QTM 385 - Experimental Methods

Lecture 13 - Introduction to Quarto and Declare Design

Danilo Freire

danilo.freire@emory.edu

Emory University

Hello, everyone! 😊

Brief recap 📚

Last class, we discussed…

The historical development of research ethics (Nuremberg Code, Tuskegee Study, Belmont Report)
Core ethical principles: respect for persons, beneficence, and justice
Informed consent requirements and procedures
Considerations for anonymity and confidentiality in research data
How Institutional Review Boards (IRBs) protect human subjects
Ethical controversies in recent studies like Facebook’s emotional contagion study
Adaptive research designs that maximise benefits and minimize harm

Ethical responsibilities toward research staff and communities
How ethical research practices improve data quality and research outcomes
The principle of equipoise in determining when experiments are justified
The need for special protections for vulnerable populations
How ethical practices help prevent attrition and strengthen research validity

Today’s plan 📅

Introduction to Quarto and DeclareDesign

Two useful tools for experimental research (and beyond)

Quarto is a great tool to write and publish reproducible documents
It fits well with R Markdown and Jupyter Notebooks, so there is very little learning curve for you!
Quarto also meets all the requirements for a good research workflow and literate programming
- It is text-based, so you can use version control (e.g., Git)
- It supports code execution and visualisation
- It allows you to write in Markdown, LaTeX, and other formats

https://quarto.org/

Introduction to Quarto and DeclareDesign

Two useful tools for experimental research (and beyond)

DeclareDesign is a package for R that helps you design and analyse experiments
We have already used it before, but today we will see more of its capabilities
As we will see, DeclareDesign is a powerful tool to plan and execute experiments
- It helps you define your research question and hypotheses
- It guides you in choosing the right design and sample size
- It provides tools to analyse your data and draw conclusions
And it is simulation-based, so you can test your design before running the experiment
I hope you can use it in your pre-analysis plans! 😉

https://declaredesign.org/

Quarto 📝

What is Quarto?

Quarto (.qmd) is a document format that combines the best features of R Markdown and Jupyter Notebooks
It is designed for reproducibility and literate programming, as mentioned before
Literate programming is a programming paradigm that combines code and documentation in a single document
- This makes your code more readable and easier to maintain
- It also helps you communicate your results more effectively
If you use R Markdown or Jupyter Notebooks, you already do literate programming!
Why is literate programming important for experimental research?
- It helps you keep track of your code and results
- It makes it easier to share your work with others
- It allows you to reproduce your analysis and results

Why Quarto?

Can’t I just use R Markdown or Jupyter Notebooks instead?

Yes, you can!
But Quarto has some advantages over R Markdown and Jupyter Notebooks
For example, Quarto supports multiple programming languages (not just R and Python)
It also has built-in support for interactive visualisations and data tables
And it is designed to work well with version control systems like Git
You can also use it to publish your documents online (like this one!), create slideshows, websites, and books
Learn it once, use it everywhere! 🤓

How to get started with Quarto?

First, you need to install Quarto
It is available for Windows, Mac, and Linux
If you use Homebrew, you can install Quarto with brew install quarto
In case you use VS Code, you can install the Quarto extension too, which will save you a lot of time
You can also use Quarto in RStudio
As Quarto was created by the same people who made RStudio, it is very easy to use it in RStudio
- Just install the Quarto R package and you are good to go!
- install.packages("quarto")

Click on the image to visit the Quarto installation page

Writing a Quarto document 📝

How to write a Quarto document?

Quarto documents are directly influenced by R Markdown
All documents have three main components:
- YAML header with metadata
- Markdown content (text)
- Code chunks (R, Python, Julia, etc.)
YAML stands for “YAML Ain’t Markup Language”
- It is a human-readable data serialisation format
- It is often used for configuration files and metadata
- In Quarto, the YAML header contains information about the document (title, author, date, etc.)

---
title: My Quarto Document
subtitle: A simple example
author: Danilo Freire
date: 2025-03-03
format: html
editor:
  render-on-save: true
---

Markdown

Headings: #, ##, ###, etc.
Emphasis: *italic* or _italics_, **boldface** or __boldface__, ~~strikethrough~~
Lists: *, 1., -
Links: [text](url)
Images: ![alt text](url)
Code: `code`
Tables:

| Header 1 | Header 2 |
|----------|----------|
| Cell 1   | Cell 2   |

Heading

Italics, boldface, and code.

List:

Item 1
Item 2
- Subitem 1

This is a link.

