# Latin Square Design

This vignette shows how to generate a Latin square design using both the FielDHub Shiny App and the scripting function latin_square() from the FielDHub package.

## 1. Using the FielDHub Shiny App

To launch the app you need to run either

FielDHub::run_app()

or

library(FielDHub)
run_app()

Once the app is running, go to Other Designs > Latin Square Design

Then, follow the following steps where we show how to generate this kind of design by an example with 5 treatments and 2 reps.

## Inputs

1. Import entries’ list? Choose whether to import a list with entry numbers and names for genotypes or treatments.
• If the selection is No, that means the app is going to generate synthetic data for entries and names of the treatment based on the user inputs.

• If the selection is Yes, the entries list must fulfill a specific format and must be a .csv file. The file must have the three columns: ROW, COLUMN and TREATMENT. All of those columns contain a list of unique names that identify each treatment. Duplicate values are not allowed, all entries must be unique. In the following table, we show an example of the entries list format. This example has an entry list with 5 treatments.

ROW COLUMN TREATMENT
Period1 Cow1 Diet1
Period2 Cow2 Diet2
Period3 Cow3 Diet3
Period4 Cow4 Diet4
Period5 Cow5 Diet5
1. Input the number of treatments in the Input # of Treatments box. In the alpha lattice design, the number of treatments must be a composite number.

2. Select the number of replications of these treatments with the Input # of Full Reps box. The number of treatments and the number of full reps set the dimensions of the field.

3. Select serpentine or cartesian in the Plot Order Layout. For this example we will use the default serpentine layout.

4. Enter the starting plot number in the Starting Plot Number box. If the experiment has multiple locations, you must enter a comma separated list of numbers the length of the number of locations for the input to be valid.

5. Enter a name for the location of the experiment in the Input Location box. A completely randomized design can only be run in a single location at a time.

6. To ensure that randomizations are consistent across sessions, we can set a seed number in the box labeled Seed Number. In this example, we will set it to 123.

7. Once we have entered the information for our experiment on the left side panel, click the Run! button to run the design.

## Outputs

After you run a Latin square design in FielDHub, there are several ways to display the information contained in the field book.

### Field Layout

When you first click the run button on a Latin square design, FielDHub displays the Field Layout tab, which shows the entries and their arrangement in the field. In the box below the display, you can change the layout of the field. You can also display a heatmap over the field by changing Type of Plot to Heatmap. To view a heatmap, you must first simulate an experiment over the described field with the Simulate! button. A pop-up window will appear where you can enter what variable you want to simulate along with minimum and maximum values.

### Field Book

The Field Book displays all the information on the experimental design in a table format. It contains the specific plot number and the row and column address of each entry, as well as the corresponding treatment on that plot. This table is searchable, and we can filter the data in relevant columns. If we have simulated data for a heatmap, an additional column for that variable appears in the field book.

## 2. Using the FielDHub function: latin_square()

You can run the same design with a function in the FielDHub package, latin_square().

First, you need to load the FielDHub package typing,

library(FielDHub)

Then, you can enter the information describing the above design like this:

lsd <- latin_square(
t = 5,
reps = 2,
plotNumber = 101,
planter = "serpentine",
seed = 1238
)

#### Details on the inputs entered in latin_square() above

• t = 5 is the number of treatments.
• reps = 2 is the number of replications (squares).
• plotNumber = 101 is the starting plot number.
• planter = "cartesian" is the plot order layout.
• locationNames = "FARGO" is an optional name for the location.
• seed = 1238 is the seed number to replicate identical randomizations.

### Access to lsd object

The latin_square() function returns a list consisting of all the information displayed in the output tabs in the FielDHub app: design information, plot layout, plot numbering, entries list, and field book. These are accessible by the $ operator, i.e. lsd$layoutRandom or lsd$fieldBook. lsd$fieldBook is a list containing information about every plot in the field, with information about the location of the plot and the treatment in each plot. As seen in the output below, the field book has columns for ID, LOCATION, PLOT, SQUARE, ROW, COLUMN, and TREATMENT.

field_book <- lsd$fieldBook head(lsd$fieldBook, 10)
   ID LOCATION PLOT SQUARE   ROW   COLUMN TREATMENT
1   1        1  101      1 Row 1 Column 1        T5
2   2        1  102      1 Row 1 Column 2        T1
3   3        1  103      1 Row 1 Column 3        T2
4   4        1  104      1 Row 1 Column 4        T4
5   5        1  105      1 Row 1 Column 5        T3
6   6        1  110      1 Row 2 Column 1        T4
7   7        1  109      1 Row 2 Column 2        T2
8   8        1  108      1 Row 2 Column 3        T3
9   9        1  107      1 Row 2 Column 4        T1
10 10        1  106      1 Row 2 Column 5        T5

### Plot the field layout

For plotting the layout in function of the coordinates ROW and COLUMN, you can use the the generic function plot() as follow,

plot(lsd)