vudc (version 1.1)

qddplot: Quantile Difference Diagram

Description

Creates quantile difference diagrams. It takes two numerical datasets, sorts them, calculates differences on the same quantiles (i.e. lowest with the lowest, median with the median, 90% with 90% etc.) and displays these differences. It is appropriate for visual illustration of Wilcoxon rank test and F-test of equality of variances.

Usage

qddplot(x, y, 
	remove.ratio = 0.1, differences.range = NA, differences.rangemin = 10, 
	differences.drawzero = TRUE, quantiles.drawhalf = TRUE, 
	quantiles.showaxis = TRUE, line.lwd = 5, xlab = "Quantile", 
	ylab = "Difference", main = "Quantile Differences", ...)

Arguments

x, y

vectors of numeric values to be compared. It is not necessary to have the same length.

remove.ratio

a real number in range [0.0, 0.5). Indicates how much leading and tailing data should not be displayed in order to avoid a bias on the diagram caused by outliers.

differences.range

numeric, indicating the value range (i.e. the y axis) to be shown. The default value is NA, indicating the maximum absolute value is considered. This can be overridden with an explicit value.

differences.rangemin

numeric, indicating the minimum value of the value range. Used in combination with differences.range=NA (the default), else ignored.

differences.drawzero

logical, indicating if the y=0 helper line should be displayed.

quantiles.drawhalf

logical, indicating if the x=0.5 helper line should be displayed.

quantiles.showaxis

logical, indicating if the custom values on the x axis should be displayed.

line.lwd

width of the main line.

xlab

title for the x axis, see plot.

ylab

title for the y axis, see plot.

main

plot title, see plot.

...

standard graphic parameters. See par for details.

Details

The quantile difference diagrams can be used to visualize the results of Wilcoxon rank tests (wilcox.test). Wilcoxon rank test basically checks if the values found in one dataset are different (more specifically: higher or lower) than those in the other. If the values in subset x are higher than values in subset y at all quantiles, then the result would look like a line completely on the same part of y coordinate (either completely on the positive or on the negative part).

In most of the cases the diagram resembles on a more or less straight line. The slope indicates the difference between variances (see also var.test). The position of the line indicates if the values in one dataset is higher than those in another; being close to 0 at 50%, if they are similar.

Examples

# Using default settings with random data.
qddplot(rnorm(100, 30, 50), rnorm(200, 10, 10));

# remove.ratio = 0.0 means the outliers are not removed.
qddplot(rnorm(100, 30, 50), rnorm(200, 10, 10), remove.ratio=0.0);

# remove.ratio = 0.25 means only the middle half is displayed, the upper and lower quantile are not.
qddplot(rnorm(100, 30, 50), rnorm(200, 10, 10), remove.ratio=0.25);

# Illustrating similar and different medians and variances on 4 quantile difference diagrams.
# This is also an illustration for setting custom main title and subtitle.
dataSetA <- seq(-20, 20) + rnorm(41);
dataSetB <- seq(-15, 25) + rnorm(41);
dataSetC <- seq(-40, 40) + rnorm(81);
dataSetD <- seq(-20, 20) + rnorm(41);
op <- par(mfrow=c(2,2));
qddplot(
	dataSetA, 
	dataSetD, 
	main = "Similar median, similar variance",
	sub = "-20...20 vs. -20...20");
qddplot(
	dataSetA, 
	dataSetB, 
	main = "Different median, similar variance",
	sub = "-20...20 vs. -15...25");
qddplot(
	dataSetA, 
	dataSetC, 
	main = "Similar median, different variance",
	sub = "-20...20 vs. -40...40");
qddplot(
	dataSetB, 
	dataSetC, 
	main = "Different median, different variance",
	sub = "-15...25 vs. -40...40"); 
par(op);

# Change plot style: thicker line in red color.
qddplot(rnorm(100, 30, 50), rnorm(200, 10, 10), line.lwd=10, col="red");

# Hide axes, helper lines and captions.
qddplot(rnorm(100, 30, 50), rnorm(200, 10, 10), differences.drawzero=FALSE, 
	quantiles.drawhalf=FALSE, quantiles.showaxis=FALSE, line.lwd=1, yaxt='n', 
	main="", sub="", xlab="", ylab="");

# Do not consider minimal range.
qddplot(rnorm(100, 1, 1), rnorm(100, 2, 1), differences.rangemin=NA);

# Set an explicit range.
qddplot(rnorm(100, 0, 200), rnorm(100, 0, 200), differences.range=40);