Append Input Parameters to Data Frame

Description

This internal function appends the input parameters and a unique run code to the data frame of simulation results. It creates a comprehensive data frame that includes both the results and the parameters used for the simulation, facilitating easier tracking and analysis of the simulation runs.

Usage

appendInputParams(df, input)

Arguments

Value

A data frame that combines the original simulation results with the input parameters used in the simulation. Additionally, a unique run code is generated and appended to each row for identification purposes.

Internal Bootstrap Sampling Function for F-tests

Description

This is an internal function used by nonparboot() to perform bootstrap resampling for F-tests. It is not intended to be called directly by the user.

Usage

bootstrap_f_sample(x_val, y_val, grp_val, grp_sizes, pre_calc)

Arguments

Value

A numeric vector of length 2 containing the bootstrapped test statistic and the effect size.

Internal Bootstrap Sampling Function for Paired T-tests

Description

This is an internal function used by nonparboot() to perform bootstrap resampling for paired t-tests.

Usage

bootstrap_pt_sample(x_val, y_val, grp_val, grp_sizes, pre_calc)

Arguments

Value

A numeric vector of length 2 containing the bootstrapped test statistic and mean difference.

Internal Bootstrap Sampling Function for T-tests

Description

This is an internal function used by nonparboot() to perform bootstrap resampling for independent t-tests.

Usage

bootstrap_t_sample(x_val, y_val, grp_val, grp_sizes, pre_calc)

Arguments

Value

A numeric vector of length 2 containing the bootstrapped test statistic and mean difference.

Simulated Data for F-test

Description

A simulated data set to experiment with nonparboot() with test = "F"

Usage

data_f

Format

data_f

A data frame with 15 rows and 2 columns:

x

A numeric variable

grp

A factor variable with group labels

Source

Simulated data

Simulated Data for F-test Using Identically Distributed Data

Description

A simulated data set to experiment with nonparboot() with test = "F" when all groups are drawn from identical distributions

Usage

data_f_id

Format

data_f_id

A data frame with 15 rows and 2 columns:

x

A numeric variable

grp

A factor variable with group labels

Source

Simulated data

Simulated Data for F-test with Missing Outcomes

Description

A simulated data set to experiment with nonparboot() with test = "F" and missing outcomes

Usage

data_f_mi

Format

data_f_mi

A data frame with 15 rows and 2 columns:

x

A numeric variable

grp

A factor variable with group labels

Source

Simulated data

Simulated Data for Paired T-test

Description

A simulated data set to experiment with nonparboot() with test = "pt"

Usage

data_pt

Format

data_pt

A data frame with 10 rows and 2 columns:

x

A numeric variable

y

A numeric variable

Source

Simulated data

Simulated Data for Paired T-test Using Identically Distributed Data

Description

A simulated data set to experiment with nonparboot() with test = "pt" when both variables are drawn from identical distributions

Usage

data_pt_id

Format

data_pt_id

A data frame with 10 rows and 2 columns:

x

A numeric variable

y

A numeric variable

Source

Simulated data

Simulated Data for Paired T-test with Missing Data

Description

A simulated data set to experiment with nonparboot() with test = "pt" and missing values

Usage

data_pt_mi

Format

data_pt_mi

A data frame with 10 rows and 2 columns:

x

A numeric variable

y

A numeric variable

Source

Simulated data

Simulated Data for Independent T-test

Description

A simulated data set to experiment with nonparboot() with test = "t"

Usage

data_t

Format

data_t

A data frame with 10 rows and 2 columns:

x

A numeric variable

grp

A factor variable with group labels

Source

Simulated data

Simulated Data for Independent T-test with Missing Outcomes

Description

A simulated data set to experiment with nonparboot() with test = "t" and missing outcome values

Usage

data_t_mi

Format

data_t_mi

A data frame with 10 rows and 2 columns:

x

A numeric variable

grp

A factor variable with group labels

Source

Simulated data

Generate a List of Available Cell Blocks

Description

This function creates and returns a named list of cell blocks, where each name corresponds to a descriptive label of the cell block, and the value is the function name associated with that cell block.

Usage

getCellBlocks()

Value

A named list where each name is a string describing a cell block (e.g., "T2 Cell Block 1.1") and each value is a string corresponding to the function name (e.g., "replext_t2_c1.1") that is associated with the simulation process for that particular cell block.

Generate UI Elements for Selected Cell Block

Description

This function generates a dynamic user interface (UI) for the Shiny app based on the selected cell block. It creates a list of Shiny UI elements, such as numeric inputs and text inputs, tailored to the requirements of the chosen cell block.

Usage

getUIParams(cellBlock)

Arguments

Value

A list of Shiny UI elements specific to the selected cell block. These UI elements include numeric inputs, text inputs, and other relevant controls required to capture user inputs for simulation parameters.

Nonparametric Bootstrap Test with Pooled Resampling for Small Sample Sizes

Description

This function performs a nonparametric bootstrap test with pooled resampling for small sample sizes, as described in Dwivedi et al. (2017). It supports t-tests (independent and paired) and F-tests (one-way ANOVA), with a user-specified number of bootstrap resamples.

Usage

nonparboot(
  data,
  x,
  y = NULL,
  grp = NULL,
  nboot,
  test = c("t", "pt", "F"),
  conf.level = 0.95,
  seed = NULL,
  na_rm = FALSE
)

Arguments

Value

A list with the following components:

• p.value: The p-value of the test.

• orig.stat: The test statistic calculated from the original data.

• ci.stat: The confidence interval for the test statistic from the bootstrap distribution.

• bootstrap.stat.dist: The distribution of the test statistic values from the bootstrap resamples.

• effect.size: The effect size (mean difference or eta-squared) calculated from the original data.

• ci.effect.size: The confidence interval for the effect size from the bootstrap distribution.

• bootstrap.effect.dist: The distribution of effect size values from the bootstrap resamples.

References

Dwivedi AK, Mallawaarachchi I, Alvarado LA (2017). "Analysis of small sample size studies using nonparametric bootstrap test with pooled resampling method." Statistics in Medicine, 36 (14), 2187-2205. https://doi.org/10.1002/sim.7263

Examples

# Example usage of nonparboot
np_res <- nonparboot(iris, x = "Sepal.Length", grp = "Species", nboot = 1000, test = "F")
print(np_res$p.value)

Shiny App for Nonparametric Bootstrap Tests with Pooled Resampling

Description

This function creates a Shiny app for performing nonparametric bootstrap tests with pooled resampling. The app allows you to conduct an independent t-test, a paired t-test, or a one-way ANOVA, depending on your input.

Usage

nonparboot_app()

Value

An interactive Shiny app.

References

Dwivedi AK, Mallawaarachchi I, Alvarado LA (2017). 'Analysis of small sample size studies using nonparametric bootstrap test with pooled resampling method.' Statistics in Medicine, 36 (14), 2187-2205. https://doi.org/10.1002/sim.7263

Examples

if(interactive()){
  nonparboot_app()
}

Remove NA values from vectors

Description

This function removes NA values from a list of vectors. If na_rm is TRUE, it removes all NA values from the input vectors. Otherwise, it returns the input vectors unchanged.

Usage

remove_na(na_rm, ...)

Arguments

Value

A list of vectors with NA values removed (if na_rm is TRUE), or the input vectors unchanged (if na_rm is FALSE).

Replext Simulation Shiny App

Description

This application attempts to replicate and extend the simulation results from the paper by Dwivedi et al. (2017). The application includes a user interface for selecting simulation parameters and a server logic to process the simulation and handle user interactions.

Usage

replext()

Details

The app's user interface consists of:

• A dropdown menu to select a cell block for the simulation, which is populated using the getCellBlocks function.

• Dynamic UI elements for inputting simulation parameters, generated based on the selected cell block.

• A button to run the simulation.

• A download button to export the simulation results.

The server logic of the app handles:

• Rendering the dynamic UI elements for simulation parameters.

• Observing the simulation run event and processing the simulation using the runSimulation function.

• Rendering a table to display the simulation results.

• Handling the data download request and exporting the results as a CSV file.

Value

A Shiny app object which can be run to start the application.

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.

Examples

if(interactive()){
  replext()
}

Replext Simulation Shiny App with Database Integration

Description

This application replicates and extends the simulation results from the paper by Dwivedi et al. (2017), now with added functionality to interact with a PostgreSQL database. The app includes a user interface for selecting simulation parameters and a server logic to process the simulation and handle user interactions, including saving and retrieving data from a database.

Usage

replext_pgsql(dbname, datatable, host, port, user, password)

Arguments

Details

The app's user interface consists of:

• A dropdown menu to select a cell block for the simulation, which is populated using the getCellBlocks function.

