replext_ts2_c2.1 {npboottprm}

Replicate and Extend Type I Error Rates for ANOVA with Skewness

Description

This function, replext_ts2_c2.1, extends the replext_ts2_c1.1 function to specifically simulate scenarios under skew normal distributions. It is tailored to explore the impact of skewness on the Type I error rates in ANOVA (Analysis of Variance), contributing to the comprehensive analysis in the context of the study by Dwivedi et al. (2017). The function allows for simulations under the assumption of skewness in all three groups.

Usage

replext_ts2_c2.1(
  M1 = 5,
  S1 = 1,
  M2 = 5,
  S2 = 1,
  M3 = 5,
  S3 = 1,
  Sk1 = 0.8,
  Sk2 = 0.8,
  Sk3 = 0.8,
  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, default is 0.8.

Sk2

Skewness parameter for the second group, default is 0.8.

Sk3

Skewness parameter for the third group, default is 0.8.

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 results similar to those from replext_ts2_c1.1, but with the added dimension of skewness. The data frame includes 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) under skew normal distribution.

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.

See Also

replext_ts2_c1.1

Examples

replext_ts2_c2.1(n1 = c(10), n2 = c(10), n3 = c(10), n_simulations = 1)