replext_ts2_c3.2 {npboottprm}

Replicate and Extend Type I Error Rates for ANOVA with Varied Skewness and Standard Deviations

Description

The replext_ts2_c3.2 function is a modification of the replext_ts2_c1.1 function, designed to explore the impact of both skewness and different standard deviations in a three-sample ANOVA setting. This variant maintains skewness in all groups but changes the default standard deviations for the second and third groups. It contributes to a more comprehensive understanding of Type I error rates in the context of the study by Dwivedi et al. (2017), especially under conditions of non-normality.

Usage

replext_ts2_c3.2(
  M1 = 5,
  S1 = 1,
  M2 = 5,
  S2 = 2,
  M3 = 5,
  S3 = 4,
  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 2.

M3

Mean for the third group, default is 5.

S3

Standard deviation for the third group, default is 4.

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 extend those from replext_ts2_c1.1. This 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 specific conditions of varying skewness and standard deviations.

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, replext_ts2_c3.1

Examples

replext_ts2_c3.2(n1 = c(10), n2 = c(10), n3 = c(10), n_simulations = 1)