signifd.analysis {BenfordTests}

Graphical Analysis of First Significant Digits

Description

signifd.analysis takes any numerical vector reduces the sample to the specified number of significant digits. The (relative) frequencies are then plotted so that a subjective analysis may be performed.

Usage

signifd.analysis(x = NULL, digits = 1, graphical_analysis = TRUE, freq = FALSE, 
alphas = 20, tick_col = "red", ci_col = "darkgreen", ci_lines = c(.05))

Arguments

x

A numeric vector.

digits

An integer determining the number of first digits to use for testing, i.e. 1 for only the first, 2 for the first two etc.

graphical_analysis

Boolean value indicating if results should be plotted.

freq

Boolean value indicating if absolute frequencies should be used.

alphas

Either a vector containing the significance levels([0,1]) that will be shaded, or an integer defining the number of evenly spaced confidence intervals.

tick_col

Color code or name that will be passed to "points" for plotting.

ci_col

Color code or name that will be passed to "polygon" for shading the different confidence intervals. May be more than one color.

ci_lines

Boolean or fractional value(s) indicating significance levels where lines are drawn

Details

Confidence intervals are calculated from the normal distribution with \mu_i = np_i and \sigma^2 = np_i(1-p_i), where i represents the considered digit. Be aware that the normal approximation only holds for "large" n.

Value

A list containing the following components:

summary

the summary printed below the graph, a matrix of digits, their (relative) frequencies and individual p-values

CIs

confidence intervals used for plotting as defined by parameter "ci_lines" or "alphas" if ci_lines==FALSE

Author(s)

Dieter William Joenssen [e-mail]

References

Benford, F. (1938) The Law of Anomalous Numbers. Proceedings of the American Philosophical Society. 78, 551–572.

Freedman, L.S. (1981) Watson's Un2 Statistic for a Discrete Distribution. Biometrika. 68, 708–711.

See Also

pbenf

Examples

#Set the random seed to an arbitrary number
set.seed(421)
#Create a sample satisfying Benford's law
X<-rbenf(n=20)
#Analyze the first digits using the the defaults
signifd.analysis(X)
#Turn off plot
signifd.analysis(X,graphical_analysis=FALSE)
#Use absolute frequencies
signifd.analysis(X,graphical_analysis=FALSE,freq=TRUE)
#Use five evenly spaced confidence intervals, no lines
#alphas is used for shadeing
signifd.analysis(X,graphical_analysis=TRUE,alphas=5,freq=TRUE,ci_lines=FALSE)
#Use fifty evenly spaced, gray confidence intervals, blue ticks, and lines at 
#the 1 and 5 percent confidence intervals
signifd.analysis(X,graphical_analysis=TRUE,alphas=50,freq=TRUE,tick_col="blue",
ci_col="gray",ci_lines=c(.01,.05))