metafor (version 0.5-4)

fsn: Fail-Safe N

Description

Function to calculate the fail-safe N.

Usage

fsn(yi, vi, sei, data=NULL, type="Rosenthal", alpha=.05, 
    target=NULL, digits=4, subset=NULL)

Arguments

yi

a vector with the observed effect sizes or outcomes.

vi

a vector with the corresponding sampling variances.

sei

a vector with the corresponding standard errors. (note: only one of the two, vi or sei, needs to be specified)

data

an optional data frame containing the variables given to the arguments above.

type

a vector indicating the method to use for the calculation of the fail-safe N. Possible options are "Rosenthal", "Orwin", or "Rosenberg". See below for more details.

alpha

target alpha level to use for the Rosenthal and Rosenberg methods (.05 by default).

target

target average effect size to use for the Orwin method. If NULL, then the target average effect size will be equal to the observed average effect size divided by 2.

digits

an integer specifying the number of decimal places to which the printed results should be rounded (default is 4).

subset

an optional vector indicating the subset of studies that should be used for the calculation. This can be a logical vector of length $k$ or a numeric vector indicating the indices of the observations to include.

Value

• An object of class c("fsn"). The object is a list containing the following components:
• type
  the method used.
• fsnum
  the calculated fail-safe N.
• alpha
  the target alpha level.
• pval
  the p-value of the observed results. NA for the Orwin method.
• meanes
  the average effect size of the observed results. NA for the Rosenthal method.
• target
  the target effect size. NA for the Rosenthal and Rosenberg methods.
• The results are formated and printed with the print.fsn function.

Details

The Rosenthal method calculates the number of studies averaging null results that would have to be added to the given set of observed outcomes to reduce the combined significance level (p-value) to a target alpha level (e.g., .05). The calculation is based on Stouffer's method to combine p-values and is described in Rosenthal (1979). The Orwin method calculates the number of studies averaging null results that would have to be added to the given set of observed outcomes to reduce the (unweighted) average effect size to a target (unweighted) average effect size. The method is described in Orwin (1983). The Rosenberg method calculates the number of studies averaging null results that would have to be added to the given set of observed outcomes to reduce significance level (p-value) of the (weighted) average effect size (based on a fixed-effects model) to a target alpha level (e.g., .05). The method is described in Rosenberg (2005).

References

Rosenthal, R. (1979) The "file drawer problem" and tolerance for null results. Psychological Bulletin, 86, 638--641. Orwin, R. G. (1983) A fail-safe N for effect size in meta-analysis. Journal of Educational Statistics, 8, 157--159. Rosenberg, M. S. (2005) The file-drawer problem revisited: A general weighted method for calculating fail-safe numbers in meta-analysis. Evolution, 59, 464--468.

See Also

ranktest, trimfill

Examples

### load BCG vaccine data
data(dat.bcg)

### calculate log risk ratios and corresponding sampling variances
dat <- escalc(measure="RR", ai=tpos, bi=tneg, ci=cpos, di=cneg, data=dat.bcg)
dat.bcg$yi <- dat$yi
dat.bcg$vi <- dat$vi

fsn(yi, vi, data=dat.bcg)
fsn(yi, vi, data=dat.bcg, type="Orwin")
fsn(yi, vi, data=dat.bcg, type="Rosenberg")