Header 1	Header 2
Cell 1	Cell 2

Markdown

Blockquotes: > quote
Horizontal rules: ---
Footnotes: [^1]
Superscript: 2^10^
Subscript: H~2~O
Math: $\LaTeX$
For equations, use $ or $$
Check the LaTeX Wiki for math symbols
More at Markdown Guide

This is a blockquote.

This is a paragraph¹.

Equation: $\mu = \frac{1}{n} \sum_{i=1}^{n} x_i$

2¹⁰ is 1024, and H₂O is water.

This is a horizontal rule.

Quarto engines

knitr

---
title: "ggplot2 demo"
  format: 
    html:
      code-fold: true
---

## Meet Quarto

Quarto enables you to weave together content and executable code into a finished document. To learn more about Quarto see <https://quarto.org>.

```{r}
#| label: plot-penguins
#| echo: false
#| message: false
#| warning: false

library(tidyverse)
library(palmerpenguins)

ggplot(penguins, 
       aes(x = flipper_length_mm, y = bill_length_mm)) +
geom_point(aes(color = species, shape = species)) +
scale_color_manual(values = c("darkorange","purple","cyan4")) +
  labs(
    title = "Flipper and bill length",
    subtitle = "Dimensions for penguins at Palmer Station LTER",
    x = "Flipper length (mm)", y = "Bill length (mm)",
    color = "Penguin species", shape = "Penguin species"
  ) +
theme_minimal()

Jupyter

---
title: "Palmer Penguins Demo"
  format: 
    html:
      code-fold: true
jupyter: python3
---


## Meet Quarto

Quarto enables you to weave together content and executable code into a finished document. To learn more about Quarto see <https://quarto.org>.

```{python}
#| echo: false
#| message: false

import pandas as pd
import seaborn as sns 
from palmerpenguins import load_penguins
sns.set_style('whitegrid')

penguins = load_penguins()

g = sns.lmplot(x="flipper_length_mm",
               y="body_mass_g",
               hue="species",
               height=7,
               data=penguins,
               palette=['#FF8C00','#159090','#A034F0']);
g.set_xlabels('Flipper Length');
g.set_ylabels('Body Mass');

PDFs

Most articles and reports are in PDF format
You will need a LaTeX distribution to create PDFs
You can install it with quarto:
- quarto install tinytex
If you use R, you can use tinytex with:
- install.packages("tinytex")
- tinytex::install_tinytex()
This is strongly recommended as a LaTeX distribution is huge and takes a long time to install
More information here

Adding references

You can add academic references to your documents using bibtex
BibTeX is a reference management software developed for LaTeX
A bibtex file is a plain text file with .bib extension
You can add references to your YAML header
Use @key to cite a reference, [@key] to cite in parentheses
The key is the first line of the reference in the .bib file (e.g., @article{nash1950equilibrium,)
More information here

The easiest way to manage references is with a reference manager like Zotero or download a BibTex reference from Google Scholar
Just search for a paper and click on the cite button
Then click on BibTeX and copy the reference to your .bib file

Example

@article{nash1950equilibrium,
  title={Equilibrium points in n-person games},
  author={Nash Jr, John F},
  journal={Proceedings of the national academy of sciences},
  volume={36},
  number={1},
  pages={48--49},
  year={1950},
  publisher={National Acad Sciences}
}

Save it on your references.bib file (or any other name, as long as you reference it in your YAML header and the file ends with .bib)
Quarto will automatically format the references
More information about BibTeX here

Example

Then you add the references to your YAML header:

---
title: "Matplotlib Demo"
author: "Norah Jones"
date: "2024-09-30"
date-format: "MMMM D, YYYY"
format: 
  pdf:
    fig-width: 3
    fig-height: 2
    margins: 2in
bibliography: references.bib
---

DeclareDesign 📊

What is DeclareDesign?