• Dynamic UI elements for inputting simulation parameters, generated based on the selected cell block.

• Buttons to run the simulation and submit the results to a PostgreSQL database.

• A table to display the simulation results and previously saved responses.

• A download button to export all responses as a CSV file.

The server logic of the app handles:

• Rendering the dynamic UI elements for simulation parameters.

• Observing the simulation run event and processing the simulation using the runSimulation function.

• Rendering a table to display the simulation results.

• Handling the submission of results and storing them in a PostgreSQL database.

• Loading existing responses from the database.

• Downloading responses as a CSV file.

Value

A Shiny app object which can be run to start the application.

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.

Examples

if (interactive()) {
  replext_pgsql(
    dbname = "your_db_name",
    datatable = "your_data_table",
    host = "localhost",
    port = 5432,
    user = "your_username",
    password = "your_password"
  )
}

Replicate and Extend Simulation Results from Table 2 Cell 1.1

Description

This function attempts to replicate and extend the simulation results from Table 2 cell block 1.1 of the paper by Dwivedi et al. (2017). The default parameter values aim to replicate the results from the paper, while modifying the parameter values allows for an extension of the results.

Usage

replext_t2_c1.1(
  M1 = 5,
  S1 = 1,
  M2 = 5,
  S2 = 1,
  Sk1 = NULL,
  Sk2 = NULL,
  n1 = c(3, 4, 5, 6, 7, 8, 9, 10, 15),
  n2 = c(3, 4, 5, 6, 7, 8, 9, 10, 15),
  n_simulations = 10000,
  nboot = 1000,
  conf.level = 0.95
)

Arguments

Value

A data frame with columns for each sample size pair (n1, n2) and the proportions of significant p-values for each test (ST, WT, NPBTT, WRST, PTT).

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.

Examples

replext_t2_c1.1(n1 = c(4), n2 = c(4), n_simulations = 1)

Replicate and Extend Simulation Results from Table 2 Cell 1.2

Description

This function is a wrapper around replext_t2_c1.1 and is specifically used for replicating and extending the simulation results from Table 2 cell block 1.2 of the paper by Dwivedi et al. (2017). It sets the standard deviation of the second group (S2) to 3 by default.

Usage

replext_t2_c1.2(
  M1 = 5,
  S1 = 1,
  M2 = 5,
  S2 = 3,
  Sk1 = NULL,
  Sk2 = NULL,
  n1 = c(3, 4, 5, 6, 7, 8, 9, 10, 15),
  n2 = c(3, 4, 5, 6, 7, 8, 9, 10, 15),
  n_simulations = 10000,
  nboot = 1000,
  conf.level = 0.95
)

Arguments

Value

A data frame with columns for each sample size pair (n1, n2) and the proportions of significant p-values for each test (ST, WT, NPBTT, WRST, PTT).

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_t2_c1.1

Examples

replext_t2_c1.2(n1 = c(4), n2 = c(4), n_simulations = 1)

Replicate and Extend Simulation Results from Table 2 Cell 2.1

Description

This function is intended to replicate and extend the simulation results from Table 2 cell block 2.1 in the paper by Dwivedi et al. (2017). It is designed for scenarios with the same skewed distribution and equal variance in both groups. The function acts as a wrapper around replext_t2_c1.1, applying specific skewness parameters as required for the cell.

Usage

replext_t2_c2.1(
  M1 = 5,
  S1 = 1,
  M2 = 5,
  S2 = 1,
  Sk1 = 0.8,
  Sk2 = 0.8,
  n1 = c(3, 4, 5, 6, 7, 8, 9, 10, 15),
  n2 = c(3, 4, 5, 6, 7, 8, 9, 10, 15),
  n_simulations = 10000,
  nboot = 1000,
  conf.level = 0.95
)

Arguments

Value

A data frame with columns for each sample size pair (n1, n2) and the proportions of significant p-values for each test (ST, WT, NPBTT, WRST, PTT).

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_t2_c1.1

Examples

replext_t2_c2.1(n1 = c(4), n2 = c(4), n_simulations = 1)

Replicate and Extend Simulation Results from Table 2 Cell 2.2

Description

This function is designed to replicate and extend the simulation results from Table 2 cell block 2.2 of the paper by Dwivedi et al. (2017). It handles scenarios with same skewed distribution but with different variances in the two groups. The function is a wrapper around replext_t2_c1.1, setting specific skewness and variance parameters as per the cell's requirements.

Usage

replext_t2_c2.2(
  M1 = 5,
  S1 = 1,
  M2 = 5,
  S2 = 3,
  Sk1 = 0.8,
  Sk2 = 0.8,
  n1 = c(3, 4, 5, 6, 7, 8, 9, 10, 15),
  n2 = c(3, 4, 5, 6, 7, 8, 9, 10, 15),
  n_simulations = 10000,
  nboot = 1000,
  conf.level = 0.95
)

Arguments

Value

A data frame with columns for each sample size pair (n1, n2) and the proportions of significant p-values for each test (ST, WT, NPBTT, WRST, PTT).

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_t2_c1.1

Examples

replext_t2_c2.2(n1 = c(4), n2 = c(4), n_simulations = 1)

Replicate and Extend Simulation Results from Table 2 Cell 3.1

Description

This function is designed to replicate and extend the simulation results from Table 2 cell block 3.1 of the paper by Dwivedi et al. (2017). It handles scenarios with different skewed distributions but equal variance in the two groups. The function is a wrapper around replext_t2_c1.1, setting specific skewness parameters as per the cell's requirements.

Usage

replext_t2_c3.1(
  M1 = 5,
  S1 = 1,
  M2 = 5,
  S2 = 1,
  Sk1 = 0.8,
  Sk2 = 1,
  n1 = c(3, 4, 5, 6, 7, 8, 9, 10, 15),
  n2 = c(3, 4, 5, 6, 7, 8, 9, 10, 15),
  n_simulations = 10000,
  nboot = 1000,
  conf.level = 0.95
)

Arguments

Value

A data frame with columns for each sample size pair (n1, n2) and the proportions of significant p-values for each test (ST, WT, NPBTT, WRST, PTT).

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_t2_c1.1

Examples

replext_t2_c3.1(n1 = c(4), n2 = c(4), n_simulations = 1)

Replicate and Extend Simulation Results from Table 2 Cell 3.2

Description

This function aims to replicate and extend the simulation results from Table 2 cell block 3.2 in the paper by Dwivedi et al. (2017). It is tailored for scenarios with different skewed distributions and unequal variance between the two groups. The function serves as a wrapper around replext_t2_c1.1, utilizing specific skewness parameters and variances as described in the cell.

Usage

replext_t2_c3.2(
  M1 = 5,
  S1 = 1,
  M2 = 5,
  S2 = 3,
  Sk1 = 0.8,
  Sk2 = 1,
  n1 = c(3, 4, 5, 6, 7, 8, 9, 10, 15),
  n2 = c(3, 4, 5, 6, 7, 8, 9, 10, 15),
  n_simulations = 10000,
  nboot = 1000,
  conf.level = 0.95
)

Arguments

Value

A data frame with columns for each sample size pair (n1, n2) and the proportions of significant p-values for each test (ST, WT, NPBTT, WRST, PTT).

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_t2_c1.1

Examples

replext_t2_c3.2(n1 = c(4), n2 = c(4), n_simulations = 1)

Replicate and Extend Simulation Results from Table 2 Cell 4.1

Description

This function is designed to replicate and extend the simulation results from Table 2 cell block 4.1 of the paper by Dwivedi et al. (2017). It addresses scenarios with unequal sample sizes but the same skewed distribution and equal variance in both groups. The function acts as a wrapper around replext_t2_c1.1, setting specific skewness parameters and sample sizes as per the cell's requirements.

Usage

replext_t2_c4.1(
  M1 = 5,
  S1 = 1,
  M2 = 5,
  S2 = 1,
  Sk1 = 0.8,
  Sk2 = 0.8,
  n1 = c(4, 3, 5, 4, 6, 4, 3, 4, 5, 6),
  n2 = c(2, 4, 3, 5, 3, 6, 7, 11, 10, 9),
  n_simulations = 10000,
  nboot = 1000,
  conf.level = 0.95
)

Arguments

Value

A data frame with columns for each sample size pair (n1, n2) and the proportions of significant p-values for each test (ST, WT, NPBTT, WRST, PTT).

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_t2_c1.1

Examples

replext_t2_c4.1(n1 = c(4), n2 = c(2), n_simulations = 1)

Replicate and Extend Simulation Results from Table 2 Cell 4.2

Description

This function is designed to replicate and extend the simulation results from Table 2 cell block 4.2 in the paper by Dwivedi et al. (2017). It is tailored for scenarios with unequal sample sizes, same skewed distribution, but different variances between the two groups. The function acts as a wrapper around replext_t2_c1.1, setting specific skewness parameters, variances, and sample sizes as described in the cell.

