Constructing experimental designs with the edibble R-package

.info-box.w-50.bg-white[
These slides are viewed best by Chrome or Firefox and occasionally need to be refreshed if elements did not load properly. Please note this web version takes a while to load. See <a href="edibble.pdf">here for the PDF </a>. 
]

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background-size: cover
class: title-slide
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# .f1.monash-blue[Constructing experimental designs with the `edibble` R-package]

.bottom_abs.width100[

Presenter: *Emi Tanaka*

Department of Econometrics and Business Statistics, &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Monash University, Melbourne, Australia

emi.tanaka@monash.edu

<a href="https://twitter.com/statsgen" style="color:black"> @statsgen</a>

9 Nov 2021 @ Applications of Statistical Procedures in Biological Data

]

---

.f1.tl[
 **Table of Contents**]

.f2.pa3.tl[

.box[4] The .yellow[**grammar of experimental designs**] with .yellow[`edibble`] .f3.grey[ ] [.f4[]](#edibble)

]

.border-box.monash-bg-blue2.center.w-70[
 These slides made using R powered by HTML/CSS/JS can be found at <a class="f2" style="color:yellow!important" href="https://emitanaka.org/slides/stats4bio2021/edibble">emitanaka.org/slides/stats4bio2021/edibble</a>
]

---

# Experimental design *basics*

---

# .f-headline[Experiment]

Essential scientific endeavors to collect data to explore, understand or verify phenomena.
]

???

Big picture terminologies

---

# .f-headline[Experimental data]

---

# .f-headline[Comparative experiments]

.f1[
Collecting data to compare the effects of different conditions under a **_controlled environment_** with the goal of drawing generalisable conclusions
]

---

# .f-subheadline[Designing comparative experiments]

.blockquote[
 ... to identify data-collection schemes that achieve sensitivity and specificity requirements despite biological and technical variability, while keeping time and resource costs low.
.right[
&mdash; Krzywinski & Altman (2014)
]
]

.footnote.f4[
Krzywinski, M., Altman, N. Designing comparative experiments. _Nat Methods_ 11, 597–598 (2014). https://doi.org/10.1038/nmeth.2974
]

Planning the controlled environment such that there is a higher confidence that effects can be attributed to selected conditions

---

# Basic terminology in comparative experiments .f3.gray[modified versions of Bailey (2008)]

.flex[
.w-50.pr3[
.info-box.f3[
A **treatment** `$(\mathcal{T})$` is the entire description of the condition applied to an experimental unit.
]

.info-box.f3[
**Experimental unit** `$(\Omega)$` is the smallest unit that the treatment can be independently applied to.
]
.info-box.f3[
**Observational unit** `$(\Omega_o)$` is the smallest unit in which the response will be measured on. 
* Not to be confused with responses `$\boldsymbol{Y}$`.
* May or may not be the same as experimental unit.
]

]
.w-50[
.info-box.f3[
**Block**, also called **cluster**, is the unit that group some other units (e.g. experimental units) such that the units within the same block (cluster) are more alike (homogeneous).
]

.info-box.f3[
A **design** `$(D: \Omega \rightarrow \mathcal{T})$` is the allotment of treatments to particular set of units.
]

.info-box.f3[
A **plan** or **layout** is the design translated into actual units. *Randomisation* is usually involved in the translation process. 
]
]]

.absolute.top-0.right-1[
[](#edibble)
]

.footnote.f5[
Bailey, R. (2008). Design of Comparative Experiments (Cambridge Series in Statistical and Probabilistic Mathematics). Cambridge: Cambridge University Press. doi:10.1017/CBO9780511611483
]

---

# Experimental structures .f3.gray[as defined by Bailey (2008)]

.flex[
.w-50[
.info-box.f3[
**Unit structure** means meaningful ways of dividing up experimental units `$(\Omega)$` and observational units `$(\Omega_o)$`.

For example:
* **Unstructured**
* **Blocking**
]
]
.w-50.pl3[
.info-box.f3[
 **Treatment structure** means meaningful ways of dividing up `$\mathcal{T}$`.

For example:
* **Unstructured**: no grouping within `$\mathcal{T}$`
* **Factorial**: all combinations of at least two factors
* **Factorial + control**
]

]]

---

# Unreplicated experiments

.center[
<img src='images/cow1.png' width='120px' style='margin-right:20px;'><img src='images/cow1.png' width='120px' style='margin-right:20px;'><img src='images/cow1.png' width='120px' style='margin-right:20px;'>

.flex[
.w-45[
.border-box[
* **Experimental units**: 3 cows
* **Observational units**: 3 cows
* **Observation**: milk yield
* **Treatments**: 3 types of supplements
* **Allotment**: supplements cows
* **Replication**: 1 each
]

]
.w-55[
{{content}}
]]

**Conclusion**: <img src='images/supplement1.png' style='height:1em'> produces most <img src='images/milk.png' style='height:1em'> therefore <img src='images/supplement1.png' style='height:1em'> is the most effective supplement for higher milk yield from cows out of the three supplements tested

<div class=' f2 '> How confident will you be of this statement? </div>

---

# Unreplicated experiments

.center[
<img src='images/cow7.png' width='120px' style='margin-right:20px;'><img src='images/cow1.png' width='120px' style='margin-right:20px;'><img src='images/cow4.png' width='120px' style='margin-right:20px;'>

]
.w-55[
**Conclusion**: <img src='images/supplement1.png' style='height:1em'> produces most <img src='images/milk.png' style='height:1em'> therefore <img src='images/supplement1.png' style='height:1em'> is the most effective supplement for higher milk yield from cows out of the three supplements tested

<div class=' f2 '> How confident will you be of this conclusion? </div>

* No individual experimental units are the same (with some exceptions)
]]

---

# Treatment replications

.center[
<img src='images/cow1.png' width='120px' style='margin-right:20px;'><img src='images/cow2.png' width='120px' style='margin-right:20px;'><img src='images/cow3.png' width='120px' style='margin-right:20px;'><img src='images/cow4.png' width='120px' style='margin-right:20px;'><img src='images/cow5.png' width='120px' style='margin-right:20px;'><img src='images/cow6.png' width='120px' style='margin-right:20px;'>

<img class='w-20' src='images/milk.png'/><img class='w-20' src='images/milk.png'/><img class='w-20' src='images/milk.png'/><img class='w-20' src='images/milk.png'/> <img class='w-20' src='images/milk.png'/><img class='w-20' src='images/milk.png'/><img class='w-20' src='images/milk.png'/><img class='w-20' src='images/milk.png'/><img class='w-20' src='images/milk.png'/><img class='w-20' src='images/milk.png'/> <img class='w-20' src='images/milk.png'/><img class='w-20' src='images/milk.png'/><img class='w-20' src='images/milk.png'/><img class='w-20' src='images/milk.png'/><img class='w-20' src='images/milk.png'/> <img class='w-20' src='images/milk.png'/><img class='w-20' src='images/milk.png'/><img class='w-20' src='images/milk.png'/> <img class='w-20' src='images/milk.png'/> <img class='w-20' src='images/milk.png'/>
]

