td_simulate {terminaldigits}

Monte Carlo simulations for independence of terminal digits

Description

The td_simulate function performs Monte Carlo simulations to assess type I errors and power for tests of independence of terminal digits for various truncated continuous distributions.

Usage

td_simulate(
  distribution,
  duplicates = 0,
  n,
  parameter_1,
  parameter_2 = NULL,
  decimals,
  significance = 0.05,
  reps = 500,
  simulations = 300,
  tolerance = 64 * .Machine$double.eps
)

Arguments

distribution

A string specifying the distribution from which to draw data for simulations. Options include "normal", "uniform", and "exponential".

duplicates

A number between 0 and 1 specifying the proportion of data to be comprised by duplicates. The default value is 0. This is appropriate for testing type I errors. For testing power, a value greater than 0 should be entered. For example, entering '0.05' would ensure that for each simulation, 5% of the data would be comprised by duplicates.

n

An integer specifying the number of observes to draw from the distribution.

parameter_1

A numeric value specifying the mean for the normal distribution, the lower bound of interval for the uniform distribution, or the rate for the exponential distribution.

parameter_2

A numeric value specifying the standard deviation for the normal distribution or the upper bound of the interval for the uniform distribution.

decimals

an integer specifying the number of decimals (including 0) to which the values drawn from the distribution should be truncated.

significance

a number between 0 and 1 defining the level for statistical significance. The default is set to 0.05.

reps

an integer specifying the number of Monte Carlo simulations to implement under the null for each draw. The default is set to 500 but this is only appropriate for initial exploration.

simulations

an integer specifying the number of Monte Carlo simulations to perform, i.e. the number of draws from the specified distribution to be tested. The default is set to 300 but this is only appropriate for initial exploration.

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 for the null hypothesis are implemented for contingency tables with fixed margins using algorithm ASA 144 (Agresti, Wackerly, and Boyett, 1979; Boyett 1979).

Value

A list containing the following components:

method

method employed

distribution

the distribution

Chisq

proportion of p-values less than or equal to defined significance level for Pearson's chi-squared test of independence

G2

proportion of p-values less than or equal to defined significance level for log-likelihood ratio test of independence

FT

proportion of p-values less than or equal to defined significance level for Freeman-Tukey test of independence

RMS

proportion of p-values less than or equal to defined significance level for root-mean-squared test of independence

O

proportion of p-values less than or equal to defined significance level for occupancy test of independence

AF

proportion of p-values less than or equal to defined significance level for average frequency test of independence

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_simulate(distribution = "normal",
n = 50,
parameter_1 = 100,
parameter_2 = 1,
decimals = 1,
reps = 100,
simulations = 100)