Usage

replext_t2_c4.2(
  M1 = 5,
  S1 = 1,
  M2 = 5,
  S2 = 3,
  Sk1 = 0.8,
  Sk2 = 0.8,
  n1 = c(4, 3, 5, 4, 6, 4, 3, 4, 5, 6),
  n2 = c(2, 4, 3, 5, 3, 6, 7, 11, 10, 9),
  n_simulations = 10000,
  nboot = 1000,
  conf.level = 0.95
)

Arguments

Value

A data frame with columns for each sample size pair (n1, n2) and the proportions of significant p-values for each test (ST, WT, NPBTT, WRST, PTT).

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_t2_c1.1

Examples

replext_t2_c4.2(n1 = c(4), n2 = c(2), n_simulations = 1)

Replicate and Extend Simulation Results for Statistical Power from Table 3 Cell 1.1

Description

This function is tailored to replicate and extend the simulation results for assessing statistical power from Table 3 cell block 1.1 in the paper by Dwivedi et al. (2017). It compares two groups with different means but equal variance and optional skewness. The function is a wrapper around replext_t2_c1.1, adapted for statistical power analysis.

Usage

replext_t3_c1.1(
  M1 = 5,
  S1 = 1,
  M2 = 7,
  S2 = 1,
  Sk1 = NULL,
  Sk2 = NULL,
  n1 = c(3, 4, 5, 6, 7, 8, 9, 10, 15, 25, 50, 100),
  n2 = c(3, 4, 5, 6, 7, 8, 9, 10, 15, 25, 50, 100),
  n_simulations = 10000,
  nboot = 1000,
  conf.level = 0.95
)

Arguments

Value

A data frame with columns for each sample size pair (n1, n2) and the proportions of significant p-values for each test (ST, WT, NPBTT, WRST, PTT), representing statistical power.

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_t2_c1.1

Examples

replext_t3_c1.1(n1 = c(10), n2 = c(10), n_simulations = 1)

Replicate and Extend Statistical Power Analysis from Table 3 Cell 1.2

Description

This function is designed to replicate and extend the statistical power analysis from Table 3 cell block 1.2 in the paper by Dwivedi et al. It focuses on scenarios with normal distribution having different means and unequal variances across two groups. It utilizes replext_t2_c1.1 for its calculations by setting specific means and standard deviations.

Usage

replext_t3_c1.2(
  M1 = 5,
  S1 = 1,
  M2 = 7,
  S2 = 3,
  Sk1 = NULL,
  Sk2 = NULL,
  n1 = c(3, 4, 5, 6, 7, 8, 9, 10, 15, 25, 50, 100),
  n2 = c(3, 4, 5, 6, 7, 8, 9, 10, 15, 25, 50, 100),
  n_simulations = 10000,
  nboot = 1000,
  conf.level = 0.95
)

Arguments

Value

A data frame with columns for each sample size pair (n1, n2) and the proportions of significant p-values for each test (ST, WT, NPBTT, WRST, PTT), representing the power analysis.

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_t2_c1.1

Examples

replext_t3_c1.2(n1 = c(10), n2 = c(10), n_simulations = 1)

Replicate and Extend Statistical Power Analysis from Table 3 Cell 2.1

Description

This function is geared towards replicating and extending the statistical power analysis from Table 3 cell block 2.1 of the paper by Dwivedi et al. (2017). It deals with scenarios involving skewed distributions with equal variance and different means in the two groups. It acts as a wrapper around replext_t2_c1.1, with specific adjustments for skewness parameters and means.

Usage

replext_t3_c2.1(
  M1 = 5,
  S1 = 1,
  M2 = 7,
  S2 = 1,
  Sk1 = 0.8,
  Sk2 = 0.8,
  n1 = c(3, 4, 5, 6, 7, 8, 9, 10, 15, 25, 50, 100),
  n2 = c(3, 4, 5, 6, 7, 8, 9, 10, 15, 25, 50, 100),
  n_simulations = 10000,
  nboot = 1000,
  conf.level = 0.95
)

Arguments

Value

A data frame with columns for each sample size pair (n1, n2) and the proportions of significant p-values for each test (ST, WT, NPBTT, WRST, PTT), reflecting the power analysis.

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_t2_c1.1

Examples

replext_t3_c2.1(n1 = c(10), n2 = c(10), n_simulations = 1)

Replicate and Extend Statistical Power Analysis from Table 3 Cell 2.2

Description

This function aims to replicate and extend the statistical power analysis from Table 3 cell block 2.2 in the paper by Dwivedi et al. (2017). It deals with scenarios involving skewed distributions with different variances and means in the two groups. It is a wrapper around replext_t2_c1.1, with adjusted means, variances, and skewness parameters.

Usage

replext_t3_c2.2(
  M1 = 5,
  S1 = 1,
  M2 = 7,
  S2 = 3,
  Sk1 = 0.8,
  Sk2 = 0.8,
  n1 = c(3, 4, 5, 6, 7, 8, 9, 10, 15, 25, 50, 100),
  n2 = c(3, 4, 5, 6, 7, 8, 9, 10, 15, 25, 50, 100),
  n_simulations = 10000,
  nboot = 1000,
  conf.level = 0.95
)

Arguments

Value

A data frame with columns for each sample size pair (n1, n2) and the proportions of significant p-values for each test (ST, WT, NPBTT, WRST, PTT), representing the power analysis.

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_t2_c1.1

Examples

replext_t3_c2.2(n1 = c(10), n2 = c(10), n_simulations = 1)

Replicate and Extend Statistical Power Analysis from Table 3 Cell 3.1

Description

This function is aimed at replicating and extending the statistical power analysis from Table 3 cell block 3.1 in the paper by Dwivedi et al. (2017). It addresses scenarios with different skewed distributions but equal variance and different means in the two groups. It utilizes replext_t2_c1.1 for calculations by setting specific skewness parameters.

Usage

replext_t3_c3.1(
  M1 = 5,
  S1 = 1,
  M2 = 7,
  S2 = 1,
  Sk1 = 0.8,
  Sk2 = 1,
  n1 = c(3, 4, 5, 6, 7, 8, 9, 10, 15, 25, 50, 100),
  n2 = c(3, 4, 5, 6, 7, 8, 9, 10, 15, 25, 50, 100),
  n_simulations = 10000,
  nboot = 1000,
  conf.level = 0.95
)

Arguments

Value

A data frame with columns for each sample size pair (n1, n2) and the proportions of significant p-values for each test (ST, WT, NPBTT, WRST, PTT), indicating the power analysis.

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_t2_c1.1

Examples

replext_t3_c3.1(n1 = c(10), n2 = c(10), n_simulations = 1)

Replicate and Extend Statistical Power Analysis from Table 3 Cell 3.2

Description

This function aims to replicate and extend the statistical power analysis from Table 3 cell block 3.2 in the paper by Dwivedi et al. (2017). It is designed for scenarios involving different skewed distributions with different variances and different means in the two groups. The function is a wrapper around replext_t2_c1.1, applying specific skewness parameters, means, and variances.

Usage

replext_t3_c3.2(
  M1 = 5,
  S1 = 1,
  M2 = 7,
  S2 = 3,
  Sk1 = 0.8,
  Sk2 = 1,
  n1 = c(3, 4, 5, 6, 7, 8, 9, 10, 15, 25, 50, 100),
  n2 = c(3, 4, 5, 6, 7, 8, 9, 10, 15, 25, 50, 100),
  n_simulations = 10000,
  nboot = 1000,
  conf.level = 0.95
)

Arguments

Value

A data frame with columns for each sample size pair (n1, n2) and the proportions of significant p-values for each test (ST, WT, NPBTT, WRST, PTT), indicating the power analysis.

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_t2_c1.1

Examples

replext_t3_c3.2(n1 = c(10), n2 = c(10), n_simulations = 1)

Replicate and Extend Statistical Power Analysis from Table 3 Cell 4.1

Description

This function is crafted to replicate and extend the statistical power analysis from Table 3 cell block 4.1 in the paper by Dwivedi et al. (2017). It focuses on scenarios with unequal sample sizes, same skewed distribution, and equal variance between the two groups. It utilizes replext_t2_c1.1 with adjusted skewness parameters, means, and specific sample sizes.

