| Type: | Package |
| Title: | Rosenthal's Fail Safe Number and Related Functions |
| Version: | 0.4 |
| Date: | 2024-12-10 |
| Author: | Michail Tsagris [aut, cre], Constantinos Frangos [aut], Christos Frangos [ctb] |
| Maintainer: | Michail Tsagris <mtsagris@uoc.gr> |
| Depends: | R (≥ 3.6.0) |
| Imports: | graphics, grDevices, Rfast, stats |
| Suggests: | Rfast2 |
| Description: | Estimation of Rosenthal's fail safe number including confidence intervals. The relevant papers are the following. Konstantinos C. Fragkos, Michail Tsagris and Christos C. Frangos (2014). "Publication Bias in Meta-Analysis: Confidence Intervals for Rosenthal's Fail-Safe Number". International Scholarly Research Notices, Volume 2014. <doi:10.1155/2014/825383>. Konstantinos C. Fragkos, Michail Tsagris and Christos C. Frangos (2017). "Exploring the distribution for the estimator of Rosenthal's fail-safe number of unpublished studies in meta-analysis". Communications in Statistics-Theory and Methods, 46(11):5672–5684. <doi:10.1080/03610926.2015.1109664>. |
| License: | GPL-2 | GPL-3 [expanded from: GPL (≥ 2)] |
| NeedsCompilation: | no |
| Packaged: | 2024-12-10 10:21:13 UTC; mtsag |
| Repository: | CRAN |
| Date/Publication: | 2024-12-10 18:50:02 UTC |
Rosenthal's Fail Safe Number and Related Functions
Description
Estimation of Rosenthal's fail safe number including confidence intervals. We have kept the same name functions as in the supplementary materials of the two relevant papers.
Details
| Package: | fsn |
| Type: | Package |
| Version: | 0.4 |
| Date: | 2024-12-10 |
| License: | GPL-2 |
Maintainers
Michail Tsagris <mtsagris@uoc.gr>
Author(s)
Michail Tsagris mtsagris@uoc.gr, Constantinos Frangos kfragkos@outlook.com and Christos Frangos cfragos@teiath.gr.
References
Konstantinos C. Fragkos, Michail Tsagris and Christos C. Frangos (2017). Exploring the distribution for the estimator of Rosenthal's "fail-safe" number of unpublished studies in meta-analysis. Communications in Statistics-Theory and Methods, 46(11):5672–5684.
Konstantinos C. Fragkos, Michail Tsagris and Christos C. Frangos (2014). Publication Bias in Meta-Analysis: Confidence Intervals for Rosenthal's Fail-Safe Number. International Scholarly Research Notices, Volume 2014.
Rosenthal R. (1979). The file drawer problem and tolerance for null results. Psychological Bulletin, 86, 638–641.
Confidence intervals for Rosenthal's fail-safe number assuming a half normal distribution with a fixed number of studies
Description
Confidence intervals for Rosenthal's fail-safe number assuming a half normal distribution with a fixed number of studies.
Usage
halfnorm.fixednr.ci(stat, se, alpha = 0.05, type = "dist", B = 1000)
Arguments
stat |
A vector with the statistics. |
se |
A vector with the standard errors of the stat. |
alpha |
The significance level, set to 0.05 by default. |
type |
The type of confidence intervals to construct. Based on distributional assumptions ("dist"), based on the method of moments ("mom"), using non-parametric bootstrap ("boot") or all of these three ("all"). |
B |
Number of bootstrap samples to generate. |
Details
The function computes confidence intervals assuming a half normal distribution assuming that the number of studies is fixed and estimating the variance either via MLE, moments or bootstrap as described in Fragkos, Tsagris & Frangos (2014).
Value
A list including:
Nr |
Rosenthal's fail safe number. |
variance |
The variance of Rosenthal's fail safe number. |
ci |
The (1-alpha)% confidence interval for the true Rosenthal's fail safe number. |
Author(s)
Michail Tsagris and Constantinos Frangos
R implementation and documentation: Michail Tsagris mtsagris@uoc.gr and Constantinos Frangos kfragkos@outlook.com.
References
Konstantinos C. Fragkos, Michail Tsagris and Christos C. Frangos (2014). Publication Bias in Meta-Analysis: Confidence Intervals for Rosenthal's Fail-Safe Number. International Scholarly Research Notices, Volume 2014.
See Also
halfnorm.randomnr.ci, den.plot, rosenthal,
convergence.rate
Examples
stat <- rnorm(30, 3, 0.2)
se <- rchisq(30, 1)
halfnorm.fixednr.ci(stat, se)
Confidence intervals for Rosenthal's fail-safe number assuming a half normal distribution with a random number of studies
Description
Confidence intervals for Rosenthal's fail-safe number assuming a half normal distribution with a random number of studies.
Usage
halfnorm.randomnr.ci(stat, se, alpha = 0.05, type = "dist")
Arguments
stat |
A vector with the statistics. |
se |
A vector with the standard errors of the stat. |
alpha |
The significance level, set to 0.05 by default. |
type |
The type of confidence intervals to construct. Based on distributional assumptions ("dist") or based on the method of moments ("mom") or both "both". |
Details
The function computes confidence intervals assuming a half normal distribution assuming that the number of studies is random and estimating the variance either via MLE or moments or bootstrap as described in Fragkos, Tsagris & Frangos (2014).
Value
A list including:
Nr |
Rosenthal's fail safe number. |
variance |
The variance of Rosenthal's fail safe number. |
ci |
The (1-alpha)% confidence interval for the true Rosenthal's fail safe number. |
Author(s)
Michail Tsagris and Constantinos Frangos
R implementation and documentation: Michail Tsagris mtsagris@uoc.gr and Constantinos Frangos kfragkos@outlook.com.