.flex[
.w-45[
.border-box[
* **Experimental units**: 6 cows
* **Observational units**: 6 cows
* **Observation**: milk yield
* **Treatments**: 3 types of supplements
* **Allotment**: supplements cows
* **Replication**: 2 each
]

]
.w-55[
**Conclusion**: <img src='images/supplement1.png' style='height:1em'> produces most <img src='images/milk.png' style='height:1em'> *on average* therefore <img src='images/supplement1.png' style='height:1em'> is the most effective supplement for higher milk yield from cows out of the three supplements tested

<div class=' f2 '> How confident will you be of this conclusion now? </div>

]]

* Treatment replications here allow us to estimate experimental unit (or error) variation

---

# Plan .circle[1] Treatment allocation for nested unit structure

.flex[
.w-50.center.pr3[
.border-box.h-100.relative.monash-bg-olive2[
<img src='images/cow1.png' width='120px' style='margin-right:20px;'><img src='images/cow2.png' width='120px' style='margin-right:20px;'><img src='images/cow3.png' width='120px' style='margin-right:20px;'> 
<img src='images/supplement1.png' width='40px'><img src='images/supplement1.png' width='40px'><img src='images/supplement3.png' width='40px'> 
<img class='w-20' src='images/milk.png'/><img class='w-20' src='images/milk.png'/><img class='w-20' src='images/milk.png'/><img class='w-20' src='images/milk.png'/> <img class='w-20' src='images/milk.png'/><img class='w-20' src='images/milk.png'/><img class='w-20' src='images/milk.png'/><img class='w-20' src='images/milk.png'/><img class='w-20' src='images/milk.png'/> <img class='w-20' src='images/milk.png'/><img class='w-20' src='images/milk.png'/><img class='w-20' src='images/milk.png'/><img class='w-20' src='images/milk.png'/><img class='w-20' src='images/milk.png'/>
]]
.w-50.center[
.border-box.h-100.relative.monash-bg-olive2[
<img src='images/cow4.png' width='120px' style='margin-right:20px;'><img src='images/cow5.png' width='120px' style='margin-right:20px;'><img src='images/cow6.png' width='120px' style='margin-right:20px;'> 
<img src='images/supplement3.png' width='40px'><img src='images/supplement2.png' width='40px'><img src='images/supplement2.png' width='40px'> 
 <img class='w-20' src='images/milk.png'/><img class='w-20' src='images/milk.png'/><img class='w-20' src='images/milk.png'/> <img class='w-20' src='images/milk.png'/> <img class='w-20' src='images/milk.png'/>
]]
]
 
.flex[
.w-45[
.border-box[
* **Units**: 2 pens with 3 cows each
* **Observational units**: 6 cows
* **Treatments**: 3 types of supplements
* **Allotment**: supplements cows
]

]
.w-55[

<div class=' f2 '> Are the treatment means of say, <img src='images/supplement1.png' style='height:1em;'> and <img src='images/supplement3.png' style='height:1em;'> comparable? </div>

<div class=' f2 '> How would you distribute the treatments? </div>
]]

---

# Plan .circle[2] Treatment allocation for nested unit structure

.flex[
.w-50.center.pr3[
.border-box.h-100.relative.monash-bg-olive2[
<img src='images/cow1.png' width='120px' style='margin-right:20px;'><img src='images/cow2.png' width='120px' style='margin-right:20px;'><img src='images/cow3.png' width='120px' style='margin-right:20px;'> 
<img src='images/supplement1.png' width='40px'><img src='images/supplement3.png' width='40px'><img src='images/supplement2.png' width='40px'> 
<img class='w-20' src='images/milk.png'/><img class='w-20' src='images/milk.png'/><img class='w-20' src='images/milk.png'/><img class='w-20' src='images/milk.png'/> <img class='w-20' src='images/milk.png'/><img class='w-20' src='images/milk.png'/><img class='w-20' src='images/milk.png'/><img class='w-20' src='images/milk.png'/><img class='w-20' src='images/milk.png'/> <img class='w-20' src='images/milk.png'/>
]]
.w-50.center[
.border-box.h-100.relative.monash-bg-olive2[
<img src='images/cow4.png' width='120px' style='margin-right:20px;'><img src='images/cow5.png' width='120px' style='margin-right:20px;'><img src='images/cow6.png' width='120px' style='margin-right:20px;'> 
<img src='images/supplement1.png' width='40px'><img src='images/supplement3.png' width='40px'><img src='images/supplement2.png' width='40px'> 
 <img class='w-20' src='images/milk.png'/><img class='w-20' src='images/milk.png'/><img class='w-20' src='images/milk.png'/><img class='w-20' src='images/milk.png'/><img class='w-20' src='images/milk.png'/> <img class='w-20' src='images/milk.png'/><img class='w-20' src='images/milk.png'/><img class='w-20' src='images/milk.png'/> <img class='w-20' src='images/milk.png'/>
]]
]
 
.flex[
.w-45[
.border-box[
* **Units**: 2 pens with 3 cows each
* **Observational units**: 6 cows
* **Treatments**: 3 types of supplements
* **Allotment**: supplements cows, .monash-blue[with restriction such that each treatment appears once in each pen]
]

]
.w-55[

* Every treatment appears once in each pen
* This is a better design since each treatment appears in every pen so you can be more confident that the treatment means are not due to the conditions of particular pens

]]

---

# Pseudo-replication

.flex[
.w-33.center[
.border-box.h-100.relative.monash-bg-olive2[
<img src='images/cow1.png' width='120px' style='margin-right:20px;'><img src='images/cow2.png' width='120px' style='margin-right:20px;'> 
<img class='w-20' src='images/milk.png'/><img class='w-20' src='images/milk.png'/><img class='w-20' src='images/milk.png'/><img class='w-20' src='images/milk.png'/> <img class='w-20' src='images/milk.png'/><img class='w-20' src='images/milk.png'/><img class='w-20' src='images/milk.png'/><img class='w-20' src='images/milk.png'/><img class='w-20' src='images/milk.png'/><img class='w-20' src='images/milk.png'/>
.bottom_abs.right-3[
<img src='images/supplement1.png' width='40px'>
]]]
.w-33.center[
.border-box.h-100.relative.monash-bg-olive2[
<img src='images/cow3.png' width='120px' style='margin-right:20px;'><img src='images/cow4.png' width='120px' style='margin-right:20px;'> 
 <img class='w-20' src='images/milk.png'/><img class='w-20' src='images/milk.png'/><img class='w-20' src='images/milk.png'/><img class='w-20' src='images/milk.png'/><img class='w-20' src='images/milk.png'/> <img class='w-20' src='images/milk.png'/><img class='w-20' src='images/milk.png'/><img class='w-20' src='images/milk.png'/>
 .bottom_abs.right-3[
<img src='images/supplement3.png' width='40px'>
]]]
.w-33.center[
.border-box.h-100.relative.monash-bg-olive2[
<img src='images/cow5.png' width='120px' style='margin-right:20px;'><img src='images/cow6.png' width='120px' style='margin-right:20px;'> 
<img class='w-20' src='images/milk.png'/> <img class='w-20' src='images/milk.png'/>
.bottom_abs.right-3[
<img src='images/supplement2.png' width='40px'>
]]]]