Usage

replext_t3_c4.1(
  M1 = 5,
  S1 = 1,
  M2 = 7,
  S2 = 1,
  Sk1 = 0.8,
  Sk2 = 0.8,
  n1 = c(4, 3, 5, 4, 6, 4),
  n2 = c(2, 4, 3, 5, 3, 6),
  n_simulations = 10000,
  nboot = 1000,
  conf.level = 0.95
)

Arguments

Value

A data frame with columns for each sample size pair (n1, n2) and the proportions of significant p-values for each test (ST, WT, NPBTT, WRST, PTT), reflecting the power analysis.

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_t2_c1.1

Examples

replext_t3_c4.1(n1 = c(4), n2 = c(3), n_simulations = 1)

Replicate and Extend Statistical Power Analysis from Table 3 Cell 4.2

Description

This function is designed to replicate and extend the statistical power analysis from Table 3 cell block 4.2 in the paper by Dwivedi et al. (2017). It addresses scenarios with unequal sample sizes, the same skewed distribution, but different variances between the two groups. The function acts as a wrapper around replext_t2_c1.1, applying specific skewness parameters, variances, and unequal sample sizes.

Usage

replext_t3_c4.2(
  M1 = 5,
  S1 = 1,
  M2 = 7,
  S2 = 3,
  Sk1 = 0.8,
  Sk2 = 0.8,
  n1 = c(4, 3, 5, 4, 6, 4),
  n2 = c(2, 4, 3, 5, 3, 6),
  n_simulations = 10000,
  nboot = 1000,
  conf.level = 0.95
)

Arguments

Value

A data frame with columns for each sample size pair (n1, n2) and the proportions of significant p-values for each test (ST, WT, NPBTT, WRST, PTT), representing the power analysis.

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_t2_c1.1

Examples

replext_t3_c4.2(n1 = c(6), n2 = c(3), n_simulations = 1)

Replicate and Extend Statistical Power Analysis from Table 3 Cell 5.1

Description

This function is designed to replicate and extend the statistical power analysis from Table 3 cell block 5.1 in the paper by Dwivedi et al. (2017). It focuses on scenarios with normal distribution and unequal sample sizes, using the same means and variances for both groups. It acts as a wrapper around replext_t2_c1.1, with modifications in means and sample sizes.

Usage

replext_t3_c5.1(
  M1 = 5,
  S1 = 1,
  M2 = 7,
  S2 = 1,
  Sk1 = NULL,
  Sk2 = NULL,
  n1 = c(3, 4, 5, 6),
  n2 = c(7, 11, 10, 9),
  n_simulations = 10000,
  nboot = 1000,
  conf.level = 0.95
)

Arguments

Value

A data frame with columns for each sample size pair (n1, n2) and the proportions of significant p-values for each test (ST, WT, NPBTT, WRST, PTT), representing the power analysis.

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_t2_c1.1

Examples

replext_t3_c5.1(n1 = c(4), n2 = c(11), n_simulations = 1)

Replicate and Extend Statistical Power Analysis from Table 3 Cell 5.2

Description

This function is tailored to replicate and extend the statistical power analysis from Table 3 cell block 5.2 in the paper by Dwivedi et al. (2017). It covers scenarios with normal distribution, unequal sample sizes, and different variances in the two groups. The function uses replext_t2_c1.1 for its calculations, with adjusted means, variances, and sample sizes.

Usage

replext_t3_c5.2(
  M1 = 5,
  S1 = 1,
  M2 = 7,
  S2 = 3,
  Sk1 = NULL,
  Sk2 = NULL,
  n1 = c(3, 4, 5, 6),
  n2 = c(7, 11, 10, 9),
  n_simulations = 10000,
  nboot = 1000,
  conf.level = 0.95
)

Arguments

Value

A data frame with columns for each sample size pair (n1, n2) and the proportions of significant p-values for each test (ST, WT, NPBTT, WRST, PTT), indicating the power analysis.

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_t2_c1.1

Examples

replext_t3_c5.2(n1 = c(4), n2 = c(11), n_simulations = 1)

Replicate and Extend Simulation Results from Table 4 Cell 1.1

Description

This function aims to replicate and extend the simulation results from Table 4 cell 1.1 of the paper by Dwivedi et al. (2017). The default parameters are set to replicate the results for the lognormal distribution scenarios as presented in the paper, while modifying the parameter values allows for an extension of these results.

Usage

replext_t4_c1.1(
  rdist = "rlnorm",
  par1_1 = 1,
  par2_1 = 0.6,
  par1_2 = 2,
  par2_2 = 1,
  n1 = c(5, 5, 10),
  n2 = c(5, 10, 10),
  n_simulations = 10000,
  nboot = 1000,
  conf.level = 0.95
)

Arguments

Value

A data frame with columns for each sample size pair (n1, n2) and the proportions of significant p-values for each test (ST, WT, NPBTT, WRST, PTTa, PTTe).

Note

When using rlnorm (lognormal distribution), 'par1' represents 'meanlog' (the mean of the logarithms) and 'par2' represents 'sdlog' (the standard deviation of the logarithms). For rpois (Poisson distribution), 'par1' is 'lambda' (the rate parameter). In the case of rchisq (Chi-squared distribution), 'par1' is 'df' (degrees of freedom) and 'par2' is 'ncp' (non-centrality parameter). Lastly, for rcauchy (Cauchy distribution), 'par1' is the 'location' parameter and 'par2' is the 'scale' parameter.

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.

Examples

replext_t4_c1.1(n1 = c(10), n2 = c(10),n_simulations = 1)

Replicate and Extend Simulation Results from Table 4 Cell 2.1

Description

This function is a specialized wrapper around 'replext_t4_c1.1' designed to replicate and extend the simulation results from Table 4 cell 2.1 of the paper by Dwivedi et al. (2017). The default parameters are modified to align with the Poisson distribution scenarios as described in the paper. Adjusting the parameters enables the extension of these results.

Usage

replext_t4_c2.1(
  rdist = "rpois",
  par1_1 = 5,
  par2_1 = NULL,
  par1_2 = 10,
  par2_2 = NULL,
  n1 = c(5, 5, 10),
  n2 = c(5, 10, 10),
  n_simulations = 10000,
  nboot = 1000,
  conf.level = 0.95
)

Arguments

Value

A data frame with columns for each sample size pair (n1, n2) and the proportions of significant p-values for each test (ST, WT, NPBTT, WRST, PTTa, PTTe).

Note

When using rlnorm (lognormal distribution), 'par1' represents 'meanlog' (the mean of the logarithms) and 'par2' represents 'sdlog' (the standard deviation of the logarithms). For rpois (Poisson distribution), 'par1' is 'lambda' (the rate parameter). In the case of rchisq (Chi-squared distribution), 'par1' is 'df' (degrees of freedom) and 'par2' is 'ncp' (non-centrality parameter). Lastly, for rcauchy (Cauchy distribution), 'par1' is the 'location' parameter and 'par2' is the 'scale' parameter.

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.

Examples

replext_t4_c2.1(n1 = c(10), n2 = c(10),n_simulations = 1)

Replicate and Extend Simulation Results from Table 4 Cell 3.1

Description

This function is a specialized wrapper around 'replext_t4_c1.1' intended to replicate and extend the simulation results from Table 4 cell 3.1 of the paper by Dwivedi et al. (2017). The default parameters are configured to match the Chi-squared distribution scenarios as detailed in the paper. Adjusting these parameters allows users to extend these results further.

Usage

replext_t4_c3.1(
  rdist = "rchisq",
  par1_1 = 3,
  par2_1 = 0,
  par1_2 = 6,
  par2_2 = 0,
  n1 = c(5, 5, 10),
  n2 = c(5, 10, 10),
  n_simulations = 10000,
  nboot = 1000,
  conf.level = 0.95
)

Arguments

Value

A data frame with columns for each sample size pair (n1, n2) and the proportions of significant p-values for each test (ST, WT, NPBTT, WRST, PTTa, PTTe).

Note

When using rlnorm (lognormal distribution), 'par1' represents 'meanlog' (the mean of the logarithms) and 'par2' represents 'sdlog' (the standard deviation of the logarithms). For rpois (Poisson distribution), 'par1' is 'lambda' (the rate parameter). In the case of rchisq (Chi-squared distribution), 'par1' is 'df' (degrees of freedom) and 'par2' is 'ncp' (non-centrality parameter). Lastly, for rcauchy (Cauchy distribution), 'par1' is the 'location' parameter and 'par2' is the 'scale' parameter.

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.

Examples

replext_t4_c3.1(n1 = c(10), n2 = c(10),n_simulations = 1)

Replicate and Extend Simulation Results from Table 4 Cell 4.1

Description

This function is a specialized wrapper around 'replext_t4_c1.1', tailored to replicate and extend the simulation results from Table 4 cell 4.1 of the paper by Dwivedi et al. (2017). It sets the default parameters to correspond with the lognormal distribution scenarios for this specific cell, allowing for both replication and extension of the results.