A package for designing and analysing data

DeclareDesign is an R package that helps you design and analyse experiments, quasi-experiments, and other observational studies
Its main goal is to provide tools for declaration, diagnosis, and redesign in code, that is, to help you plan and execute your research before data analysis
DeclareDesign can be thought of in 2 parts
- The data fabrication step (this is the bulk of the code)
- The evaluation step, where users can change initial assumptions and see how well their design actually worked (this is the computationally intensive part of the code)
The great thing about DeclareDesign is that, as far as I understand, you can simulate any kind of design you can think of (e.g., experiments, regression discontinuity, difference-in-differences, even qualitative research!)
However, most studies are not that complex, so you will rarely need to use all of DeclareDesign’s capabilities
The authors have written a book that explains the package in detail
And they have also created a companion package, DesignLibrary, with pre-built designs that you can use right away! 🤓

Six components of a DeclareDesign study

Population: Set of units about which inferences are sought and their characteristics
- Where should the theory apply? Who are the units of interest?
Potential outcomes: Outcomes each unit might exhibit depending on how causal process changes the world
- Rooted in theory; non-compliance, spillovers and attrition affect potential outcomes
Sampling strategy: Strategy used to select units to include in study
- How are we selecting units to analyse?
Assignment: Manner in which units are assigned to reveal one potential outcome or another
- Randomisation strategy used
Estimand: Quantities that we want to learn about in the world, in terms of potential outcomes
- What are we trying to estimate? ATE? Difference in means? Other quantities?
Estimator: Procedure for generating estimates of the quantities we want to learn about
- This is your statistical model (e.g., OLS, IV, etc.)

DeclareDesign in action

First, you need to install DeclareDesign with install.packages("DeclareDesign") and DesignLibrary with install.packages("DesignLibrary")
Under the hood, DeclareDesign uses fabricatr to generate data, randomizr to randomise units, and estimatr to estimate causal effects
All functions start with declare_, and you can chain them together with +
Once you have your design, you can run it with diagnose_design and draw_data
Then you can also use ggplot2 to visualise your results or dplyr to summarise them
The authors have written a tutorial that explains how to use DeclareDesign
And they have also created a gallery with examples of different designs

Design component	Function	Description
Model	`declare_model()`	background variables and potential outcomes
Inquiry	`declare_inquiry()`	research questions
Data strategy	`declare_sampling()`	sampling procedures
	`declare_assignment()`	assignment procedures
	`declare_measurement()`	measurement procedures
Answer strategy	`declare_estimator()`	estimation procedures
	`declare_test()`	testing procedures

Chapter 18 of the book explains how to use DeclareDesign for experimental causal inference. Lots of examples! Some we are going to see today 🤓

Example

Two-arm experiment

library(DeclareDesign)
library(tidyverse)
set.seed(385)

sample_size <- 50

two_arm <-
  declare_model(
    N = 10000,
    X = rep(c(0, 1), each = N / 2),
    U = rnorm(N, sd = 0.25),
    potential_outcomes(Y ~ 0.2 * Z + X + U)
  ) +
  declare_inquiry(ATE = mean(Y_Z_1 - Y_Z_0)) +
  declare_sampling(S = complete_rs(N = N, n = sample_size)) +
  declare_assignment(Z = complete_ra(N = N, m = sample_size/2)) +
  declare_measurement(Y = reveal_outcomes(Y ~ Z)) +
  declare_estimator(Y ~ Z, .method = lm_robust, inquiry = "ATE")

diagnosis_two_arm <- diagnose_design(two_arm)
diagnosis_two_arm


Research design diagnosis based on 500 simulations. Diagnosis completed in 2 secs. Diagnosand estimates with bootstrapped standard errors in parentheses (100 replicates).

  Design Inquiry Estimator Outcome Term N Sims Mean Estimand Mean Estimate
 two_arm     ATE estimator       Y    Z    500          0.20          0.21
                                                      (0.00)        (0.01)
   Bias SD Estimate   RMSE  Power Coverage
   0.01        0.16   0.16   0.24     0.96
 (0.01)      (0.00) (0.00) (0.02)   (0.01)

Power is a bit too low…

Let’s redesign the experiment

set.seed(385)

two_arm_power <-
  two_arm |>
  redesign(sample_size = c(50, 100, 250, 500)) |>
  diagnose_designs() |>
  tidy() |>
  filter(diagnosand == "power")

two_arm_power |>
  select(design, sample_size, diagnosand, estimate)

    design sample_size diagnosand estimate
1 design_1          50      power    0.236
2 design_2         100      power    0.398
3 design_3         250      power    0.788
4 design_4         500      power    0.986

ggplot(two_arm_power, aes(sample_size, estimate)) + 
  geom_point() +
  geom_smooth(method = "loess", color = "blue") +
  geom_hline(yintercept = 0.8, color = "red") +
  labs(x = "Sample Size", y = "Statistical Power") +
  theme_minimal()