References
Konstantinos C. Fragkos, Michail Tsagris and Christos C. Frangos (2014). Publication Bias in Meta-Analysis: Confidence Intervals for Rosenthal's Fail-Safe Number. International Scholarly Research Notices, Volume 2014.
See Also
halfnorm.fixednr.ci den.plot, rosenthal,
convergence.rate
Examples
stat <- rnorm(30, 3, 0.2)
se <- rchisq(30, 1)
halfnorm.fixednr.ci(stat, se)
Density of Nr assuming a truncated normal or a folded normal
Description
Density of Nr assuming a truncated normal or a folded normal.
Usage
truncnorm.nr.density(nr, k, alpha = 0.05)
foldnorm.nr.density(nr, k, alpha = 0.05)
Arguments
nr |
The value of Nr, which must be positive aparently. |
k |
The number of studies. |
alpha |
The significance level, set to 0.05 by default. |
Details
The function calculates the density of Nr assuming either a truncated normal (Equation (9)) or a folded normal (Equation (15)) in Fragkos, Tsagris & Frangos (2017).
Value
The density value of Nr assuming either a truncated normal or a folded normal.
Author(s)
Michail Tsagris, Constantinos Frangos, and Christos Frangos.
R implementation and documentation: Michail Tsagris mtsagris@uoc.gr, Constantinos Frangos kfragkos@outlook.com and Christos Frangos cfragos@teiath.gr.
References
Konstantinos C. Fragkos, Michail Tsagris and Christos C. Frangos (2017). Exploring the distribution for the estimator of Rosenthal's "fail-safe" number of unpublished studies in meta-analysis. Communications in Statistics-Theory and Methods, 46(11):5672–5684.
See Also
den.plot, rosenthal, convergence.rate
Examples
truncnorm.nr.density(100, k = 30)
foldnorm.nr.density(100, k = 30)
Numerical estimation of the convergence rate of Rosenthal's fail-safe number Nr
Description
Numerical estimation of the convergence rate of Rosenthal's fail-safe number Nr.
Usage
convergence.rate(k = seq( 10, 5000, by = 10), R = 1000, alpha = 0.05)
Arguments
k |
A grid of number of studies to consider. |
R |
The number of repeats for each number of studies. |
alpha |
The significance level, set to 0.05 by default. |
Details
This function replicates the Figures 6 and 5 in Fragkos, Tsagris and Frangos (2017).
Value
Two plots, the absolute relative error of Nr agains the number of studies and the logarithm of absolute relative error against the logarithm of the number of studies and the coefficients of the regression model of the second plot. The second coefficient is the numerically estimated convergence rate of Nr.
Author(s)
Michail Tsagris and Constantinos Frangos
R implementation and documentation: Michail Tsagris mtsagris@uoc.gr and Constantinos Frangos kfragkos@outlook.com.
References
Konstantinos C. Fragkos, Michail Tsagris and Christos C. Frangos (2017). Exploring the distribution for the estimator of Rosenthal's "fail-safe" number of unpublished studies in meta-analysis. Communications in Statistics-Theory and Methods, 46(11):5672–5684.
See Also
den.plot, truncnorm.nr.density, rosenthal
Examples
convergence.rate(k = seq( 50, 500, by = 50), R = 1000, alpha = 0.05)
Plot of both densities of Nr
Description
Plot of both densities of Nr.
Usage
den.plot(k, max_k = 20 * k, dist = "truncnorm")
Arguments
k |
The number of studies. |
max_k |
The maximum number for which the densities are calcualted. It is set to
|
dist |
The distribution to plot, either "truncnorm", "foldnorm" or "both". |
Details
The function plot the density of Nr assuming a truncated normal (Equation (9)) or a folded normal (Equation (15)) in Fragkos, Tsagris and Frangos (2017).
Value
The density plot of Nr assuming either a truncated normal or a folded normal.
Author(s)
Michail Tsagris and Constantinos Frangos
R implementation and documentation: Michail Tsagris mtsagris@uoc.gr and Constantinos Frangos kfragkos@outlook.com.
References
Konstantinos C. Fragkos, Michail Tsagris and Christos C. Frangos (2017). Exploring the distribution for the estimator of Rosenthal's "fail-safe" number of unpublished studies in meta-analysis. Communications in Statistics-Theory and Methods, 46(11):5672–5684.
See Also
truncnorm.nr.density, rosenthal
Examples
den.plot(30, dist = "both")
Rosenthal's fail-safe number Nr
Description
Rosenthal's fail-safe number Nr.
Usage
rosenthal(stat, se, alpha = 0.05)
Arguments
stat |
A vector with the statistics (be careful: not the test statistics). |
se |
A vector with the standard errors of the stat. |
alpha |
The significance level, set to 0.05 by default. |
Details
The function Calculates of Rosenthal's fail-safe number Nr.
Value
A vector with two values, Rosenthal's fail-safe number Nr and the rule of
thumb, 5k + 10, where k denotes the number of studies.
Author(s)
Michail Tsagris and Constantinos Frangos
R implementation and documentation: Michail Tsagris mtsagris@uoc.gr and Constantinos Frangos kfragkos@outlook.com.
References
Konstantinos C. Fragkos, Michail Tsagris and Christos C. Frangos (2017). Exploring the distribution for the estimator of Rosenthal's "fail-safe" number of unpublished studies in meta-analysis. Communications in Statistics-Theory and Methods, 46(11):5672–5684.
Rosenthal R. (1979). The file drawer problem and tolerance for null results. Psychological Bulletin, 86, 638–641.
See Also
truncnorm.nr.density, den.plot, convergence.rate
Examples
stat <- rnorm(30, 3, 0.2)
se <- rchisq(30, 1)
rosenthal(stat, se)