Usage

replext_t4_c4.1(
  rdist = "rlnorm",
  par1_1 = 1,
  par2_1 = 0.6,
  par1_2 = 3,
  par2_2 = 4,
  n1 = c(5, 5, 10),
  n2 = c(5, 10, 10),
  n_simulations = 10000,
  nboot = 1000,
  conf.level = 0.95
)

Arguments

Value

A data frame with columns for each sample size pair (n1, n2) and the proportions of significant p-values for each test (ST, WT, NPBTT, WRST, PTTa, PTTe).

Note

When using rlnorm (lognormal distribution), 'par1' represents 'meanlog' (the mean of the logarithms) and 'par2' represents 'sdlog' (the standard deviation of the logarithms). For rpois (Poisson distribution), 'par1' is 'lambda' (the rate parameter). In the case of rchisq (Chi-squared distribution), 'par1' is 'df' (degrees of freedom) and 'par2' is 'ncp' (non-centrality parameter). Lastly, for rcauchy (Cauchy distribution), 'par1' is the 'location' parameter and 'par2' is the 'scale' parameter.

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.

Examples

replext_t4_c4.1(n1 = c(10), n2 = c(10), n_simulations = 1)

Replicate and Extend Simulation Results from Table 4 Cell 5.1

Description

This function is a specialized version of 'replext_t4_c1.1', designed to replicate and extend the simulation results from Table 4 cell 5.1 of the paper by Dwivedi et al. (2017). It adjusts the default parameters to match the Cauchy distribution scenarios as described in this particular cell, facilitating both replication and extension of these results.

Usage

replext_t4_c5.1(
  rdist = "rcauchy",
  par1_1 = 5,
  par2_1 = 2,
  par1_2 = 10,
  par2_2 = 4,
  n1 = c(5, 5, 10),
  n2 = c(5, 10, 10),
  n_simulations = 10000,
  nboot = 1000,
  conf.level = 0.95
)

Arguments

Value

A data frame with columns for each sample size pair (n1, n2) and the proportions of significant p-values for each test (ST, WT, NPBTT, WRST, PTTa, PTTe).

Note

When using rlnorm (lognormal distribution), 'par1' represents 'meanlog' (the mean of the logarithms) and 'par2' represents 'sdlog' (the standard deviation of the logarithms). For rpois (Poisson distribution), 'par1' is 'lambda' (the rate parameter). In the case of rchisq (Chi-squared distribution), 'par1' is 'df' (degrees of freedom) and 'par2' 'ncp' (non-centrality parameter). Lastly, for rcauchy (Cauchy distribution), 'par1' is the 'location' parameter and 'par2' is the 'scale' parameter.

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.

Examples

replext_t4_c5.1(n1 = c(10), n2 = c(10), n_simulations = 1)

Replicate and Extend Simulation Results from Table 4 Cell 6.1

Description

This function, a specialized variant of 'replext_t4_c1.1', is designed to replicate and extend the simulation results from Table 4 cell 6.1 of the paper by Dwivedi et al. (2017). It employs different distributions for the two groups, using Chi-squared and Poisson distributions respectively, in line with the specific cell conditions.

Usage

replext_t4_c6.1(
  rdist = c("rchisq", "rpois"),
  par1_1 = 6,
  par2_1 = 0,
  par1_2 = 10,
  par2_2 = NULL,
  n1 = c(5, 5, 10),
  n2 = c(5, 10, 10),
  n_simulations = 10000,
  nboot = 1000,
  conf.level = 0.95
)

Arguments

Value

A data frame with columns for each sample size pair (n1, n2) and the proportions of significant p-values for each test (ST, WT, NPBTT, WRST, PTTa, PTTe).

Note

When using rlnorm (lognormal distribution), 'par1' represents 'meanlog' (the mean of the logarithms) and 'par2' represents 'sdlog' (the standard deviation of the logarithms). For rpois (Poisson distribution), 'par1' is 'lambda' (the rate parameter). In the case of rchisq (Chi-squared distribution), 'par1' is 'df' (degrees of freedom) and 'par2' is typically 0 as 'ncp' (non-centrality parameter) is not often used. Lastly, for rcauchy (Cauchy distribution), 'par1' is the 'location' parameter and 'par2' is the 'scale' parameter.

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.

Examples

replext_t4_c6.1(n1 = c(10), n2 = c(10), n_simulations = 1)

Replicate and Extend Simulation Results from Table 4 Cell 7.1

Description

This function is a customized version of 'replext_t4_c1.1', created to replicate and extend the simulation results from Table 4 cell 7.1 of the paper by Dwivedi et al. (2017). It is configured to use different distributions for each group, specifically a lognormal distribution for the first group and a Chi-squared distribution for the second group, aligning with the specific cell conditions.

Usage

replext_t4_c7.1(
  rdist = c("rlnorm", "rchisq"),
  par1_1 = 1,
  par2_1 = 0.6,
  par1_2 = 6,
  par2_2 = 0,
  n1 = c(5, 5, 10),
  n2 = c(5, 10, 10),
  n_simulations = 10000,
  nboot = 1000,
  conf.level = 0.95
)

Arguments

Value

A data frame with columns for each sample size pair (n1, n2) and the proportions of significant p-values for each test (ST, WT, NPBTT, WRST, PTTa, PTTe).

Note

When using rlnorm (lognormal distribution), 'par1' represents 'meanlog' (the mean of the logarithms) and 'par2' represents 'sdlog' (the standard deviation of the logarithms). For rpois (Poisson distribution), 'par1' is 'lambda' (the rate parameter). In the case of rchisq (Chi-squared distribution), 'par1' is 'df' (degrees of freedom) and 'par2' is typically 0 as 'ncp' (non-centrality parameter) is not often used. Lastly, for rcauchy (Cauchy distribution), 'par1' is the 'location' parameter and 'par2' is the 'scale' parameter.

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.

Examples

replext_t4_c7.1(n1 = c(10), n2 = c(10), n_simulations = 1)

Replicate and Extend Simulation Results for Paired Distributions

Description

This function aims to replicate and extend the simulation results from Table 5 cell 1.1 of the paper by Dwivedi et al. (2017) for paired distributions with the option to use either normal or skew normal distributions. It allows specifying means, standard deviations, skewness, and correlation for two paired distributions.

Usage

replext_t5_c1.1(
  M1 = 5,
  S1 = 1,
  M2 = 5,
  S2 = 1,
  Sk1 = 0,
  Sk2 = 0,
  correl = 0.8,
  n = c(3, 4, 5, 6, 7, 8, 9, 10, 15, 25),
  n_simulations = 10000,
  nboot = 1000,
  conf.level = 0.95
)

Arguments

Value

A data frame with columns for each sample size and the proportions of significant p-values for each test (PT, NPBTT, WRST, PTT).

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.

Examples

replext_t5_c1.1(n = c(10), n_simulations = 1)

Replicate and Extend Simulation Results for Paired Distributions with Different Variances

Description

This function is a wrapper around 'replext_t5_c1.1' and is specifically aimed at replicating and extending simulation results from Table 5 cell 1.2 of the paper by Dwivedi et al. (2017). It is tailored for paired distributions with the option to use either normal or skew normal distributions, differing in standard deviations between the two groups.

Usage

replext_t5_c1.2(
  M1 = 5,
  S1 = 1,
  M2 = 5,
  S2 = 3,
  Sk1 = 0,
  Sk2 = 0,
  correl = 0.8,
  n = c(3, 4, 5, 6, 7, 8, 9, 10, 15, 25),
  n_simulations = 10000,
  nboot = 1000,
  conf.level = 0.95
)

Arguments

Value

A data frame with columns for each sample size and the proportions of significant p-values for each test (PT, NPBTT, WRST, PTT), similar to 'replext_t5_c1.1' but with differing standard deviations for the groups.

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.

Examples

replext_t5_c1.2(n = c(10), n_simulations = 1)

Replicate and Extend Simulation Results for Paired Distributions with Skewness

Description

This function, serving as a wrapper around 'replext_t5_c1.1', is designed to replicate and extend the simulation results from Table 5 cell 1.3 of the paper by Dwivedi et al. (2017). It focuses on paired distributions featuring both normal and skew normal distributions, with specified skewness parameters for each group.

