replext_ts2_c1.1 {npboottprm}

Replicate and Extend Type I Error Rates for ANOVA in a Three-Sample Setting

Description

This function aims to replicate and extend the Type I error rate analysis for ANOVA (Analysis of Variance) from the supplemental tables of the paper by Dwivedi et al. (2017). It allows for the simulation of three-sample scenarios with the option to use either normal or skew normal distributions, and performs various statistical tests to assess the Type I error rates.

Usage

replext_ts2_c1.1(
  M1 = 5,
  S1 = 1,
  M2 = 5,
  S2 = 1,
  M3 = 5,
  S3 = 1,
  Sk1 = NULL,
  Sk2 = NULL,
  Sk3 = NULL,
  n1 = c(2, 3, 4, 5, 6, 7, 8, 9, 10, 15),
  n2 = c(2, 3, 4, 5, 6, 7, 8, 9, 10, 15),
  n3 = c(2, 3, 4, 5, 6, 7, 8, 9, 10, 15),
  n_simulations = 10000,
  nboot = 1000,
  conf.level = 0.95
)

Arguments

M1

Mean for the first group, default is 5.

S1

Standard deviation for the first group, default is 1.

M2

Mean for the second group, default is 5.

S2

Standard deviation for the second group, default is 1.

M3

Mean for the third group, default is 5.

S3

Standard deviation for the third group, default is 1.

Sk1

Skewness parameter for the first group, NULL implies normal distribution.

Sk2

Skewness parameter for the second group, NULL implies normal distribution.

Sk3

Skewness parameter for the third group, NULL implies normal distribution.

n1

Vector of sample sizes for the first group.

n2

Vector of sample sizes for the second group.

n3

Vector of sample sizes for the third group, must be the same length as n1 and n2.

n_simulations

Number of simulations to run, default is 10,000.

nboot

Number of bootstrap samples for the nonparametric bootstrap test, default is 1000.

conf.level

Confidence level for calculating p-value thresholds, default is 0.95.

Value

A data frame with columns for each sample size combination (n1, n2, n3) and the proportions of significant p-values for each test (ANOVA, Kruskal-Wallis, Nonparametric Bootstrap F-test, Permutation F-test).

References

Dwivedi AK, Mallawaarachchi I, Alvarado LA. Analysis of small sample size studies using nonparametric bootstrap test with pooled resampling method. Stat Med. 2017 Jun 30;36(14):2187-2205. doi: 10.1002/sim.7263. Epub 2017 Mar 9. PMID: 28276584.

Examples

replext_ts2_c1.1(n1 = c(10), n2 = c(10), n3 = c(10), n_simulations = 1)