replext_ts2_c3.1 {npboottprm}

Replicate and Extend Type I Error Rates for ANOVA with Diverse Skewness Parameters

Description

The replext_ts2_c3.1 function is designed to replicate and extend Type I error rate analysis for ANOVA (Analysis of Variance) with a specific focus on the impact of different skewness parameters across the three groups. This function is a variation of replext_ts2_c1.1, providing an opportunity to explore how varying degrees of skewness in each group affect the statistical inferences in ANOVA, as part of the extended analysis in the context of the study by Dwivedi et al. (2017).

Usage

replext_ts2_c3.1(
  M1 = 5,
  S1 = 1,
  M2 = 5,
  S2 = 1,
  M3 = 5,
  S3 = 1,
  Sk1 = 0.8,
  Sk2 = 0.8,
  Sk3 = 1,
  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 1.

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 that build upon those from replext_ts2_c1.1. 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 the specified skewness conditions for each group.

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_c3.1(n1 = c(10), n2 = c(10), n3 = c(10), n_simulations = 1)