Usage

replext_t5_c1.3(
  M1 = 5,
  S1 = 1,
  M2 = 5,
  S2 = 1,
  Sk1 = 0.5,
  Sk2 = 0.5,
  correl = 0.8,
  n = c(3, 4, 5, 6, 7, 8, 9, 10, 15, 25),
  n_simulations = 10000,
  nboot = 1000,
  conf.level = 0.95
)

Arguments

Value

A data frame with columns for each sample size and the proportions of significant p-values for each test (PT, NPBTT, WRST, PTT), similar to 'replext_t5_c1.1' but with skewness parameters for the groups.

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.

Examples

replext_t5_c1.3(n = c(10), n_simulations = 1)

Replicate and Extend Simulation Results for Paired Distributions with Skewness and Different Variances

Description

This function is a wrapper around 'replext_t5_c1.1', targeting the replication and extension of simulation results from Table 5 cell 2.1 of the paper by Dwivedi et al. (2017). It focuses on paired distributions that combine normal and skew normal behaviors with different standard deviations and specified skewness parameters for each group.

Usage

replext_t5_c2.1(
  M1 = 5,
  S1 = 1,
  M2 = 5,
  S2 = 3,
  Sk1 = 0.5,
  Sk2 = 0.5,
  correl = 0.8,
  n = c(3, 4, 5, 6, 7, 8, 9, 10, 15, 25),
  n_simulations = 10000,
  nboot = 1000,
  conf.level = 0.95
)

Arguments

Value

A data frame with columns for each sample size and the proportions of significant p-values for each test (PT, NPBTT, WRST, PTT), similar to 'replext_t5_c1.1' but with variations in standard deviations and skewness.

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.

Examples

replext_t5_c2.1(n = c(10), n_simulations = 1)

Replicate and Extend Simulation Results for Paired Distributions with Different Skewness Levels

Description

This function is a specialized version of 'replext_t5_c1.1', tailored to replicate and extend the simulation results from Table 5 cell 2.2 of the paper by Dwivedi et al. (2017). It is designed for paired distributions that exhibit both normal and skew normal characteristics, with different skewness parameters for each group while maintaining the same means and standard deviations.

Usage

replext_t5_c2.2(
  M1 = 5,
  S1 = 1,
  M2 = 5,
  S2 = 1,
  Sk1 = 0.2,
  Sk2 = 0.8,
  correl = 0.8,
  n = c(3, 4, 5, 6, 7, 8, 9, 10, 15, 25),
  n_simulations = 10000,
  nboot = 1000,
  conf.level = 0.95
)

Arguments

Value

A data frame with columns for each sample size and the proportions of significant p-values for each test (PT, NPBTT, WRST, PTT), with a focus on differing skewness levels between the two groups.

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.

Examples

replext_t5_c2.2(n = c(10), n_simulations = 1)

Replicate and Extend Simulation Results for Paired Distributions with Varied Skewness and Standard Deviations

Description

replext_t5_c2.3 is a wrapper function around replext_t5_c1.1, specifically designed to replicate and extend the simulation results from Table 5 cell 2.3 of the paper by Dwivedi et al. (2017). It focuses on paired distributions that exhibit skew normal characteristics with differing skewness parameters and standard deviations for each group.

Usage

replext_t5_c2.3(
  M1 = 5,
  S1 = 1,
  M2 = 5,
  S2 = 3,
  Sk1 = 0.2,
  Sk2 = 0.8,
  correl = 0.8,
  n = c(3, 4, 5, 6, 7, 8, 9, 10, 15, 25),
  n_simulations = 10000,
  nboot = 1000,
  conf.level = 0.95
)

Arguments

Value

A data frame with columns for each sample size and the proportions of significant p-values for each test (PT, NPBTT, WRST, PTT), focusing on variations in skewness and standard deviations between the groups.

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.

Examples

replext_t5_c2.3(n = c(10), n_simulations = 1)

Replicate and Extend Statistical Power Simulation Results for Paired Distributions

Description

This function is a wrapper around 'replext_t5_c1.1' and is specifically aimed at replicating and extending statistical power simulation results from Table 6 cell 1.1 of the paper by Dwivedi et al. (2017).

Usage

replext_t6_c1.1(
  M1 = 5,
  S1 = 1,
  M2 = 7,
  S2 = 1,
  Sk1 = 0,
  Sk2 = 0,
  correl = 0.8,
  n = c(3, 4, 5, 6, 7, 8, 9, 10, 15, 25, 50, 100),
  n_simulations = 10000,
  nboot = 1000,
  conf.level = 0.95
)

Arguments

Value

A data frame with columns for each sample size and the proportions of significant p-values for each test (PT, NPBTT, WRST, PTT), similar to 'replext_t5_c1.1' but with differing standard deviations for the groups.

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.

Examples

replext_t6_c1.1(n = c(10), n_simulations = 1)

Replicate and Extend Statistical Power Simulation Results for Paired Distributions with Different Variances

Description

This function is a wrapper around 'replext_t5_c1.1' and is specifically aimed at replicating and extending statistical power simulation results from Table 6 cell 1.2 of the paper by Dwivedi et al. (2017).

Usage

replext_t6_c1.2(
  M1 = 5,
  S1 = 1,
  M2 = 7,
  S2 = 3,
  Sk1 = 0,
  Sk2 = 0,
  correl = 0.8,
  n = c(3, 4, 5, 6, 7, 8, 9, 10, 15, 25, 50, 100),
  n_simulations = 10000,
  nboot = 1000,
  conf.level = 0.95
)

Arguments

Value

A data frame with columns for each sample size and the proportions of significant p-values for each test (PT, NPBTT, WRST, PTT), similar to 'replext_t5_c1.1' but with differing standard deviations for the groups.

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.

Examples

replext_t6_c1.2(n = c(10), n_simulations = 1)

Replicate and Extend Statistical Power Simulation Results for Paired Distributions with Skewness

Description

This function, serving as a wrapper around 'replext_t5_c1.1', is designed to replicate and extend the statistical power simulation results from Table 6 cell 1.3 of the paper by Dwivedi et al. (2017).

Usage

replext_t6_c1.3(
  M1 = 5,
  S1 = 1,
  M2 = 7,
  S2 = 1,
  Sk1 = 0.5,
  Sk2 = 0.5,
  correl = 0.8,
  n = c(3, 4, 5, 6, 7, 8, 9, 10, 15, 25, 50, 100),
  n_simulations = 10000,
  nboot = 1000,
  conf.level = 0.95
)

Arguments

Value

A data frame with columns for each sample size and the proportions of significant p-values for each test (PT, NPBTT, WRST, PTT), similar to 'replext_t5_c1.1' but with skewness parameters for the groups.

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.

Examples

replext_t6_c1.3(n = c(10), n_simulations = 1)

Replicate and Extend Statistical Power Simulation Results for Paired Distributions with Skewness and Different Variances

Description

This function is a wrapper around 'replext_t5_c1.1', targeting the replication and extension of statistical power simulation results from Table 6 cell 2.1 of the paper by Dwivedi et al. (2017).

Usage

replext_t6_c2.1(
  M1 = 5,
  S1 = 1,
  M2 = 7,
  S2 = 3,
  Sk1 = 0.5,
  Sk2 = 0.5,
  correl = 0.8,
  n = c(3, 4, 5, 6, 7, 8, 9, 10, 15, 25, 50, 100),
  n_simulations = 10000,
  nboot = 1000,
  conf.level = 0.95
)

Arguments

Value

A data frame with columns for each sample size and the proportions of significant p-values for each test (PT, NPBTT, WRST, PTT), similar to 'replext_t5_c1.1' but with variations in standard deviations and skewness.

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.

Examples

replext_t6_c2.1(n = c(10), n_simulations = 1)

Replicate and Extend Statistical Power Simulation Results for Paired Distributions with Different Skewness Levels

Description

This function is a specialized version of 'replext_t5_c1.1', tailored to replicate and extend the statistical power simulation results from Table 6 cell 2.2 of the paper by Dwivedi et al. (2017).

Usage

replext_t6_c2.2(
  M1 = 5,
  S1 = 1,
  M2 = 7,
  S2 = 1,
  Sk1 = 0.2,
  Sk2 = 0.8,
  correl = 0.8,
  n = c(3, 4, 5, 6, 7, 8, 9, 10, 15, 25, 50, 100),
  n_simulations = 10000,
  nboot = 1000,
  conf.level = 0.95
)

Arguments

Value

A data frame with columns for each sample size and the proportions of significant p-values for each test (PT, NPBTT, WRST, PTT), with a focus on differing skewness levels between the two groups.

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.

Examples

replext_t6_c2.2(n = c(10), n_simulations = 1)

Replicate and Extend Statistical Power Simulation Results for Paired Distributions with Varied Skewness and Standard Deviations

Description

replext_t6_c2.3 is a wrapper function around replext_t5_c1.1, specifically designed to replicate and extend the statistical power simulation results from Table 6 cell 2.3 of the paper by Dwivedi et al. (2017).