Two-arm experiments with covariates

set.seed(385)

model <-
  declare_model(
    N = 10000,
    X = rep(c(0, 1), each = N / 2),
    U = rnorm(N, sd = 0.25),
    potential_outcomes(Y ~ 0.2 * Z + X + U)
  ) 
inquiry <-
  declare_inquiry(ATE = mean(Y_Z_1 - Y_Z_0))
sampling <-
  declare_sampling(S = complete_rs(N = N, n = sample_size))
assignment <-
  declare_assignment(Z = complete_ra(N = N, m = sample_size/2))
measurement <-
  declare_measurement(Y = reveal_outcomes(Y ~ Z))
answer_strategy <-
  declare_estimator(Y ~ Z, .method = lm_robust, inquiry = "ATE", label = "OLS")

two_arms_a <-
  model +
  inquiry +
  sampling +
  assignment +
  measurement +
  answer_strategy

diagnosis_two_arms_a <- diagnose_design(two_arms_a)
diagnosis_two_arms_a


Research design diagnosis based on 500 simulations. Diagnosis completed in 2 secs. Diagnosand estimates with bootstrapped standard errors in parentheses (100 replicates).

     Design Inquiry Estimator Outcome Term N Sims Mean Estimand Mean Estimate
 two_arms_a     ATE       OLS       Y    Z    500          0.20          0.21
                                                         (0.00)        (0.01)
   Bias SD Estimate   RMSE  Power Coverage
   0.01        0.16   0.16   0.24     0.96
 (0.01)      (0.00) (0.00) (0.02)   (0.01)

Two-arm experiments with covariates

set.seed(385)

two_arm_cov <-
  model +
  inquiry +
  sampling +
  assignment +
  measurement +
  declare_estimator(Y ~ Z, covariates = ~ X, .method = lm_lin, inquiry = "ATE", label = "OLS with covariates")

diagnosis_two_arm_cov <- diagnose_design(two_arm_cov)
diagnosis_two_arm_cov


Research design diagnosis based on 500 simulations. Diagnosis completed in 2 secs. Diagnosand estimates with bootstrapped standard errors in parentheses (100 replicates).

      Design Inquiry           Estimator Outcome Term N Sims Mean Estimand
 two_arm_cov     ATE OLS with covariates       Y    Z    500          0.20
                                                                    (0.00)
 Mean Estimate   Bias SD Estimate   RMSE  Power Coverage
          0.20  -0.00        0.07   0.07   0.81     0.95
        (0.00) (0.00)      (0.00) (0.00) (0.02)   (0.01)

Two-arm experiments without covariates

simulations_ta <- get_simulations(diagnosis_two_arm)

# first create summary for vertical lines
summary_ta <- 
  simulations_ta |> 
  group_by(estimator) |> 
  summarize(estimand = mean(estimand))

# then plot simulations
ggplot(simulations_ta) +
  geom_histogram(aes(estimate),
                 bins = 40, fill = "#72B4F3") +
  geom_vline(data = summary_ta,
             aes(xintercept = estimand),
             lty = "dashed", color = "#C6227F") +
  annotate("text", y = 300, x = 0.18, label = "Estimand",
           color = "#C6227F", hjust = 1) +
  facet_wrap(~ estimator) +
  labs(x = "Estimate", y = "Count of simulations") +
  theme_minimal()

Two-arm experiments with covariates

simulations_tac <- get_simulations(diagnosis_two_arm_cov)

summary_tac <- 
  simulations_tac |> 
  group_by(estimator) |> 
  summarize(estimand = mean(estimand))

# then plot simulations
ggplot(simulations_tac) +
  geom_histogram(aes(estimate),
                 bins = 40, fill = "#72B4F3") +
  geom_vline(data = summary_tac,
             aes(xintercept = estimand),
             lty = "dashed", color = "#C6227F") +
  annotate("text", y = 300, x = 0.18, label = "Estimand",
           color = "#C6227F", hjust = 1) +
  facet_wrap(~ estimator) +
  labs(x = "Estimate", y = "Count of simulations") +
  theme_minimal()

Block randomisation two-arm experiment

set.seed(385)

block_randomisation <-
  model +
  inquiry +
  declare_sampling(S = strata_rs(strata = X, n = 50)) +
  declare_assignment(Z = block_ra(blocks = X)) +
  measurement +
  declare_estimator(Y ~ Z, covariates = ~ X, .method = lm_lin, inquiry = "ATE", label = "Lin")

diagnosis_block_randomisation <- diagnose_design(block_randomisation)
diagnosis_block_randomisation


Research design diagnosis based on 500 simulations. Diagnosis completed in 4 secs. Diagnosand estimates with bootstrapped standard errors in parentheses (100 replicates).