.flex[
.w-45[
.border-box[
* **Units**: 3 pens with 2 cows each
* **Observational units**: 6 cows
* **Treatments**: 3 types of supplements
* **Allotment**: supplements .monash-blue[pens]
* **Replication**: ??
]

]
.w-55[
{{content}}
]]

<div class=' f2 '> What are the experimental units? </div>

---

# Pseudo-replication

]
.w-55[
<div class=' f2 '> What are the experimental units? </div>

* Experimental units are the 3 pens. 
{{content}}
]]

* Meaning there is only one replication of each treatment.
{{content}}

--
* Meaning you cannot estimate the error variation in the pen stratum.
{{content}}

--
* Pseudo-replication means that you treat **repetition** as replication in the analysis

---

# Systematic designs

]
.w-55[
<div class=' f2 '> What could go wrong with this? </div>

{{content}}
]]

* The order of the experimental units may be **_confounded_** with some extraneous factor
{{content}}
--

* Like say, the order of the experimental units was determined by the speed (fast to slow) of the cow to get to the feed
{{content}}
--

* This means that the more active cows are given <img src='images/supplement1.png' style='height:1em'> and leasat active ones are given <img src='images/supplement2.png' style='height:1em'>

---

# Randomised designs

<img src='images/supplement2.png' width='40px'><img src='images/supplement1.png' width='40px'><img src='images/supplement2.png' width='40px'><img src='images/supplement3.png' width='40px'><img src='images/supplement1.png' width='40px'><img src='images/supplement3.png' width='40px'>
]

]
.w-55[

* Randomisation protects you against bias and potential unwanted confounding with extraneous factors

{{content}}
]]

* Bias comes in many forms: obvious to not-so obvious,  known to unknown, and so on.

{{content}}
--

* Randomisation doesn't mean it'll completely shield you from all biases!

{{content}}
--

* You can get a systematic order by chance! This doesn't mean you should keep on randomising your design until get the layout you want! You should instead add another unit structure before randomisation.

---

# Factorial treatment structure .circle[1]

.flex[
.w-40[
<img src='images/grain9.png' width='80px' style='margin-right:20px;'><img src='images/grain4.png' width='80px' style='margin-right:20px;'><img src='images/grain7.png' width='80px' style='margin-right:20px;'><img src='images/grain1.png' width='80px' style='margin-right:20px;'> 
<img src='images/water1.png' width='40px'><img src='images/brand1.png' width='40px'><img src='images/water2.png' width='40px'><img src='images/brand2.png' width='40px'><img src='images/water2.png' width='40px'><img src='images/brand2.png' width='40px'><img src='images/water1.png' width='40px'><img src='images/brand1.png' width='40px'> 
<img src='images/grain2.png' width='80px' style='margin-right:20px;'><img src='images/grain5.png' width='80px' style='margin-right:20px;'><img src='images/grain3.png' width='80px' style='margin-right:20px;'><img src='images/grain8.png' width='80px' style='margin-right:20px;'> 
<img src='images/water1.png' width='40px'><img src='images/brand2.png' width='40px'><img src='images/water1.png' width='40px'><img src='images/brand1.png' width='40px'><img src='images/water2.png' width='40px'><img src='images/brand1.png' width='40px'><img src='images/water1.png' width='40px'><img src='images/brand2.png' width='40px'> 
<img src='images/grain6.png' width='80px' style='margin-right:20px;'><img src='images/grain11.png' width='80px' style='margin-right:20px;'><img src='images/grain12.png' width='80px' style='margin-right:20px;'><img src='images/grain10.png' width='80px' style='margin-right:20px;'> 
<img src='images/water2.png' width='40px'><img src='images/brand1.png' width='40px'><img src='images/water2.png' width='40px'><img src='images/brand1.png' width='40px'><img src='images/water2.png' width='40px'><img src='images/brand2.png' width='40px'><img src='images/water1.png' width='40px'><img src='images/brand2.png' width='40px'> 
]
.w-35[
.border-box.w-100[
* **Experimental units**: 12 plots
* **Observational units**: 12 plots
* **Observation**: wheat yield
* **Treatments**: combination of:
 * .monash-blue[Water]: irrigated or rain-fed
 * .monash-blue[Fertilizer]: type A or type B
* **Allotment**: 
 * Water plots
 * Fertilizer plots
* **Assignment**: random order
]
<div class=' f2 '> How many treatments are there? </div>
]
.w-25[
{{content}}
]
]

<table class=" lightable-classic" style='font-family: "Arial Narrow", "Source Sans Pro", sans-serif; width: auto !important; margin-left: auto; margin-right: auto;'>
 <thead>
 <tr>
 <th style="text-align:center;"> Treatment </th>
 <th style="text-align:center;"> Replication </th>
 </tr>
 </thead>
<tbody>
 <tr>
 <td style="text-align:center;"> <img src="images/water1.png" width="40px"><img src="images/brand1.png" width="40px"> </td>
 <td style="text-align:center;"> 3 </td>
 </tr>
 <tr>
 <td style="text-align:center;"> <img src="images/water1.png" width="40px"><img src="images/brand2.png" width="40px"> </td>
 <td style="text-align:center;"> 3 </td>
 </tr>
 <tr>
 <td style="text-align:center;"> <img src="images/water2.png" width="40px"><img src="images/brand1.png" width="40px"> </td>
 <td style="text-align:center;"> 3 </td>
 </tr>
 <tr>
 <td style="text-align:center;"> <img src="images/water2.png" width="40px"><img src="images/brand2.png" width="40px"> </td>
 <td style="text-align:center;"> 3 </td>
 </tr>
</tbody>
</table>

<table class=" lightable-classic" style='font-family: "Arial Narrow", "Source Sans Pro", sans-serif; width: auto !important; margin-left: auto; margin-right: auto;'>
 <thead>
 <tr>
 <th style="text-align:center;"> Treatment factor </th>
 <th style="text-align:center;"> Count </th>
 </tr>
 </thead>
<tbody>
 <tr>
 <td style="text-align:center;"> <img src="images/brand1.png" width="40px"> </td>
 <td style="text-align:center;"> 6 </td>
 </tr>
 <tr>
 <td style="text-align:center;"> <img src="images/brand2.png" width="40px"> </td>
 <td style="text-align:center;"> 6 </td>
 </tr>
 <tr>
 <td style="text-align:center;"> <img src="images/water1.png" width="40px"> </td>
 <td style="text-align:center;"> 6 </td>
 </tr>
 <tr>
 <td style="text-align:center;"> <img src="images/water2.png" width="40px"> </td>
 <td style="text-align:center;"> 6 </td>
 </tr>
</tbody>
</table>

