Summarizing usage of Siegel's methods in the literature (November 7, 2014)

Let's summarize all the parameters used with Siegel's method from the literature. Let's start by parsing them.

set.seed(0)
literature_range <- read.table("literature_range.txt", na.strings = "", col.names = c("task_range", 
    "mach_range", "task_hetero", "mach_hetero", "row_consis", "col_consis"))
literature_CV <- read.table("literature_CV.txt", na.strings = "", col.names = c("task_range", 
    "mach_range", "task_hetero", "mach_hetero", "row_consis", "col_consis", 
    "mean"))

Now, for the range-based method:

library(ggplot2)
p <- ggplot(data = literature_range, aes(x = task_range, y = mach_range, shape = interaction(task_hetero, 
    mach_hetero), color = interaction(task_hetero, mach_hetero), fill = interaction(task_hetero, 
    mach_hetero)))
p <- p + geom_point(size = 4)
library(scales)
loglog_trans <- trans_new("loglog", transform = function(z) {
    log(log(z))
}, inverse = function(z) {
    exp(exp(z))
})
p <- p + scale_y_continuous(name = expression(R[mach]), trans = loglog_trans, 
    breaks = c(10, 100, 1000, 1e+05, 1e+07, 1e+09))
p <- p + scale_x_continuous(name = expression(R[task]), trans = loglog_trans, 
    breaks = c(10, 100, 3000, 1e+05, 1e+07, 1e+09))
breaks <- c("high.high", "low.high", "high.low", "low.low", "NA.NA")
labels <- c("hihi", "lohi", "hilo", "lolo", "NA")
p <- p + scale_color_discrete(name = "Heterogeneity", breaks = breaks, labels = labels)
p <- p + scale_shape_manual(name = "Heterogeneity", values = c(21, 24, 25, 23, 
    4), breaks = breaks, labels = labels)
p <- p + scale_fill_discrete(name = "Heterogeneity", breaks = breaks, labels = labels)
p <- p + theme(legend.position = "bottom")
p

plot of chunk claimed-range-properties-plot

Some values are not shown (they come from the same article).

And for the CVB method:

p <- ggplot(data = literature_CV, aes(x = task_range, y = mach_range, shape = interaction(task_hetero, 
    mach_hetero), color = interaction(task_hetero, mach_hetero), fill = interaction(task_hetero, 
    mach_hetero)))
p <- p + geom_point(size = 4)
p <- p + scale_x_continuous(name = expression(V[task]), breaks = seq(0, 2, 0.2), 
    limits = extendrange(c(0.05, 1.05)))
p <- p + scale_y_continuous(name = expression(V[mach]), breaks = seq(0, 2, 0.2), 
    limits = extendrange(c(0.05, 1.05)))
breaks <- c("high.high", "low.high", "high.low", "low.low", "med.med", "NA.NA")
labels <- c("hihi", "lohi", "hilo", "lolo", "medmed", "NA")
p <- p + scale_color_discrete(name = "Heterogeneity", breaks = breaks, labels = labels)
p <- p + scale_shape_manual(name = "Heterogeneity", values = c(21, 24, 25, 23, 
    22, 4), breaks = breaks, labels = labels)
p <- p + scale_fill_discrete(name = "Heterogeneity", breaks = breaks, labels = labels)
p <- p + theme(legend.position = "bottom")
p
## Warning: Removed 3 rows containing missing values (geom_point).

plot of chunk claimed-CV-properties-plot

We can see all the parameters that have been used (a small jitter has been inserted in order to show superposing points).

The next step is to generate equivalent figures but with the expected heterogeneity values using our measures.