10  Experimental

Today I’m going to use faux to generate some simulated data for a factorial experimental design and make some plots.

Setup

library(faux)      # for data simulation
library(ggplot2)   # for plotting
library(patchwork) # for multi-panel plots
theme_set(theme_bw(base_size = 16))
set.seed(8675309)  # for reproducibility

10.1 Data

The sim_design() function is meant to make the simulation of data for factorial designs easier. You can name the factors and their levels (see extensive vignettes), but here we’ll just use the generic naming from faux and only specify the number of levels of each factor. By default, it simulates 100 observations in each between group, with means of 0 and standard deviations of 1. The function also produces a design plot.

10.1.1 One factor

Code

b2 <- sim_design(between = 2, 
                 mu = c(0, 0.5))

For within-subject designs, you have to specify the correlation between each level. If there are any within factors, the check_sim_stats() table will include the sampled correlations. You can turn off the design plot with plot = FALSE.

Code

w2 <- sim_design(within = 2, 
                 mu = c(0, 0),
                 sd = c(1, 5),
                 r = 0.5,
                 plot = FALSE)
check_sim_stats(w2)

n	var	W1a	W1b	mean	sd
100	W1a	1.00	0.45	-0.07	1.05
100	W1b	0.45	1.00	-0.47	5.52

10.1.2 Two factors

You can also give the factors names and labels. You can set the correlations separately for each between-subject cell.

Code

# df version uses row and column labels, 
# so allows rows and columns to be out of order
mu <- data.frame(cat = c(0, 0.5),
                 dog = c(0.25, 1),
                 row.names = c("am", "pm"))

w2b2 <- sim_design(within = list(time = c("am", "pm")), 
                   between = list(pet = c("cat", "dog")),
                   mu = mu,
                   dv = list(y = "Something Score"),
                   r = list(cat = 0,
                            dog = .5),
                   long = TRUE)

Code

check_sim_stats(w2b2)

pet	n	var	am	pm	mean	sd
cat	100	am	1.00	0.05	-0.07	1.03
cat	100	pm	0.05	1.00	0.52	0.94
dog	100	am	1.00	0.58	0.19	1.07
dog	100	pm	0.58	1.00	1.07	0.94

10.2 Plots

10.2.1 Data Plots

Now it’s time for the fun part: making plots! The plot() function makes it easy to plot data made with faux. See the plotting vignette for more details.

The output is a ggplot, so you can add more ggplot options to it.

Code

plot(b2, geoms = c("violin", "box"), palette = "Accent") +
  ggtitle("Between-Subject Factor")

10.2.2 Design Plots

You can also plot the design (not the data). If you plot a violin, the shape will be estimated by simulating a very large sample with these parameters.

Code

get_design(w2) %>%
  plot(geoms = c("violin", "pointrangeSD"), palette = "Dark2") +
  ggtitle("Within-Subject Factor")

10.2.3 Combo Plots

Create a design plot for the main effects and interaction in w2b2. You can specify the order color, x, facet row(s), facet col(s) [this function needs a little work to be more intuitive]. Add a title and custom colours (you’ll get a warning about the duplicate scale for fill; just ignore it).

Code

geoms <- c("violin", "pointrangeSD")
b_colors <- scale_color_manual(values = c("red3", "dodgerblue3"), guide = "none")
w_colors <- scale_color_manual(values = c("darkorchid", "darkorange"), guide = "none")
b_fill <- scale_fill_manual(values = c("red3", "dodgerblue3"), guide = "none")
w_fill <- scale_fill_manual(values = c("darkorchid", "darkorange"), guide = "none")

plot_b2 <- get_design(w2b2) %>% 
  plot(geoms = geoms, "pet", "pet") + 
  b_colors + b_fill +
  labs(x = NULL, title = "Main Effect of Pet Type")

plot_w2 <- get_design(w2b2) %>% 
  plot(geoms = geoms, "time", "time") + 
  w_colors + w_fill +
  labs(x = NULL, title = "Main Effect of Time of Day")

plot_w2b2 <- get_design(w2b2) %>% 
  plot(geoms = geoms, "time", "pet") + 
  w_colors + w_fill +
  labs(x = NULL, title = "Interaction between Time of Day and Pet Type")

plot_b2w2 <- get_design(w2b2) %>% 
  plot(geoms = geoms, "pet", "time") + 
  b_colors + b_fill +
  labs(x = NULL, title = "Interaction between Pet Type and Time of Day")

Combine with patchwork

Code

layout <- paste("AB", "CC", "DD", sep = "\n")
plot_b2  + plot_w2 + plot_w2b2 + plot_b2w2 +
  plot_layout(design = layout)

Plots of the parameters for a simulated 2B2W experimental design.