# designr: Balanced factorial designs

designr is an R package to create and simulate crossed factorial designs.

## Installation

Install from CRAN within R using:

install.packages("designr")

Install the development version in R using devtools:

devtools::install_github("mmrabe/designr", build_vignettes = TRUE)

## Random and fixed factors

designr supports factorial designs with an arbitrary number of fixed and random factors. Fixed factors are factors for which levels are known and typically defined by the experimenter, e.g. an experimental condition or a quasi-experimental variable such as a subject’s age group. Conversely, the instances of random factors are usually not known before data collection. Examples for random factors are subjects or items in a typical psychological experiment, with the individual tested subjects and used items being the instances of those random factors.

## Simple fixed-effects design

A fixed-effects design without repeated measurement is created as easily as this:

design1 <-
fixed.factor("Age", levels=c("young", "old")) +
fixed.factor("Material",  levels=c("word", "image"))
design1
## Factor design with 2 factor(s):
##  - Fixed factor Age with 2 level(s) (young, old) and 1 replication(s)
##  - Fixed factor Material with 2 level(s) (word, image) and 1 replication(s)
##
## Design matrix with 4 planned observations:
## # A tibble: 4 x 2
##   Age   Material
##   <fct> <fct>
## 1 young word
## 2 old   word
## 3 young image
## 4 old   image


As can be seen, this experimental design requires 4 observations.

Assume we want to test different groups of subjects. Each subject will only be old or young but be tested with stimuli of both categories word and image. In a typical behavioral experiment, Age would now be a between-subject/within-item factor and Material a within-subject/between-item factor. In other words, Material is now nested within the instances of Subject, whereas Subject is grouped by Age.

design2 <-
fixed.factor("Age", levels=c("young", "old")) +
fixed.factor("Material",  levels=c("word", "image")) +
random.factor("Subject", groups = "Age")
design.codes(design2)
## # A tibble: 4 x 3
##   Subject  Age   Material
##   <fct>    <fct> <fct>
## 1 Subject1 old   word
## 2 Subject1 old   image
## 3 Subject2 young word
## 4 Subject2 young image


The minimal experimental design will still require 4 observations, assigning one subject to each level of the between-subject factor Age.

## Nested designs

Note that design1 is nested within design2. This means that instead of defining design2 like we did above, we can also derive it from the existing design1 by adding the random factor Subject like so:

design2 <-
design1 +
random.factor("Subject", groups = "Age")

## Crossed random factors

Oftentimes, experiments will have more than one random factor, for example Subject and Item. This is because items in behavioral experiments are often prepared upfront and not randomly generated upon presentation. In that case we would like to make sure that each item is presented equally often across all subjects and within-item conditions. Suppose that we are extending our example from above by a second random factor Item. Contrary to SubjectItem is grouped by Material because each item can only be a word or image but it may be presented to both old and young subjects.

design3 <-
fixed.factor("Age", levels=c("young", "old")) +
fixed.factor("Material",  levels=c("word", "image")) +
random.factor("Subject", groups = "Age") +
random.factor("Item", groups = "Material")
design.codes(design3)
## # A tibble: 4 x 4
##   Subject  Item  Age   Material
##   <fct>    <fct> <fct> <fct>
## 1 Subject1 Item1 old   image
## 2 Subject1 Item2 old   word
## 3 Subject2 Item1 young image
## 4 Subject2 Item2 young word


In this design, we plan to test 2 subjects, one young and one old, and each of them will be presented two items, an image and a word. The items will appear equally often in the levels of Age and subjects will see an equal number of items in all levels of Material.

## Counterbalancing

Note that in the example above, each item really only appears once per subject. However, suppose we introduce a third fixed factor, which varies within subjects and within items, i.e. it is neither a subject nor item level fixed property. This could be something like the contrast on the screen or some other experimental manipulation that is pseudo-randomly varied for each subject and each item.

The resulting design may look something like this:

design4 <-
fixed.factor("Age", levels=c("young", "old")) +
fixed.factor("Material",  levels=c("word", "image")) +
fixed.factor("Contrast",  levels=c("high", "low")) +
random.factor("Subject", groups = "Age") +
random.factor("Item", groups = "Material")
design.codes(design4)
## # A tibble: 8 x 5
##   Subject  Item  Age   Material Contrast
##   <fct>    <fct> <fct> <fct>    <fct>
## 1 Subject1 Item1 old   image    high
## 2 Subject1 Item1 old   image    low
## 3 Subject1 Item2 old   word     high
## 4 Subject1 Item2 old   word     low
## 5 Subject2 Item1 young image    high
## 6 Subject2 Item1 young image    low
## 7 Subject2 Item2 young word     high
## 8 Subject2 Item2 young word     low


In a fully crossed and balanced experimental design, each item would now be presented twice per subject, once with high and once with low contrast. This can be absolutely legitimate, depending on the research question. In many behavioral experiments, however, the experimenter may wish to prevent the same item from being presented twice because that could introduce unwanted effects.

Essentially, what we want to do is to group each Subject×Item pairing by Contrast, i.e. we want to ensure that each item assigned to a subject is only assigned in either high or low contrast. We can therefore add the interaction of Subject and Item as a random factor, grouped by Contrast:

design5 <-
fixed.factor("Age", levels=c("young", "old")) +
fixed.factor("Material",  levels=c("word", "image")) +
fixed.factor("Contrast",  levels=c("high", "low")) +
random.factor("Subject", groups = "Age") +
random.factor("Item", groups = "Material") +
random.factor(c("Subject","Item"), groups = "Contrast")
design.codes(design5)
## # A tibble: 16 x 5
##    Subject  Item  Age   Material Contrast
##    <fct>    <fct> <fct> <fct>    <fct>
##  1 Subject1 Item1 old   image    high
##  2 Subject1 Item2 old   image    low
##  3 Subject1 Item3 old   word     high
##  4 Subject1 Item4 old   word     low
##  5 Subject2 Item1 old   image    low
##  6 Subject2 Item2 old   image    high
##  7 Subject2 Item3 old   word     low
##  8 Subject2 Item4 old   word     high
##  9 Subject3 Item1 young image    high
## 10 Subject3 Item2 young image    low
## 11 Subject3 Item3 young word     high
## 12 Subject3 Item4 young word     low
## 13 Subject4 Item1 young image    low
## 14 Subject4 Item2 young image    high
## 15 Subject4 Item3 young word     low
## 16 Subject4 Item4 young word     high


The design now contains 16 planned observations for 4 subjects and 4 items. Each subject will be presented each item exactly once and an equal number of items (1) in each combination of Material×Contrast. Moreover, each item will be presented equally often in each combination of Age×Contrast.

For a more detailed example, see the design-to-dataframe vignette (by executing vignette("design-to-dataframe")) and the manual pages of the package.