              Design Inquiry Estimator Outcome Term N Sims Mean Estimand
 block_randomisation     ATE       Lin       Y    Z    500          0.20
                                                                  (0.00)
 Mean Estimate   Bias SD Estimate   RMSE  Power Coverage
          0.20   0.00        0.05   0.05   0.97     0.94
        (0.00) (0.00)      (0.00) (0.00) (0.01)   (0.01)

simulations_br <- get_simulations(diagnosis_block_randomisation)

summary_br <- 
  simulations_br |> 
  group_by(estimator) |> 
  summarize(estimand = mean(estimand))

# then plot simulations
ggplot(simulations_br) +
  geom_histogram(aes(estimate),
                 bins = 40, fill = "#72B4F3") +
  geom_vline(data = summary_br,
             aes(xintercept = estimand),
             lty = "dashed", color = "#C6227F") +
  annotate("text", y = 300, x = 0.18, label = "Estimand",
           color = "#C6227F", hjust = 1) +
  facet_wrap(~ estimator) +
  labs(x = "Estimate", y = "Count of simulations") +
  theme_minimal()

Blocked and clustered randomisation

set.seed(385)

ICC <- 0.9

block_cluster <-
  declare_model(
    cluster =
      add_level(
        N = 10,
        cluster_size = rep(seq(10, 50, 10), 2),
        cluster_shock =
          scale(cluster_size + rnorm(N, sd = 5)) * sqrt(ICC),
        cluster_tau = rnorm(N, sd = sqrt(ICC))
      ),
    individual =
      add_level(
        N = cluster_size,
        individual_shock = rnorm(N, sd = sqrt(1 - ICC)),
        individual_tau = rnorm(N, sd = sqrt(1 - ICC)),
        Y_Z_0 = cluster_shock + individual_shock,
        Y_Z_1 = Y_Z_0 + cluster_tau + individual_tau
      )
  ) +
  declare_inquiry(ATE = mean(Y_Z_1 - Y_Z_0)) +
  declare_assignment(Z = block_and_cluster_ra(clusters = cluster, blocks = cluster_size)) +
  declare_measurement(Y = reveal_outcomes(Y ~ Z)) +
  declare_estimator(Y ~ Z,
                    clusters = cluster,
                    inquiry = "ATE")

diagnosis_block_cluster <- diagnose_design(block_cluster)
diagnosis_block_cluster


Research design diagnosis based on 500 simulations. Diagnosis completed in 2 secs. Diagnosand estimates with bootstrapped standard errors in parentheses (100 replicates).

        Design Inquiry Estimator Outcome Term N Sims Mean Estimand
 block_cluster     ATE estimator       Y    Z    500          0.01
                                                            (0.01)
 Mean Estimate   Bias SD Estimate   RMSE  Power Coverage
         -0.02  -0.03        0.52   0.41   0.00     1.00
        (0.02) (0.02)      (0.01) (0.01) (0.00)   (0.00)

Redesigning over values of ICC

set.seed(385)

block_cluster_icc <-
  block_cluster |>
  redesign(ICC = seq(0.1, 0.9, by = 0.4)) |> 
  diagnose_designs() |>
  tidy()

block_cluster_icc |>
  select(design, ICC, diagnosand, estimate) |>
  filter(diagnosand %in% c("mean_estimate", "sd_estimate"))

    design ICC    diagnosand    estimate
1 design_1 0.1 mean_estimate  0.00151772
2 design_1 0.1   sd_estimate  0.22702412
3 design_2 0.5 mean_estimate -0.01250764
4 design_2 0.5   sd_estimate  0.41689454
5 design_3 0.9 mean_estimate  0.04037843
6 design_3 0.9   sd_estimate  0.53993123

DesignLibrary 📚

DesignLibrary

Making your life easier!

