replext_ts2_c4.1 {npboottprm}

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

Description

The replext_ts2_c4.1 function is a specialized version of replext_ts2_c1.1, designed to analyze Type I error rates in ANOVA settings with skewness in data distributions and tailored combinations of sample sizes for each group. This function explores the impact of non-normality (skewness) and varying group sizes, thereby extending the analysis framework of the study by Dwivedi et al. (2017).

Usage

replext_ts2_c4.1(
  M1 = 5,
  S1 = 1,
  M2 = 5,
  S2 = 1,
  M3 = 5,
  S3 = 1,
  Sk1 = 0.8,
  Sk2 = 0.8,
  Sk3 = 0.8,
  n1 = c(2, 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 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 specific sample sizes for the first group.

n2

Vector of specific sample sizes for the second group.

n3

Vector of specific sample sizes for the third group, not necessarily 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 extending those from replext_ts2_c1.1, focusing on the combined effects of skewness and specific sample size configurations. The data frame includes columns for each unique 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) in these particular scenarios.

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_c4.1(n1 = c(10), n2 = c(10), n3 = c(10), n_simulations = 1)