BenfordTests (version 1.2.0)

signifd.analysis: 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

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

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.

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))