DesignLibrary is a companion package to DeclareDesign and it includes several common designs
You can use these designs as templates for your own experiments!
Let’s see how to create a simple two-arm experiment with DesignLibrary

library(DesignLibrary)

# two_arm_designer(
  # N = 100,
  # assignment_prob = 0.5,
  # control_mean = 0,
  # control_sd = 1,
  # ate = 1,
  # treatment_mean = control_mean + ate,
  # treatment_sd = control_sd,
  # rho = 1,
  # args_to_fix = NULL
# )

two_arm_design <- two_arm_designer(ate = 2, N = 1000)

two_arm_design


Research design declaration summary

Step 1 (population): declare_population(N = N, u_0 = rnorm(N), u_1 = rnorm(n = N, mean = rho * u_0, sd = sqrt(1 - rho^2))) 

Step 2 (potential outcomes): declare_potential_outcomes(Y ~ (1 - Z) * (u_0 * control_sd + control_mean) + Z * (u_1 * treatment_sd + treatment_mean)) 

Step 3 (inquiry): declare_inquiry(ATE = mean(Y_Z_1 - Y_Z_0)) -------------------

Step 4 (assignment): declare_assignment(Z = complete_ra(N, prob = assignment_prob)) 

Step 5 (reveal): declare_reveal() ----------------------------------------------

Step 6 (estimator): declare_estimator(Y ~ Z, inquiry = estimand) ---------------

Run of the design:

 inquiry estimand estimator term estimate std.error statistic   p.value
     ATE        2 estimator    Z     1.94    0.0654      29.7 3.38e-139
 conf.low conf.high  df outcome
     1.81      2.07 998       Y

DesignLibrary

Clustered designs

You can create complex designs easily too!

# A design with varying block size and varying cluster size
cluster_sampling_design <- cluster_sampling_designer(
  N_blocks = 2,
  N_clusters_in_block = 100,
  N_i_in_cluster = 50,
  n_clusters_in_block = 10,
  n_i_in_cluster = 10,
  icc = 0.1)

cluster_sampling_design


Research design declaration summary

Step 1 (population): declare_population(data = fixed_pop) ----------------------

Step 2 (inquiry): declare_inquiry(mean(Y), label = "Ybar") ---------------------

Step 3 (sampling): declare_sampling(S1 = strata_and_cluster_rs(strata = block, clusters = cluster, n = n_clusters_in_block), filter = S1 == 1) 

Step 4 (sampling): declare_sampling(S2 = strata_rs(strata = cluster, n = n_i_in_cluster), filter = S2 == 1) 

Step 5 (estimator): declare_estimator(Y ~ 1, model = lm_robust, clusters = cluster, inquiry = estimand, label = "Clustered Standard Errors") 

Run of the design:

 inquiry estimand                 estimator        term estimate std.error
    Ybar     3.98 Clustered Standard Errors (Intercept)     3.82     0.168
 statistic  p.value conf.low conf.high df outcome
      22.8 3.01e-15     3.47      4.18 19       Y

Summary 📚

Today we learned…

The basics of Quarto and DeclareDesign
How to write a Quarto document that includes text, code, and visualisations
The importance of literate programming for reproducible research
How to use DeclareDesign to plan and execute experiments
The six components of a DeclareDesign study
How to use DesignLibrary to create common designs

Quarto cheat sheet

Source: https://raw.githubusercontent.com/rstudio/cheatsheets/master/quarto.pdf

DeclareDesign cheat sheet

Source: https://raw.githubusercontent.com/rstudio/cheatsheets/master/declaredesign.pdf

And that’s all for today! 🎉

QTM 385 - Experimental Methods

Hello, everyone! 😊

Brief recap 📚

Last class, we discussed…

Today’s plan 📅

Introduction to Quarto and DeclareDesign

Two useful tools for experimental research (and beyond)

Introduction to Quarto and DeclareDesign

Two useful tools for experimental research (and beyond)

Quarto 📝

What is Quarto?

Why Quarto?

Can’t I just use R Markdown or Jupyter Notebooks instead?

How to get started with Quarto?

Writing a Quarto document 📝

How to write a Quarto document?

Markdown

Heading

Markdown

Quarto engines

knitr

Jupyter

PDFs

Adding references

Example

Example

DeclareDesign 📊

What is DeclareDesign?

A package for designing and analysing data

Six components of a DeclareDesign study

DeclareDesign in action

Example

Two-arm experiment

Power is a bit too low…

Let’s redesign the experiment

Two-arm experiments with covariates

Two-arm experiments with covariates

Two-arm experiments without covariates

Two-arm experiments with covariates

Block randomisation two-arm experiment

Blocked and clustered randomisation

Redesigning over values of ICC

DesignLibrary 📚

DesignLibrary

Making your life easier!

DesignLibrary

Clustered designs

Summary 📚

Today we learned…

Further readings

Quarto cheat sheet

DeclareDesign cheat sheet

And that’s all for today! 🎉

Have a great week! 🎉