td_independence {terminaldigits}

Test of independence of terminal digits

Description

The td_independence function tests the independence of terminal digits from preceding digits by constructing a contingency table of counts where rows constitute unique preceding digits and columns constitute unique terminal digits. A test of independence for a contingency tables is then implemented via Monte Carlo simulation.

Usage

td_independence(
  x,
  decimals,
  reps = 10000,
  test = "Chisq",
  tolerance = 64 * .Machine$double.eps
)

Arguments

x

a numeric vector

decimals

an integer specifying the number of decimals. This can be zero if the terminal digit is not a decimal.

reps

a positive integer specifying the number of Monte Carlo simulations. The default is set to 10,000 which may be appropriate for exploratory analysis. A higher number of simulation should be selected for more precise results.

test

a string specifying the test of independence. The default is Pearson's chi-squared statistic ("Chisq"). Also available is the log-likelihood ratio statistic ("G2"), the Freeman-Tukey statistic ("FT"), and the Root-mean-square statistic ("RMS").

tolerance

sets an upper bound for rounding errors when evaluating whether a statistic for a simulation is greater than or equal to the statistic for the observed data. The default is identical to the tolerance set for simulations in the chisq.test function from the stats package in R.

Details

Monte Carlo simulations are implemented for contingency tables with fixed margins using algorithm ASA 144 (Agresti, Wackerly, and Boyett, 1979; Boyett 1979).

Value

A list with class "htest" containing the following components:

statistic

the value of the test statistic

p_value

the simulated p-value for the test

method

a character string describing the test

data.name

a character string give the name of the data

References

Agresti, A., Wackerly, D., & Boyett, J. M. (1979). Exact conditional tests for cross-classifications: approximation of attained significance levels. Psychometrika, 44(1), 75-83.

Boyett, J. M. (1979). Algorithm AS 144: Random r × c tables with given row and column totals. Journal of the Royal Statistical Society. Series C (Applied Statistics), 28(3), 329-332.

Examples

td_independence(decoy$weight, decimals = 2, reps = 2000)