---

# Factorial treatment structure .circle[2]

.flex[
.w-40[
<img src='images/grain9.png' width='80px' style='margin-right:20px;'><img src='images/grain4.png' width='80px' style='margin-right:20px;'><img src='images/grain7.png' width='80px' style='margin-right:20px;'><img src='images/grain1.png' width='80px' style='margin-right:20px;'> 
<img src='images/water2.png' width='40px'><img src='images/brand1.png' width='40px'><img src='images/water2.png' width='40px'><img src='images/brand2.png' width='40px'><img src='images/water1.png' width='40px'><img src='images/brand2.png' width='40px'><img src='images/water1.png' width='40px'><img src='images/brand1.png' width='40px'> 
<img src='images/grain2.png' width='80px' style='margin-right:20px;'><img src='images/grain5.png' width='80px' style='margin-right:20px;'><img src='images/grain3.png' width='80px' style='margin-right:20px;'><img src='images/grain8.png' width='80px' style='margin-right:20px;'> 
<img src='images/water1.png' width='40px'><img src='images/brand2.png' width='40px'><img src='images/water2.png' width='40px'><img src='images/brand2.png' width='40px'><img src='images/water1.png' width='40px'><img src='images/brand1.png' width='40px'><img src='images/water2.png' width='40px'><img src='images/brand1.png' width='40px'> 
<img src='images/grain6.png' width='80px' style='margin-right:20px;'><img src='images/grain11.png' width='80px' style='margin-right:20px;'><img src='images/grain12.png' width='80px' style='margin-right:20px;'><img src='images/grain10.png' width='80px' style='margin-right:20px;'> 
<img src='images/water2.png' width='40px'><img src='images/brand2.png' width='40px'><img src='images/water1.png' width='40px'><img src='images/brand2.png' width='40px'><img src='images/water2.png' width='40px'><img src='images/brand1.png' width='40px'><img src='images/water1.png' width='40px'><img src='images/brand1.png' width='40px'> 
]
.w-35[
.border-box.w-100[
* **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**: 
 * .monash-blue[Water and fertilizer plots]
* **Assignment**: random order
]

]
.w-25[
<table class=" lightable-classic" style='font-family: "Arial Narrow", "Source Sans Pro", sans-serif; width: auto !important; margin-left: auto; margin-right: auto;'>
 <thead>
 <tr>
 <th style="text-align:left;"> Treatment </th>
 <th style="text-align:right;"> Replication </th>
 </tr>
 </thead>
<tbody>
 <tr>
 <td style="text-align:left;"> <img src="images/water1.png" width="40px"><img src="images/brand1.png" width="40px"> </td>
 <td style="text-align:right;"> 3 </td>
 </tr>
 <tr>
 <td style="text-align:left;"> <img src="images/water1.png" width="40px"><img src="images/brand2.png" width="40px"> </td>
 <td style="text-align:right;"> 3 </td>
 </tr>
 <tr>
 <td style="text-align:left;"> <img src="images/water2.png" width="40px"><img src="images/brand1.png" width="40px"> </td>
 <td style="text-align:right;"> 3 </td>
 </tr>
 <tr>
 <td style="text-align:left;"> <img src="images/water2.png" width="40px"><img src="images/brand2.png" width="40px"> </td>
 <td style="text-align:right;"> 3 </td>
 </tr>
</tbody>
</table>

<table class=" lightable-classic" style='font-family: "Arial Narrow", "Source Sans Pro", sans-serif; width: auto !important; margin-left: auto; margin-right: auto;'>
 <thead>
 <tr>
 <th style="text-align:center;"> Treatment factor </th>
 <th style="text-align:center;"> Count </th>
 </tr>
 </thead>
<tbody>
 <tr>
 <td style="text-align:center;"> <img src="images/brand1.png" width="40px"> </td>
 <td style="text-align:center;"> 6 </td>
 </tr>
 <tr>
 <td style="text-align:center;"> <img src="images/brand2.png" width="40px"> </td>
 <td style="text-align:center;"> 6 </td>
 </tr>
 <tr>
 <td style="text-align:center;"> <img src="images/water1.png" width="40px"> </td>
 <td style="text-align:center;"> 6 </td>
 </tr>
 <tr>
 <td style="text-align:center;"> <img src="images/water2.png" width="40px"> </td>
 <td style="text-align:center;"> 6 </td>
 </tr>
</tbody>
</table>
]
]

---

# Factorial treatment structure, nested unit structure, and treatment constraint

.flex[
.w-25[
.border-box[
<img src='images/grain9.png' width='80px' style='margin-right:20px;'><img src='images/grain4.png' width='80px' style='margin-right:20px;'> 
<img src='images/water1.png' width='40px'><img src='images/brand1.png' width='40px'><img src='images/water1.png' width='40px'><img src='images/brand2.png' width='40px'> 
]
.border-box[
<img src='images/grain2.png' width='80px' style='margin-right:20px;'><img src='images/grain5.png' width='80px' style='margin-right:20px;'> 
<img src='images/water2.png' width='40px'><img src='images/brand1.png' width='40px'><img src='images/water2.png' width='40px'><img src='images/brand2.png' width='40px'> 
]
.border-box[
<img src='images/grain6.png' width='80px' style='margin-right:20px;'><img src='images/grain11.png' width='80px' style='margin-right:20px;'> 
<img src='images/water2.png' width='40px'><img src='images/brand2.png' width='40px'><img src='images/water2.png' width='40px'><img src='images/brand1.png' width='40px'> 
]]
.w-25[
.border-box[
<img src='images/grain7.png' width='80px' style='margin-right:20px;'><img src='images/grain1.png' width='80px' style='margin-right:20px;'> 
<img src='images/water1.png' width='40px'><img src='images/brand1.png' width='40px'><img src='images/water1.png' width='40px'><img src='images/brand2.png' width='40px'> 
]
.border-box[
<img src='images/grain3.png' width='80px' style='margin-right:20px;'><img src='images/grain8.png' width='80px' style='margin-right:20px;'> 
<img src='images/water2.png' width='40px'><img src='images/brand2.png' width='40px'><img src='images/water2.png' width='40px'><img src='images/brand1.png' width='40px'> 
]
.border-box[
<img src='images/grain12.png' width='80px' style='margin-right:20px;'><img src='images/grain10.png' width='80px' style='margin-right:20px;'> 
<img src='images/water1.png' width='40px'><img src='images/brand1.png' width='40px'><img src='images/water1.png' width='40px'><img src='images/brand2.png' width='40px'> 
]]
.w-50[
.border-box.w-100[
* **Units**: 6 strips with 2 plots each
* **Observational units**: 12 plots
* **Observation**: wheat yield
* **Treatments**: combination of:
 * Water: irrigated or rain-fed
 * Fertilizer: type A or type B
* **Allotment**: 
 * .monash-blue[Water strip]
 * .monash-blue[Fertilizer plot]
* **Assignment**: random order
]

]
]

---

.tl.f2[
.box[A] Completely Randomised Design

]
---

# .box[A] Completely Randomised Design (CRD)

.border-box.margin-auto[
* **Experimental units**: 6 cows
* **Observational units**: 6 cows
* **Observation**: milk yield
* **Treatments**: 3 types of supplements
* **Allotment**: supplements cows
* **Replication**: 2 each
* **Assignment**: random order
]

---

# .box[B] Randomised Complete Block Design (RCBD)

.border-box.margin-auto.w-40[
* **Units**: 2 pens with 3 cows each
* **Observational units**: 6 cows
* **Treatments**: 3 types of supplements
* **Allotment**: supplements cows, with restriction such that each treatment appears once in each pen
* **Assignment**: random order
]