Usage

replext_t6_c2.3(
  M1 = 5,
  S1 = 1,
  M2 = 7,
  S2 = 3,
  Sk1 = 0.2,
  Sk2 = 0.8,
  correl = 0.8,
  n = c(3, 4, 5, 6, 7, 8, 9, 10, 15, 25, 50, 100),
  n_simulations = 10000,
  nboot = 1000,
  conf.level = 0.95
)

Arguments

Value

A data frame with columns for each sample size and the proportions of significant p-values for each test (PT, NPBTT, WRST, PTT), focusing on variations in skewness and standard deviations between the groups.

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.

Examples

replext_t6_c2.3(n = c(10), n_simulations = 1)

Replicate and Extend Simulation Results from Table S1 Cell 1.1

Description

This function is a specialized wrapper around 'replext_t4_c1.1' designed to replicate and extend the type I error simulation results from Table S1 cell 1.1 of the paper by Dwivedi et al. (2017).

Usage

replext_ts1_c1.1(
  rdist = "rlnorm",
  par1_1 = 1,
  par2_1 = 0.6,
  par1_2 = 1,
  par2_2 = 0.6,
  n1 = c(5, 5, 10),
  n2 = c(5, 10, 10),
  n_simulations = 10000,
  nboot = 1000,
  conf.level = 0.95
)

Arguments

Value

A data frame with columns for each sample size pair (n1, n2) and the proportions of significant p-values for each test (ST, WT, NPBTT, WRST, PTTa, PTTe).

Note

When using rlnorm (lognormal distribution), 'par1' represents 'meanlog' (the mean of the logarithms) and 'par2' represents 'sdlog' (the standard deviation of the logarithms). For rpois (Poisson distribution), 'par1' is 'lambda' (the rate parameter). In the case of rchisq (Chi-squared distribution), 'par1' is 'df' (degrees of freedom) and 'par2' is 'ncp' (non-centrality parameter). Lastly, for rcauchy (Cauchy distribution), 'par1' is the 'location' parameter and 'par2' is the 'scale' parameter.

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.

Examples

replext_ts1_c1.1(n1 = c(10), n2 = c(10),n_simulations = 1)

Replicate and Extend Simulation Results from Table S1 Cell 2.1

Description

This function is a specialized wrapper around 'replext_t4_c1.1' designed to replicate and extend the type I error simulation results from Table S1 cell 2.1 of the paper by Dwivedi et al. (2017). The default parameters are modified to align with the Poisson distribution scenarios as described in the paper. Adjusting the parameters enables the extension of these results.

Usage

replext_ts1_c2.1(
  rdist = "rpois",
  par1_1 = 5,
  par2_1 = NULL,
  par1_2 = 5,
  par2_2 = NULL,
  n1 = c(5, 5, 10),
  n2 = c(5, 10, 10),
  n_simulations = 10000,
  nboot = 1000,
  conf.level = 0.95
)

Arguments

Value

A data frame with columns for each sample size pair (n1, n2) and the proportions of significant p-values for each test (ST, WT, NPBTT, WRST, PTTa, PTTe).

Note

When using rlnorm (lognormal distribution), 'par1' represents 'meanlog' (the mean of the logarithms) and 'par2' represents 'sdlog' (the standard deviation of the logarithms). For rpois (Poisson distribution), 'par1' is 'lambda' (the rate parameter). In the case of rchisq (Chi-squared distribution), 'par1' is 'df' (degrees of freedom) and 'par2' is 'ncp' (non-centrality parameter). Lastly, for rcauchy (Cauchy distribution), 'par1' is the 'location' parameter and 'par2' is the 'scale' parameter.

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.

Examples

replext_ts1_c2.1(n1 = c(10), n2 = c(10),n_simulations = 1)

Replicate and Extend Simulation Results from Table S1 Cell 3.1

Description

This function is a specialized wrapper around 'replext_t4_c1.1' intended to replicate and extend the type I error simulation results from Table S1 cell 3.1 of the paper by Dwivedi et al. (2017). The default parameters are configured to match the Chi-squared distribution scenarios as detailed in the paper. Adjusting these parameters allows users to extend these results further.

Usage

replext_ts1_c3.1(
  rdist = "rchisq",
  par1_1 = 3,
  par2_1 = 0,
  par1_2 = 3,
  par2_2 = 0,
  n1 = c(5, 5, 10),
  n2 = c(5, 10, 10),
  n_simulations = 10000,
  nboot = 1000,
  conf.level = 0.95
)

Arguments

Value

A data frame with columns for each sample size pair (n1, n2) and the proportions of significant p-values for each test (ST, WT, NPBTT, WRST, PTTa, PTTe).

Note

When using rlnorm (lognormal distribution), 'par1' represents 'meanlog' (the mean of the logarithms) and 'par2' represents 'sdlog' (the standard deviation of the logarithms). For rpois (Poisson distribution), 'par1' is 'lambda' (the rate parameter). In the case of rchisq (Chi-squared distribution), 'par1' is 'df' (degrees of freedom) and 'par2' is 'ncp' (non-centrality parameter). Lastly, for rcauchy (Cauchy distribution), 'par1' is the 'location' parameter and 'par2' is the 'scale' parameter.

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.

Examples

replext_ts1_c3.1(n1 = c(10), n2 = c(10),n_simulations = 1)

Replicate and Extend Type I Error Rates for ANOVA in a Three-Sample Setting

Description

This function aims to replicate and extend the Type I error rate analysis for ANOVA (Analysis of Variance) from the supplemental tables of the paper by Dwivedi et al. (2017). It allows for the simulation of three-sample scenarios with the option to use either normal or skew normal distributions, and performs various statistical tests to assess the Type I error rates.

Usage

replext_ts2_c1.1(
  M1 = 5,
  S1 = 1,
  M2 = 5,
  S2 = 1,
  M3 = 5,
  S3 = 1,
  Sk1 = NULL,
  Sk2 = NULL,
  Sk3 = NULL,
  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

Value

A data frame with 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).

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.

Examples

replext_ts2_c1.1(n1 = c(10), n2 = c(10), n3 = c(10), n_simulations = 1)

Replicate and Extend Type I Error Rates for ANOVA in a Different Setting

Description

This wrapper function is designed to reproduce or extend the Type I error rate analysis for ANOVA (Analysis of Variance) in a different setting as compared to replext_ts2_c1.1. It utilizes different default values for the standard deviations of the second and third groups, allowing for a different simulation setup. It is part of the analysis extending the supplemental tables of the paper by Dwivedi et al. (2017).

Usage

replext_ts2_c1.2(
  M1 = 5,
  S1 = 1,
  M2 = 5,
  S2 = 2,
  M3 = 5,
  S3 = 4,
  Sk1 = NULL,
  Sk2 = NULL,
  Sk3 = NULL,
  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

Value

A data frame similar to replext_ts2_c1.1 with 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), but with the modified default parameters.

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_c1.2(n1 = c(10), n2 = c(10), n3 = c(10), n_simulations = 1)

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

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)

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

Description

The replext_ts2_c2.2 function extends the replext_ts2_c1.1 function by incorporating skewness in data distributions and utilizing different default values for standard deviations in the second and third groups. This function is specifically designed to investigate the influence of skewness combined with varying standard deviations on the Type I error rates in ANOVA (Analysis of Variance). It aligns with the broader analytical goals set in the study by Dwivedi et al. (2017), offering insights into the behavior of statistical tests under these conditions.

Usage

replext_ts2_c2.2(
  M1 = 5,
  S1 = 1,
  M2 = 5,
  S2 = 2,
  M3 = 5,
  S3 = 4,
  Sk1 = 0.8,
  Sk2 = 0.8,
  Sk3 = 0.8,
  n1 = c(2, 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

Value

A data frame with results that extend those from replext_ts2_c1.1, focusing on the impact of skewness and varying standard deviations. 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 these specific conditions.

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_c2.1

Examples

replext_ts2_c2.2(n1 = c(10), n2 = c(10), n3 = c(10), n_simulations = 1)

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

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)

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

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)

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

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)

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

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)

Replicate and Extend Statistical Power Analysis for ANOVA in a Three-Sample Setting

Description

This function aims to replicate and extend the statistical power analysis for ANOVA (Analysis of Variance) from the supplemental tables of the paper by Dwivedi et al. (2017). It allows for the simulation of three-sample scenarios with the option to use either normal or skew normal distributions, and performs various statistical tests to assess the statistical power. The function is a wrapper around replext_ts2_c1.1.

