replext_ts2_c4.2 {npboottprm}

Replicate and Extend Type I Error Rates for ANOVA with Specific Sample Size Combinations

Description

replext_ts2_c4.2 is designed to explore the impact of specific combinations of sample sizes on the Type I error rates in ANOVA (Analysis of Variance) under conditions of skewness and varying standard deviations. This function extends replext_ts2_c1.1 by utilizing unique sample size combinations along with altered default standard deviations and skewness parameters. It is part of a broader analysis aimed at understanding statistical behavior in skewed and heteroscedastic scenarios, aligning with the research context provided by Dwivedi et al. (2017).

Usage

replext_ts2_c4.2(
  M1 = 5,
  S1 = 1,
  M2 = 5,
  S2 = 2,
  M3 = 5,
  S3 = 4,
  Sk1 = 0.8,
  Sk2 = 0.8,
  Sk3 = 0.8,
  n1 = c(2, 2, 2, 3, 2, 2, 3, 2, 3, 2),
  n2 = c(2, 3, 3, 4, 2, 3, 4, 2, 4, 2),
  n3 = c(3, 3, 4, 3, 6, 6, 4, 7, 5, 8),
  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 0.8.

n1

Vector of sample sizes for the first group, with specific combinations.

n2

Vector of sample sizes for the second group, with specific combinations.

n3

Vector of sample sizes for the third group, with specific combinations.

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 extending those from replext_ts2_c1.1. This data frame provides insights into the Type I error rates for each test (ANOVA, Kruskal-Wallis, Nonparametric Bootstrap F-test, Permutation F-test) under the conditions of skewness, varying sample sizes, and varying standrd 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

Examples

replext_ts2_c4.2(n1 = c(10), n2 = c(10), n3 = c(10), n_simulations = 1)