---

# .box[C] Factorial Design

.flex[
.w-50[
<img src='images/grain9.png' width='80px' style='margin-right:20px;'><img src='images/grain4.png' width='80px' style='margin-right:20px;'><img src='images/grain7.png' width='80px' style='margin-right:20px;'><img src='images/grain1.png' width='80px' style='margin-right:20px;'> 
<img src='images/water2.png' width='40px'><img src='images/brand1.png' width='40px'><img src='images/water2.png' width='40px'><img src='images/brand2.png' width='40px'><img src='images/water1.png' width='40px'><img src='images/brand2.png' width='40px'><img src='images/water1.png' width='40px'><img src='images/brand1.png' width='40px'> 
<img src='images/grain2.png' width='80px' style='margin-right:20px;'><img src='images/grain5.png' width='80px' style='margin-right:20px;'><img src='images/grain3.png' width='80px' style='margin-right:20px;'><img src='images/grain8.png' width='80px' style='margin-right:20px;'> 
<img src='images/water1.png' width='40px'><img src='images/brand2.png' width='40px'><img src='images/water2.png' width='40px'><img src='images/brand2.png' width='40px'><img src='images/water1.png' width='40px'><img src='images/brand1.png' width='40px'><img src='images/water2.png' width='40px'><img src='images/brand1.png' width='40px'> 
<img src='images/grain6.png' width='80px' style='margin-right:20px;'><img src='images/grain11.png' width='80px' style='margin-right:20px;'><img src='images/grain12.png' width='80px' style='margin-right:20px;'><img src='images/grain10.png' width='80px' style='margin-right:20px;'> 
<img src='images/water2.png' width='40px'><img src='images/brand2.png' width='40px'><img src='images/water1.png' width='40px'><img src='images/brand2.png' width='40px'><img src='images/water2.png' width='40px'><img src='images/brand1.png' width='40px'><img src='images/water1.png' width='40px'><img src='images/brand1.png' width='40px'> 
]
.w-50[
.border-box[
* **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**: 
 * .monash-blue[Water and fertilizer plots]
* **Assignment**: random order
]

]

---

# .box[D] Split-Plot Design

.border-box.margin-auto[
* **Units**: 6 strips with 2 plots each
* **Observational units**: 12 plots
* **Observation**: wheat yield
* **Treatments**: combination of:
 * Water: irrigated or rain-fed
 * Fertilizer: type A or type B
* **Allotment**: 
 * Water strip
 * Fertilizer plot
* **Assignment**: random order
]

]
]

---

# *Current state* of experimental design tools

---

# .f-headline[CRAN Task View of Design of Experiments ] .f1[& Analysis of Experimental Data]

contains

# .f-headline[📦 .monash-blue[109 R-packages ]]

In contrast, only a handful of libraries exist in Python (namely `pyDOE`, `pyDOE2`, `dexpy`, `experimenter` and `GPdoemd`).

???

* Sheer quantity and variation in the output experimental design in the R-packages are arguably unmatched with any other programming languages
* E.g. in Python, there are only a handful of libraries that generate design of experiment exist (namely pyDOE, pyDOE2, dexpy, experimenter and GPdoemd) with limited outputs.
* This demonstrates how R is a programming language with large statistical community contributions

---

# Design of experiments area appear to have the least collaboration

]
]
.w-50[
<div id="networktable" style="width:100%;height:auto;" class="datatables html-widget"></div>
<script type="application/json" data-for="networktable">{"x":{"filter":"none","data":[["Analysis of Pharmacokinetic Data","Hydrological Data and Modeling","Design of Experiments (DoE) & Analysis of Experimental Data","Chemometrics and Computational Physics","Optimization and Mathematical Programming","Clinical Trial Design, Monitoring, and Analysis","Medical Image Analysis","Extreme Value Analysis","Statistical Genetics","Missing Data","Cluster Analysis & Finite Mixture Models","Meta-Analysis","Official Statistics & Survey Statistics","Probability Distributions","Processing and Analysis of Tracking Data","Bayesian Inference","Teaching Statistics","Machine Learning & Statistical Learning","Graphic Displays & Dynamic Graphics & Graphic Devices & Visualization","Empirical Finance","Time Series Analysis","Differential Equations","Functional Data Analysis","High-Performance and Parallel Computing with R","Numerical Mathematics","Natural Language Processing","Handling and Analyzing Spatio-Temporal Data","Psychometric Models and Methods","Analysis of Ecological and Environmental Data","Multivariate Statistics","Survival Analysis","Robust Statistical Methods","Reproducible Research","Model Deployment with R","Databases with R","gRaphical Models in R","Econometrics","Statistics for the Social Sciences","Analysis of Spatial Data","Web Technologies and Services","Phylogenetics, Especially Comparative Methods"],[18,96,109,82,135,60,23,24,22,160,110,154,132,251,47,138,45,103,39,167,342,28,42,87,113,54,88,242,97,116,251,59,99,32,38,32,150,86,179,201,81],[16.6666666666667,21.875,24.7706422018349,29.2682926829268,29.6296296296296,30,30.4347826086957,33.3333333333333,36.3636363636364,37.5,39.0909090909091,43.5064935064935,43.9393939393939,44.6215139442231,46.8085106382979,51.4492753623188,53.3333333333333,53.3980582524272,53.8461538461538,55.0898203592814,56.7251461988304,57.1428571428571,59.5238095238095,60.9195402298851,61.0619469026549,61.1111111111111,63.6363636363636,67.7685950413223,71.1340206185567,71.551724137931,73.3067729083665,74.5762711864407,74.7474747474748,75,76.3157894736842,78.125,78.6666666666667,79.0697674418605,83.2402234636871,89.5522388059701,91.358024691358],[3.27777777777778,3.01041666666667,2.26605504587156,2.58536585365854,3,2.7,2.73913043478261,2.70833333333333,5.86363636363636,4.10625,3.45454545454545,2.57142857142857,3.38636363636364,2.83665338645418,3.29787234042553,3.26811594202899,5.48888888888889,5.47572815533981,5.46153846153846,3.47904191616766,3.0672514619883,5.32142857142857,3.21428571428571,4.47126436781609,3.42477876106195,3.31481481481481,3.78409090909091,3.06198347107438,4.5979381443299,4.3448275862069,2.83665338645418,3.50847457627119,5.72727272727273,6.125,3.57894736842105,4.15625,3.54,4.40697674418605,4.21787709497207,3.02985074626866,4.12345679012346],[2.73980582299411,2.7625114114236,1.5314130598584,2.24406608203681,2.30832367941656,2.10165390883998,2.17876927946089,1.98864530395129,7.77845286701212,9.88461537284999,3.53912953491214,2.37596115496388,3.61009552911756,3.42946222539023,2.93342724038847,3.07933980760372,7.4272906543804,13.4265209166551,7.33716621708722,5.89857888066994,4.85068946829346,6.8909687080591,3.24252020536958,7.36560056197723,5.78761811007916,2.59770634732762,4.79331158445427,3.63596046425851,5.45943333791466,4.61208893212621,2.4934336075738,3.58816484338554,11.7965908096782,5.35663592071524,3.33394968223,4.14347037810017,3.9111439477301,4.40421698182347,5.4455954747573,3.47550060820192,5.52354667774561]],"container":"<table class=\"display\">\n <thead>\n <tr>\n <th>Topic<\/th>\n <th># of packages<\/th>\n <th>% of packages connected within topic<\/th>\n <th>Average # of authors<\/th>\n <th>Standard dev. # of authors<\/th>\n <\/tr>\n <\/thead>\n<\/table>","options":{"dom":"t","pageLength":-1,"scrollY":"400px","columnDefs":[{"targets":2,"render":"function(data, type, row, meta) {\n return type !== 'display' ? data : DTWidget.formatRound(data, 2, 3, \",\", \".\");\n }"},{"targets":3,"render":"function(data, type, row, meta) {\n return type !== 'display' ? data : DTWidget.formatRound(data, 2, 3, \",\", \".\");\n }"},{"targets":4,"render":"function(data, type, row, meta) {\n return type !== 'display' ? data : DTWidget.formatRound(data, 2, 3, \",\", \".\");\n }"},{"className":"dt-right","targets":[1,2,3,4]}],"order":[],"autoWidth":false,"orderClasses":false,"lengthMenu":[-1,10,25,50,100]}},"evals":["options.columnDefs.0.render","options.columnDefs.1.render","options.columnDefs.2.render"],"jsHooks":[]}</script>

