How many missing studies would drag the effect down to trivial

Rosenthal's count asks how many nulls would make the result non-significant, which ties the answer to the sample size rather than to the effect. Orwin's asks how many would push the pooled effect below whatever magnitude the reader considers trivial, and it lets the missing studies carry a non-zero effect of their own – both of which make the number mean something substantive rather than procedural.

Usage

Maorw(d_obs, d_crit, d_filldraw, k)

Arguments

d_obs

Observed pooled effect.

d_crit

Effect size considered trivial.

d_filldraw

Mean effect assumed for the unretrieved studies.

k

Number of studies in the meta-analysis.

Value

List with Nfs, Nfs_ceiling, d_obs, d_crit, d_fill, k.

Details

Formula: N_fs = k (d_obs - d_crit)/(d_crit - d_fill) – Orwin (1983) eq. (2).

References

Orwin, R. G. (1983). Journal of Educational Statistics 8(2):157-159. doi:10.2307/1164923 .

Examples

Maorw(d_obs = 0.5, d_crit = 0.2, d_filldraw = 0, k = 10)$Nfs   # 10 (0.5 - 0.2) / 0.2 = 15
#> [1] 15