How many missing null studies would sink a significant result

The file-drawer count answers a question about publication bias with a number, which is its appeal and also its flaw: it assumes the missing studies average exactly zero effect, which no plausible selection mechanism produces. Read it as an upper bound on fragility, never as evidence that bias is absent.

Usage

Mafsn(z_scores, alpha = 0.05)

Arguments

z_scores: One-tailed z statistics of the included studies.
alpha: One-tailed level.

Value

List with Nfs, z_combined, z_alpha, k.

Details

Formula: N_fs = (sum z_i)^2 / z_alpha^2 - k with z_alpha the one-tailed critical value – Rosenthal (1979) eq. (2).

References

Rosenthal, R. (1979). Psychological Bulletin 86(3):638-641. doi:10.1037/0033-2909.86.3.638 .

Examples

V <- c(1, 2, 3, 4, 5, 6, 7, 8)
Mafsn(V)
#> $Nfs
#> [1] 471.0165
#> 
#> $z_combined
#> [1] 12.72792
#> 
#> $z_alpha
#> [1] 1.644854
#> 
#> $k
#> [1] 8
#> 
#> $method
#> [1] "Rosenthal's fail-safe N"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"