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Authors tend to work in silos limited knowledge sharing across silos perhaps

---

# Top downloaded R-packages in the design of experiments

<img src="images/top-trend-plot-scrub-1.png" width="648" style="display: block; margin: auto;" />
]
.w-20[

**Top 5 in 2016**
<table id="table-cran2016" class=" lightable-classic" style='font-family: "Arial Narrow", "Source Sans Pro", sans-serif; width: auto !important; margin-left: auto; margin-right: auto;'>
 <thead>
 <tr>
 <th style="text-align:left;"> Package </th>
 <th style="text-align:right;"> Downloads </th>
 </tr>
 </thead>
<tbody>
 <tr>
 <td style="text-align:left;"> agricolae </td>
 <td style="text-align:right;"> 73,521 </td>
 </tr>
 <tr>
 <td style="text-align:left;"> AlgDesign </td>
 <td style="text-align:right;"> 57,037 </td>
 </tr>
 <tr>
 <td style="text-align:left;"> ez </td>
 <td style="text-align:right;"> 37,488 </td>
 </tr>
 <tr>
 <td style="text-align:left;"> lhs </td>
 <td style="text-align:right;"> 23,518 </td>
 </tr>
 <tr>
 <td style="text-align:left;"> DoE.base </td>
 <td style="text-align:right;"> 20,651 </td>
 </tr>
</tbody>
</table>
]
.w-20[

**Top 5 in 2020**
<table id="table-cran2020" class=" lightable-classic" style='font-family: "Arial Narrow", "Source Sans Pro", sans-serif; width: auto !important; margin-left: auto; margin-right: auto;'>
 <thead>
 <tr>
 <th style="text-align:left;"> Package </th>
 <th style="text-align:right;"> Downloads </th>
 </tr>
 </thead>
<tbody>
 <tr>
 <td style="text-align:left;"> agricolae </td>
 <td style="text-align:right;"> 171,813 </td>
 </tr>
 <tr>
 <td style="text-align:left;"> lhs </td>
 <td style="text-align:right;"> 165,415 </td>
 </tr>
 <tr>
 <td style="text-align:left;"> AlgDesign </td>
 <td style="text-align:right;"> 153,582 </td>
 </tr>
 <tr>
 <td style="text-align:left;"> DiceKriging </td>
 <td style="text-align:right;"> 92,287 </td>
 </tr>
 <tr>
 <td style="text-align:left;"> DiceDesign </td>
 <td style="text-align:right;"> 88,160 </td>
 </tr>
</tbody>
</table>
]
]

.f3[(total download based on logs from the RStudio CRAN mirror scrubbed by [Danyang Dai](https://twitter.com/Daidaidai2014))] 
]

---

# `agricolae`

a case of classical named randomised designs

---

# .box[A] `agricolae::design.crd`

**Completely randomised design** for `$t = 3$` treatments with `$2$` replicates each
<pre><code>
trt <- c("A", "B", "C")
agricolae::.bg-yellow[design.crd](trt = trt, r = 2) 
</code></pre>

.overflow-scroll.h---340[

```
## $parameters
## $parameters$design
## [1] "crd"
## 
## $parameters$trt
## [1] "A" "B" "C"
## 
## $parameters$r
## [1] 2 2 2
## 
## $parameters$serie
## [1] 2
## 
## $parameters$seed
## [1] 241038711
## 
## $parameters$kinds
## [1] "Super-Duper"
## 
## $parameters[[7]]
## [1] TRUE
## 
## 
## $book
##   plots r trt
## 1   101 1   B
## 2   102 1   C
## 3   103 1   A
## 4   104 2   A
## 5   105 2   C
## 6   106 2   B
```
]

</div>

---

# .box[B] `agricolae::design.rcbd`

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

.overflow-scroll.h---340[

```
## $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
```
]

</div>

---

# .box[C] `agricolae::design.ab()`

**Factorial design** for `$t = 3 \times 2$` treatments with `$2$` replication for each treatment

<pre><code>
agricolae::.bg-yellow[design.ab](trt = c(3, 2), r = 2, design = "crd") 
</code></pre>

.overflow-scroll.h---340[

```
## $parameters
## $parameters$design
## [1] "factorial"
## 
## $parameters$trt
## [1] "1 1" "1 2" "2 1" "2 2" "3 1" "3 2"
## 
## $parameters$r
## [1] 2 2 2 2 2 2
## 
## $parameters$serie
## [1] 2
## 
## $parameters$seed
## [1] 34955907
## 
## $parameters$kinds
## [1] "Super-Duper"
## 
## $parameters[[7]]
## [1] TRUE
## 
## $parameters$applied
## [1] "crd"
## 
## 
## $book
##    plots r A B
## 1    101 1 2 2
## 2    102 1 2 1
## 3    103 1 1 2
## 4    104 2 2 1
## 5    105 1 3 1
## 6    106 2 2 2
## 7    107 1 1 1
## 8    108 2 3 1
## 9    109 2 1 2
## 10   110 2 1 1
## 11   111 1 3 2
## 12   112 2 3 2
```
]

Note *not* A/B testing!

</div>

---

# .box[D] `agricolae::design.split()`

**Split-plot design** for `$t = 2 \times 4$` treatments with `$2$` replication for each treatment

.overflow-scroll.h---300[

```
## $parameters
## $parameters$design
## [1] "split"
## 
## $parameters[[2]]
## [1] TRUE
## 
## $parameters$trt1
## [1] "I" "R"
## 
## $parameters$applied
## [1] "crd"
## 
## $parameters$r
## [1] 2 2
## 
## $parameters$serie
## [1] 2
## 
## $parameters$seed
## [1] -1981495681
## 
## $parameters$kinds
## [1] "Super-Duper"
## 
## 
## $book
##    plots splots r trt1 trt2
## 1    101      1 1    R    D
## 2    101      2 1    R    C
## 3    101      3 1    R    B
## 4    101      4 1    R    A
## 5    102      1 1    I    A
## 6    102      2 1    I    C
## 7    102      3 1    I    D
## 8    102      4 1    I    B
## 9    103      1 2    R    B
## 10   103      2 2    R    C
## 11   103      3 2    R    A
## 12   103      4 2    R    D
## 13   104      1 2    I    C
## 14   104      2 2    I    A
## 15   104      3 2    I    B
## 16   104      4 2    I    D
```
]

</div>

---

.blockquote.w-100.f1[
.pl3[
Good design considers units and treatments first, and then allocates treatments to units. It does not choose from a menu of named designs.

