based on facial features

But what about hair, nose and other facial features?

Drawing faces 4 Rethinking function arguments as facial parts

Let's reframe how we think

face(eyes = "googly",
     mouth = "smile",
     shape = "round",
     hair = "none",
     nose = "simple")

face(eyes = "googly",
     mouth = "smile",
     shape = "round",
     hair = "mohawk",
     nose = "simple")

But about other facial features?

Drawing faces 5 Object oriented programming

Rethink everything as an object

Drawing faces 5 Object oriented programming

Rethink everything as an object

library(portrait)
face()

Drawing faces 5 Object oriented programming

Rethink everything as an object

library(portrait)
face() +
  cat_shape()

Drawing faces 5 Object oriented programming

Rethink everything as an object

library(portrait)
face() +
  cat_shape() +
  cat_eyes()

Drawing faces 5 Object oriented programming

Rethink everything as an object

library(portrait)
face() +
  cat_shape() +
  cat_eyes() +
  cat_nose()

Drawing faces 5 Object oriented programming

Rethink everything as an object

library(portrait)
face() +
  cat_shape() +
  cat_eyes() +
  cat_nose() +
  cat_whiskers()

Drawing faces 5 Object oriented programming

Rethink everything as an object

library(portrait)
face() +
  dog_shape() +
  cat_eyes(fill = "red") +
  cat_nose() +
  cat_whiskers()

Drawing faces 5 Object oriented programming

Rethink everything as an object

library(portrait)
face() +
  dog_shape() + 
  cat_eyes(fill = "red") + 
  cat_nose() +
  cat_whiskers(size = 6,
               color = "brown") +
  sketch_mouth(smile = 0.3,
               size = 3)

The grammar of experimental design with edibble

library(edibble)
start_design("My experiment")

The grammar of experimental design with edibble

library(edibble)
start_design("My experiment") %>% 
  set_units(wholeplot = 4)

The grammar of experimental design with edibble

library(edibble)
start_design("My experiment") %>% 
  set_units(wholeplot = 4) %>% 
  set_units(subplot = nested_in(wholeplot, 2))

The grammar of experimental design with edibble

library(edibble)
start_design("My experiment") %>% 
  set_units(wholeplot = 4,
            subplot = nested_in(wholeplot, 2))

The grammar of experimental design with edibble

library(edibble)
start_design("My experiment") %>% 
  set_units(wholeplot = 4, 
            subplot = nested_in(wholeplot, 2)) %>% 
  set_trts(water = c("irrigated", "rainfed"),
           fertilizer = c("A", "B"))

The grammar of experimental design with edibble

library(edibble)
start_design("My experiment") %>% 
  set_trts(water = c("irrigated", "rainfed"),
           fertilizer = c("A", "B")) %>%
  set_units(wholeplot = 4, 
            subplot = nested_in(wholeplot, 2))

The grammar of experimental design with edibble

library(edibble)
start_design("My experiment") %>% 
  set_trts(water = c("irrigated", "rainfed")) %>%
  set_units(wholeplot = 4) %>% 
  set_trts(fertilizer = c("A", "B")) %>%
  set_units(subplot = nested_in(wholeplot, 2))

The grammar of experimental design with edibble

library(edibble)
start_design("My experiment") %>% 
  set_units(wholeplot = 4, 
            subplot = nested_in(wholeplot, 2)) %>% 
  set_trts(water = c("irrigated", "rainfed"), 
           fertilizer = c("A", "B")) %>% 
  allot_trts(water ~ wholeplot,
                fertilizer ~ subplot)

The grammar of experimental design with edibble

library(edibble)
start_design("My experiment") %>% 
  set_units(wholeplot = 4, 
            subplot = nested_in(wholeplot, 2)) %>% 
  set_trts(water = c("irrigated", "rainfed"), 
           fertilizer = c("A", "B")) %>% 
  allot_trts(water ~ wholeplot, 
                fertilizer ~ subplot) %>% 
  assign_trts("random", seed = 1)

The grammar of experimental design with edibble

library(edibble)
start_design("My experiment") %>% 
  set_units(wholeplot = 4,
            subplot = nested_in(wholeplot, 2)) %>% 
  set_trts(water = c("irrigated", "rainfed"),
           fertilizer = c("A", "B")) %>% 
  allot_trts(water ~ wholeplot,
                fertilizer ~ subplot) %>% 
  assign_trts("random", seed = 1) %>% 
  serve_table()

The grammar of experimental design with edibble

library(edibble)
start_design("Modified design") %>% 
  set_units(block = 2,
            subplot = nested_in(block, 4)) %>%
  set_trts(water = c("irrigated", "rainfed"),
           fertilizer = c("A", "B")) %>% 
  allot_trts(water:fertilizer ~ subplot) %>%
  assign_trts("random", seed = 1) %>% 
  serve_table()

The grammar of experimental design with edibble

library(edibble)
start_design("Modified design") %>% 
  set_units(block = 2,
            subplot = nested_in(block, 4)) %>% 
  set_trts(water = c("irrigated", "rainfed"),
           fertilizer = c("A", "B")) %>% 
  allot_trts(water:fertilizer ~ subplot) %>%  
  assign_trts("random", seed = 1) %>% 
  set_rcrds_of(subplot = c("yield", "disease"),
               block = "manager") %>%
  serve_table()

The grammar of experimental design with edibble

out <- start_design("Modified design") %>% 
  set_units(block = 2,
            subplot = nested_in(block, 4)) %>% 
  set_trts(water = c("irrigated", "rainfed"),
           fertilizer = c("A", "B")) %>% 
  allot_trts(water:fertilizer ~ subplot) %>%  
  assign_trts("random", seed = 1) %>% 
  set_rcrds_of(subplot = c("yield", "disease"), 
               block = "manager") %>% 
  expect_rcrds(yield = to_be_numeric(with_value(">=", 0)),
               disease = to_be_factor(levels = c("none", "moderate",  "severe"))) %>%
  serve_table()

export_design(out, file = "design-layout.xlsx", overwrite = TRUE)

• The exported file has data validation features embedded