Usage

replext_ts3_c1.1(
  M1 = 5,
  S1 = 1,
  M2 = 6,
  S2 = 1,
  M3 = 7,
  S3 = 1,
  Sk1 = NULL,
  Sk2 = NULL,
  Sk3 = NULL,
  n1 = c(2, 3, 4, 5, 6, 7, 8, 9, 10, 15, 25, 50, 100),
  n2 = c(2, 3, 4, 5, 6, 7, 8, 9, 10, 15, 25, 50, 100),
  n3 = c(2, 3, 4, 5, 6, 7, 8, 9, 10, 15, 25, 50, 100),
  n_simulations = 10000,
  nboot = 1000,
  conf.level = 0.95
)

Arguments

Value

A data frame with 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).

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.

Examples

replext_ts3_c1.1(n1 = c(10), n2 = c(10), n3 = c(10), n_simulations = 1)

Replicate and Extend Statistical Power Analysis for ANOVA

Description

This function is a wrapper around replext_ts2_c1.1. The function is designed to reproduce or extend the statistical power analysis for ANOVA (Analysis of Variance) from Dwivedi et al. (2017) supplemental table 3, cell 1.2.

Usage

replext_ts3_c1.2(
  M1 = 5,
  S1 = 1,
  M2 = 6,
  S2 = 2,
  M3 = 7,
  S3 = 4,
  Sk1 = NULL,
  Sk2 = NULL,
  Sk3 = NULL,
  n1 = c(2, 3, 4, 5, 6, 7, 8, 9, 10, 15, 25, 50, 100),
  n2 = c(2, 3, 4, 5, 6, 7, 8, 9, 10, 15, 25, 50, 100),
  n3 = c(2, 3, 4, 5, 6, 7, 8, 9, 10, 15, 25, 50, 100),
  n_simulations = 10000,
  nboot = 1000,
  conf.level = 0.95
)

Arguments

Value

A data frame with 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).

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_ts3_c1.2(n1 = c(10), n2 = c(10), n3 = c(10), n_simulations = 1)

Replicate and Extend Statistical Power Analysis for ANOVA with Skewness

Description

This function is a wrapper around replext_ts2_c1.1. The function is designed to reproduce or extend the statistical power analysis for ANOVA (Analysis of Variance) from Dwivedi et al. (2017) supplemental table 3, cell 2.1.

Usage

replext_ts3_c2.1(
  M1 = 5,
  S1 = 1,
  M2 = 6,
  S2 = 1,
  M3 = 7,
  S3 = 1,
  Sk1 = 0.8,
  Sk2 = 0.8,
  Sk3 = 0.8,
  n1 = c(2, 3, 4, 5, 6, 7, 8, 9, 10, 15, 25, 50, 100),
  n2 = c(2, 3, 4, 5, 6, 7, 8, 9, 10, 15, 25, 50, 100),
  n3 = c(2, 3, 4, 5, 6, 7, 8, 9, 10, 15, 25, 50, 100),
  n_simulations = 10000,
  nboot = 1000,
  conf.level = 0.95
)

Arguments

Value

A data frame with 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).

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_ts3_c2.1(n1 = c(10), n2 = c(10), n3 = c(10), n_simulations = 1)

Replicate and Extend Statistical Power Analysis for ANOVA with Skewness and Varied Standard Deviations

Description

This function is a wrapper around replext_ts2_c1.1. The function is designed to reproduce or extend the statistical power analysis for ANOVA (Analysis of Variance) from Dwivedi et al. (2017) supplemental table 3, cell 2.2.

Usage

replext_ts3_c2.2(
  M1 = 5,
  S1 = 1,
  M2 = 6,
  S2 = 2,
  M3 = 7,
  S3 = 4,
  Sk1 = 0.8,
  Sk2 = 0.8,
  Sk3 = 0.8,
  n1 = c(2, 3, 4, 5, 6, 7, 8, 9, 10, 15, 25, 50, 100),
  n2 = c(2, 3, 4, 5, 6, 7, 8, 9, 10, 15, 25, 50, 100),
  n3 = c(2, 3, 4, 5, 6, 7, 8, 9, 10, 15, 25, 50, 100),
  n_simulations = 10000,
  nboot = 1000,
  conf.level = 0.95
)

Arguments

Value

A data frame with 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).

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_ts3_c2.2(n1 = c(10), n2 = c(10), n3 = c(10), n_simulations = 1)

Replicate and Extend Statistical Power Analysis for ANOVA with Diverse Skewness Parameters

Description

This function is a wrapper around replext_ts2_c1.1. The function is designed to reproduce or extend the statistical power analysis for ANOVA (Analysis of Variance) from Dwivedi et al. (2017) supplemental table 3, cell 3.1.

Usage

replext_ts3_c3.1(
  M1 = 5,
  S1 = 1,
  M2 = 6,
  S2 = 1,
  M3 = 7,
  S3 = 1,
  Sk1 = 0.8,
  Sk2 = 0.8,
  Sk3 = 1,
  n1 = c(2, 3, 4, 5, 6, 7, 8, 9, 10, 15, 25, 50, 100),
  n2 = c(2, 3, 4, 5, 6, 7, 8, 9, 10, 15, 25, 50, 100),
  n3 = c(2, 3, 4, 5, 6, 7, 8, 9, 10, 15, 25, 50, 100),
  n_simulations = 10000,
  nboot = 1000,
  conf.level = 0.95
)

Arguments

Value

A data frame with 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).

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_ts3_c3.1(n1 = c(10), n2 = c(10), n3 = c(10), n_simulations = 1)

Replicate and Extend Statistical Power Analysis for ANOVA with Varied Skewness and Standard Deviations

Description

This function is a wrapper around replext_ts2_c1.1. The function is designed to reproduce or extend the statistical power analysis for ANOVA (Analysis of Variance) from Dwivedi et al. (2017) supplemental table 3, cell 3.2.

Usage

replext_ts3_c3.2(
  M1 = 5,
  S1 = 1,
  M2 = 6,
  S2 = 2,
  M3 = 7,
  S3 = 4,
  Sk1 = 0.8,
  Sk2 = 0.8,
  Sk3 = 1,
  n1 = c(2, 3, 4, 5, 6, 7, 8, 9, 10, 15, 25, 50, 100),
  n2 = c(2, 3, 4, 5, 6, 7, 8, 9, 10, 15, 25, 50, 100),
  n3 = c(2, 3, 4, 5, 6, 7, 8, 9, 10, 15, 25, 50, 100),
  n_simulations = 10000,
  nboot = 1000,
  conf.level = 0.95
)

Arguments

Value

A data frame with 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).

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_ts3_c3.2(n1 = c(10), n2 = c(10), n3 = c(10), n_simulations = 1)

Replicate and Extend Statistical Power Analysis for ANOVA with Skewness in Specific Sample Size Combinations

Description

This function is a wrapper around replext_ts2_c1.1. The function is designed to reproduce or extend the statistical power analysis for ANOVA (Analysis of Variance) from Dwivedi et al. (2017) supplemental table 3, cell 4.1.

Usage

replext_ts3_c4.1(
  M1 = 5,
  S1 = 1,
  M2 = 6,
  S2 = 1,
  M3 = 7,
  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

Value

A data frame with 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).

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_ts3_c4.1(n1 = c(10), n2 = c(10), n3 = c(10), n_simulations = 1)

Replicate and Extend Statistical Power Analysis for ANOVA with Specific Sample Size Combinations

Description

This function is a wrapper around replext_ts2_c1.1. The function is designed to reproduce or extend the statistical power analysis for ANOVA (Analysis of Variance) from Dwivedi et al. (2017) supplemental table 3, cell 4.2.

Usage

replext_ts3_c4.2(
  M1 = 5,
  S1 = 1,
  M2 = 6,
  S2 = 2,
  M3 = 7,
  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

Value

A data frame with 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).

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_ts3_c4.2(n1 = c(10), n2 = c(10), n3 = c(10), n_simulations = 1)

Execute Simulation Based on User Inputs

Description

This internal function manages the simulation process in a Shiny app environment. It dynamically selects the appropriate simulation function based on the selected cell block and passes user inputs to this function. The function also handles the setting of a random number seed, if provided, to ensure reproducibility of results.

Usage

runSimulation(input)

Arguments

Value

The result of the simulation function that corresponds to the selected cell block. This result is typically a data frame containing the outcomes of the simulation.

Convert Comma-Separated String to Character Vector

Description

This internal function takes a string of comma-separated values and converts it into a character vector. It is used to process user inputs from the Shiny app's UI, particularly when these inputs need to be retained as character data.

Usage

text_to_char_vector(text_input)

Arguments

Value

A character vector converted from the comma-separated string. If the input is an empty string or consists only of whitespace, returns an empty character vector.