---

# `AlgDesign`

a case of optimised (model-based) designs

---

# `AlgDesign::gen.factorial()`

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

```r
dat <- AlgDesign::gen.factorial(levels = 3, 
 nVars = 3, 
 center = FALSE, 
 varNames = c("irrigation", 
 "fertilizer", 
 "variety"), 
 factors = "all")
dat
```
.overflow-scroll.h---240[

```
##    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

```r
AlgDesign::optFederov(frml = ~ ., # assume additive effects
                      data = dat, 
                      nTrials = 14, 
                      criterion = "D") 
```
.overflow-scroll.h---240[

```
## $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.

```r
AlgDesign::optBlock(frml = ~ ., # assume additive effects
                    withinData = dat, 
                    blocksizes = rep(9, 3),
                    criterion = "D")
```
.overflow-scroll.h---240[

```
## $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
```
]

---

# .f-headline[Context is key in experimental design]

---

# .yellow[*Software design*] for an everyday user

---

# .f-headline[Benefits of programming]

]
.w-70.tl.f1[
{{content}}

]
.w-10[

]]

1. Computational reproducibility
{{content}}
--

1. Allows greater flexibility
{{content}}
--

1. Can promote higher order thinking {{content}}
--
*if the software is designed with the user in mind*

---

# .f-headline[Software design for users]

]
.w-70.tl.f1[
{{content}}

]
.w-10[

]]

* A user interacts with the **software interface** 
{{content}}
--
* The interface design can make a *huge difference to an everyday user*

---

# Drawing faces .circle[1] .grey[Specific instructions for the computer]

# Drawing a .monash-blue[happy] face

---

```r
library(grid)
# face shape
grid.circle(x = 0.5, y = 0.5, r = 0.5)
```
]
]
.w-50[
.f4[

<img src="images/happy-1-1.png" width="432" style="display: block; margin: auto;" />
]

]

---

```r
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"))
```
]
]
.w-50[
.f4[

<img src="images/happy-2-1.png" width="432" style="display: block; margin: auto;" />
]

]

---

```r
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)
```
]
]
.w-50[
.f4[

<img src="images/happy-3-1.png" width="432" style="display: block; margin: auto;" />
]

]

---

# Drawing faces .circle[1] .grey[Specific instructions for the computer]

# Drawing a .monash-blue[sad] face

---

```r
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)
```
]
]
.w-50[
.f4[

.animated.delay-1s.zoomIn[
<img src="images/sad-1-1.png" width="432" style="display: block; margin: auto;" />
]
]
]

]

---

# Drawing faces .circle[2] .grey[Functional instructions for the computer]

# Use .monash-blue[functions] to draw faces

---

```r
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)
}
```

]
.w-40[

]
]

---

]
.w-40[

```r
face1()
```

]
.w-50[

]

]
]
]

---

]
.w-40[

```r
face1()
```

]
.w-50[

```r
face2()
```

]
]
]
]

---

]
.w-40[

```r
face1()
```

```r
face1()
```

]
.w-50[

```r
face2()
```

<img src="images/sad-fn-1.png" width="68.4" style="display: block; margin: auto;" />
]
]
]
]

???

* I can repeatedly call the function
* Drawing happy or sad faces are easier now

---

]
.w-40[
.flex[
.w-50.pr2[

```r
face1()
```

```r
face1()
```

]
.w-50[

```r
face2()
```

```r
face1()
```

<img src="images/happy-fn-1.png" width="68.4" style="display: block; margin: auto;" />
]]]]

---

]
.w-40[
.flex[
.w-50.pr2[

```r
face1()
```

```r
face1()
```

```r
face2()
```

<img src="images/sad-fn-1.png" width="68.4" style="display: block; margin: auto;" />
]
.w-50[

```r
face2()
```

```r
face1()
```

<img src="images/happy-fn-1.png" width="68.4" style="display: block; margin: auto;" />
]]]]

---

]
.w-40[
.flex[
.w-50.pr2[

```r
face1()
```

```r
face1()
```

```r
face2()
```

<img src="images/sad-fn-1.png" width="68.4" style="display: block; margin: auto;" />
]
.w-50[

```r
face2()
```

```r
face1()
```

```r
face1()
```

<img src="images/happy-fn-1.png" width="68.4" style="display: block; margin: auto;" />
]]]]

---

# Drawing faces .circle[3] .grey[Human-centered design]

# Adapt computational systems .monash-blue[for human] use with syntactic sugar

---

```r
face1()
```

<img src="images/happy-fn-1.png" width="144" style="display: block; margin: auto;" />
]
.w-33.pr2[

```r
face2()
```

<img src="images/sad-fn-1.png" width="144" style="display: block; margin: auto;" />
]
.w-33.pr2[
```r
face3()
```
.center.f-headline[
?

]
]
]

**Alternative function names:**

]
.w-33.pr2[
```r
face_angry()
```

]]

Now what do you expect for the output?

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

---

.f1[The differences between facial features are small, but you need an **entire new function** that contains instructions for the *whole* face and a **new function name**.]

How would you design the system to draw faces?

---

# Drawing faces .circle[4] .grey[Rethinking function arguments as facial parts]

# Let's .monash-blue[reframe] how we think

---

https://github.com/emitanaka/portrait

```r
library(portrait)
```

* Let's **_reframe_** how we think
* A face is made up of:
  * eyes
  * mouth
  * shape

]
.w-70[
]]

---

https://github.com/emitanaka/portrait

```r
library(portrait)
```

* Let's **_reframe_** how we think
* A face is made up of:
  * eyes
  * mouth
  * shape

]
.w-70[

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

<img src="images/face-googly-1.png" width="144" style="display: block; margin: auto;" />
]
.w-50[
{{content}}
]]

]]

```r
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?

---

* A face is made up of:
 * eyes
 * mouth
 * shape
 * **hair** 
 * **nose**

]
.w-70[
* Adding more arguments:

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

<img src="images/face-googly-2-1.png" width="144" style="display: block; margin: auto;" />
]
.w-50[

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

<img src="images/face-googly-3-1.png" width="144" style="display: block; margin: auto;" />
]]]

]

But about other facial features?

---

# Drawing faces .circle[5] .grey[Object oriented programming]

# Rethink everything as an .monash-blue[object]

---

.flex.h-100[
.w-50.pr3[

```r
library(portrait)
*face()
```

]
.w-30.pl3[
.output-box.w-100[
<img src="images/face1-1.png" width="288" style="display: block; margin: auto;" />
]]

]

---

.flex.h-100[
.w-50.pr3[

```r
library(portrait)
face() +
* cat_shape()
```

]
.w-30.pl3[
.output-box.w-100[
<img src="images/face2-1.png" width="288" style="display: block; margin: auto;" />
]]

]

---

.flex.h-100[
.w-50.pr3[

