rqq {lawstat}

Test of Normality Using RQQ Plots

Description

Produce robust quantile-quantile (RQQ) and classical quantile-quantile (QQ) plots for graphical assessment of normality and optionally add a line, a QQ line, to the produced plot. The QQ line may be chosen to be a 45-degree line or to pass through the first and third quartiles of the data. NAs from the data are omitted.

Usage

rqq(
  y,
  plot.it = TRUE,
  square.it = TRUE,
  scale = c("MAD", "J", "classical"),
  location = c("median", "mean"),
  line.it = FALSE,
  line.type = c("45 degrees", "QQ"),
  col.line = 1,
  lwd = 1,
  outliers = FALSE,
  alpha = 0.05,
  ...
)

Arguments

y

the input data.

plot.it

logical. Should the result be plotted?

square.it

logical. Should the plot scales be square? The default is TRUE.

scale

the choice of a scale estimator, i.e., the classical or robust estimate of the standard deviation.

location

the choice of a location estimator, i.e., the mean or median.

line.it

logical. Should the line be plotted? No line is the default.

line.type

If line.it = TRUE, the choice of a line to be plotted, i.e., the 45-degree line or the line passing through the first and third quartiles of the data.

col.line

the color of the line (if plotted).

lwd

the line width (if plotted).

outliers

logical. Should the outliers be listed in the output?

alpha

significance level of outliers. If outliers = TRUE, then all observations that are less than the 100*alpha-th standard normal percentile or greater than the 100*(1-alpha)-th standard normal percentile will be listed in the output.

...

other parameters passed to the plot function.

Details

An RQQ plot is a modified QQ plot where data are robustly standardized by the median and robust measure of spread (rather than mean and classical standard deviation as in the basic QQ plots) and then are plotted against the expected standard normal order statistics (Gel et al. 2005; Weisberg 2005). Under normality, the plot of the standardized observations should follow the 45-degree line, or QQ line. Both the median and robust standard deviation are significantly less sensitive to outliers than mean and classical standard deviation and therefore are more preferable in many practical situations to assess graphically deviations from normality (if any). We choose median and MAD as a robust measure of location and spread for our RQQ plots since this standardization typically provides a clearer graphical diagnostics of normality. In particular, deviations from the QQ line are usually more noticeable in RQQ plots in the case of outliers and heavy tails. Users can also choose to plot the 45-degree line or the 1st-3rd quartile line (see the argument line.type). No line is the default.

Value

A list with the following numeric components:

x

the x-coordinates of the points that were/would be plotted.

y

the original data vector, i.e., the corresponding y-coordinates, including NAs (if any).

Author(s)

W. Wallace Hui, Yulia R. Gel, Joseph L. Gastwirth, Weiwen Miao

References

Gel Y, Miao W, Gastwirth JL (2005). “The importance of checking the assumptions underlying statistical analysis: graphical methods for assessing normality.” Jurimetrics, 46, 3.

Weisberg S (2005). Applied Linear Regression, 3 edition. John Wiley & Sons, Hoboken, NJ.

See Also

rjb.test, sj.test, qqnorm, qqplot, qqline

Examples

## Simulate 100 observations from standard normal distribution:
y = rnorm(100)
rqq(y)

## Using Michigan data
data(michigan)
rqq(michigan)