Visualize critical values / pairwise comparisons from posthoc Tukey in R

Question

I'm trying to get a fine-grain visualisation of critical values I got from posthoc Tukey. There are some good guidelines out there for visualizing pairwise comparisons, but I need something more refined. The idea is that I would have a plot where each small square would represent a critical value from the matrix below, coded in such manner that:

• if the value is higher or equal to 5.45 - it's a black square;
• if the value is lower or equal to -5.45 - it's a gray square;
• if the value is between -5.65 and 5.65 - it's a white square.

The data matrix is here.

Or maybe you would have better suggestion how to visualize those critical values?

EDIT: Following comments from @Aaron and @DWin I want to provide a bit more context for the above data and justification for my question. I am looking at the mean ratings of acceptability for seven virtual characters, each of them is animated on 5 different levels. So, I have two factors there - character (7 levels) and motion (5 levels). Because I have found interaction between those two factors, I decided to look at differences between the means for all the characters for all levels of motion , which resulted in this massive matrix, as an output of posthoc Tukey. It's probably too much detail now, but please don't throw me out to Cross Validated, they will eat me alive...

Answer 1

This is fairly straightforward with image:

d <- as.matrix(read.table("http://dl.dropbox.com/u/2505196/postH.dat"))    
image(x=1:35, y=1:35, as.matrix(d), breaks=c(min(d), -5.45, 5.45, max(d)), 
      col=c("grey", "white", "black"))

For just half, set half to missing with d[upper.tri(d)] <- NA and add na.rm=TRUE to the min and max functions.

Answer 2

Here is a ggplot2 solution. I'm sure there are simpler ways to accomplish this -- I guess I got carried away!

library(ggplot2)

# Load data.
postH = read.table("~/Downloads/postH.dat")
names(postH) = paste("item", 1:35, sep="") # add column names.
postH$item_id_x = paste("item", 1:35, sep="") # add id column.

# Convert data.frame to long form.
data_long = melt(postH, id.var="item_id_x", variable_name="item_id_y")

# Convert to factor, controlling the order of the factor levels.
data_long$item_id_y = factor(as.character(data_long$item_id_y), 
                        levels=paste("item", 1:35, sep=""))
data_long$item_id_x = factor(as.character(data_long$item_id_x), 
                        levels=paste("item", 1:35, sep=""))

# Create critical value labels in a new column.
data_long$critical_level = ifelse(data_long$value >= 5.45, "high",
                             ifelse(data_long$value <= -5.65, "low", "middle"))

# Convert to labels to factor, controlling the order of the factor levels.
data_long$critical_level = factor(data_long$critical_level,
                                  levels=c("high", "middle", "low"))

# Named vector for ggplot's scale_fill_manual
critical_level_colors = c(high="black", middle="grey80", low="white")

# Calculate grid line positions manually.
x_grid_lines = seq(0.5, length(levels(data_long$item_id_x)), 1)
y_grid_lines = seq(0.5, length(levels(data_long$item_id_y)), 1)

# Create plot.
plot_1 = ggplot(data_long, aes(xmin=as.integer(item_id_x) - 0.5,
                               xmax=as.integer(item_id_x) + 0.5,
                               ymin=as.integer(item_id_y) - 0.5,
                               ymax=as.integer(item_id_y) + 0.5,
                               fill=critical_level)) +
     theme_bw() +
     opts(panel.grid.minor=theme_blank(), panel.grid.major=theme_blank()) +
     coord_cartesian(xlim=c(min(x_grid_lines), max(x_grid_lines)),
                     ylim=c(min(y_grid_lines), max(y_grid_lines))) +
     scale_x_continuous(breaks=seq(1, length(levels(data_long$item_id_x))),
                        labels=levels(data_long$item_id_x)) +
     scale_y_continuous(breaks=seq(1, length(levels(data_long$item_id_x))),
                        labels=levels(data_long$item_id_y)) +
     scale_fill_manual(name="Critical Values", values=critical_level_colors) +
     geom_rect() +
     geom_hline(yintercept=y_grid_lines, colour="grey40", size=0.15) +
     geom_vline(xintercept=x_grid_lines, colour="grey40", size=0.15) +
     opts(axis.text.y=theme_text(size=9)) +
     opts(axis.text.x=theme_text(size=9, angle=90)) +
     opts(title="Critical Values Matrix")

# Save to pdf file.
pdf("plot_1.pdf", height=8.5, width=8.5)
print(plot_1)
dev.off()