```r
library(portrait)
face() +
  cat_shape() +
* cat_eyes()
```

]
.w-30.pl3[
.output-box.w-100[
<img src="images/face3-1.png" width="288" style="display: block; margin: auto;" />
]]
]

---

.flex.h-100[
.w-50.pr3[

```r
library(portrait)
face() +
 cat_shape() +
 cat_eyes() +
* cat_nose()
```
]
.w-30.pl3[
.output-box.w-100[
<img src="images/face4-1.png" width="288" style="display: block; margin: auto;" />
]]]

---

.flex.h-100[
.w-50.pr3[

```r
library(portrait)
face() +
  cat_shape() +
  cat_eyes() +
  cat_nose() +
* cat_whiskers()
```

]
.w-30.pl3[
.output-box.w-100[
<img src="images/face5-1.png" width="288" style="display: block; margin: auto;" />
]
]
]

---

.flex.h-100[
.w-50.pr3[

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

]
.w-30.pl3[
.output-box.w-100[
<img src="images/face6-1.png" width="288" style="display: block; margin: auto;" />
]
]
]

---

.flex.h-100[
.w-50.pr3[

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

]
.w-30.pl3[
.output-box.w-100[
<img src="images/face7-1.png" width="288" style="display: block; margin: auto;" />
]
]
]

---

# .f1[Software design for everyday users]

.f2.pl3[
1. Imperative instructions for the computer more work for humans
1. Recipe functions One function to draw one complete face
1. Syntactic syntax Make it easier for humans to read code
1. A function with multiple arguments One function to draw multiple complete faces
1. Finite number of functions to draw _infinite_ possible _incomplete_ and complete faces
]

.f1[
The tool **_you choose_** to use can .monash-blue[**enforce a certain way of thinking**] and may restrict you on what you can do.
]

???

* You can lock yourself in a system that doesn't help you grow.

---

# The .yellow[**grammar of experimental designs**] with .yellow[`edibble`]

---

# The *grammar of experimental design* with `edibble`

.flex.h-100[
.w-65[

```r
library(edibble)
*start_design("My experiment")
```

]
.w-35.pl3.pr3.monash-bg-gray10[

.output-box.f6.truncate[
<img src="images//edibble-part1.svg" width="350%" style="display: block; margin: auto;" />

]

---

# The *grammar of experimental design* with `edibble`

.flex.h-100[
.w-65[

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

]
.w-35.pl3.pr3.monash-bg-gray10[

.output-box.f6.w-100.truncate[
<img src="images//edibble-part2.svg" width="350%" style="display: block; margin: auto;" />

]

---

# The *grammar of experimental design* with `edibble`

.flex.h-100[
.w-65[

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

]
.w-35.pl3.pr3.monash-bg-gray10[

.output-box.f6.w-100.truncate[
<img src="images//edibble-part3.svg" width="350%" style="display: block; margin: auto;" />

]

---

# The *grammar of experimental design* with `edibble`

.flex.h-100[
.w-65[

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

]
.w-35.pl3.pr3.monash-bg-gray10[

.output-box.f6.w-100.truncate[
<img src="images//edibble-part4.svg" width="350%" style="display: block; margin: auto;" />

]

]
]

---

# The *grammar of experimental design* with `edibble`

.flex.h-100[
.w-65[

```r
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"))
```

]
.w-35.pl3.pr3.monash-bg-gray10[

.output-box.f6.w-100.truncate[
<img src="images//edibble-part5.svg" width="350%" style="display: block; margin: auto;" />

]

---

# The *grammar of experimental design* with `edibble`

```r
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)) 
```

]
.w-35.pl3.pr3.monash-bg-gray10[

.output-box.f6.w-100.truncate[
<img src="images//edibble-part6.svg" width="350%" style="display: block; margin: auto;" />

]

---

# The *grammar of experimental design* with `edibble`

.flex.h-100[
.w-65[

```r
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)) 
```

]
.w-35.pl3.pr3.monash-bg-gray10[

.output-box.f6.w-100.truncate[
<img src="images//edibble-part7.svg" width="350%" style="display: block; margin: auto;" />

]

---

# The *grammar of experimental design* with `edibble`

.flex.h-100[
.w-65[

```r
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)
```

]
.w-35.pl3.pr3.monash-bg-gray10[

.output-box.f6.w-100.truncate[
<img src="images//edibble-part8.svg" width="350%" style="display: block; margin: auto;" />

]

---

# The *grammar of experimental design* with `edibble`

.flex.h-100[
.w-65[

```r
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)
```

]
.w-35.pl3.pr3.monash-bg-gray10[

.output-box.f6.w-100.truncate[
<img src="images//edibble-part9.svg" width="350%" style="display: block; margin: auto;" />

]

---

# The *grammar of experimental design* with `edibble`

.flex.h-100[
.w-65[

```r
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()
```

]
.w-35.pl3.pr3.monash-bg-gray10[

.output-box.f6.w-100.truncate[
<img src="images//edibble-final.svg" width="200%" style="display: block; margin: auto;" />

]

---

# The *grammar of experimental design* with `edibble`

.flex.h-100[
.w-65[

```r
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()
```

]
.w-35.pl3.pr3.monash-bg-gray10[

.output-box.f6.w-100.truncate[
<img src="images//edibble-rcbd.svg" width="200%" style="display: block; margin: auto;" />

]

* The resulting design is what we call "randomised complete block design"

]

---

# The *grammar of experimental design* with `edibble`

.flex.h-100[
.w-65[

```r
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 functions are reminiscent of the fundamental experimental terminology [](#terms)

]
.w-35.pl3.pr3.monash-bg-gray10[

.output-box.f6.w-100.truncate[
<img src="images//edibble-rcbd-response.svg" width="135%" style="display: block; margin: auto;" />

]

---

# The *grammar of experimental design* with `edibble`

```r
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()
```

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

* The exported file has data validation features embedded

---

---

.f1[
* Our understanding of experimental design is **growing** and so the tool should **evolve** with better understanding
{{content}}
]
--

* The idea for `edibble` was conceived early 2019, the code base was released publicly on 31st Dec 2020. 
{{content}}
--

* Since its initial public realease, underlying structure in `edibble` has evolved drastically for the better  
{{content}}
--

* The development of a good tool is a community effort so...

---

# .f1[Get in touch!]

.f2[
* The purpose of `edibble` is to help you plan experiments better
* `edibble` gets better with feedback
]

<ul class="fa-ul f2">
 <li>Slides: <a href='https://emitanaka.org/slides/stats4bio2021/edibble'>emitanaka.org/slides/stats4bio2021/edibble</a>
</li>
 <li> Package documentation: <a href='https://edibble.emitanaka.org'>edibble.emitanaka.org</a></li>
 <li>Source code: <a href='https://github.com/emitanaka/edibble'>github.com/emitanaka/edibble</a></li>
 <li><a href="mailto:emi.tanaka@monash.edu">emi.tanaka@monash.edu</a> <a href="https://twitter.com/statsgen">@statsgen</a></li>
</ul>

.f2[
* Feature requests or issues with `edibble`? Submit or upvote here: <a href='https://github.com/emitanaka/edibble/issues'>github.com/emitanaka/edibble/issues</a>, send me an email or tell me now!
]

???

* `edibble` is a community effort
* make use