Table 2.
Summary of tests for publication bias
| Adjusted effect | Test for publication bias | ||
|---|---|---|---|
| All cognitive measures: k = 38, Δuc = -0.13 (p = 0.011) | |||
| 1. | Rank correlationa | r = -.24 (p = .036) | |
| 2. | Peter et al.’s (2006) regression test | Δ = 0.03 (p = .604) | B = -13.43 (p = .009) |
| 3. | PET/PEESEb | Δ = 0.04 (p = .513) | B = -3.29 (p = .002) |
| 4. | Modified PET/ PEESEc | Δ = 0.03 (p = .604) | B = -3.36 (p = .009) |
| 5. | Selection modelsd | Δ = 0.03 (p = .419) | χ2 = 29.53 (p < .001) |
| 6. | Modified selection modelsc | Δ = 0.01 (p = .702) | χ2 = 26.48 (p < .001) |
| 7. | puniform*e | Δ = -0.02 (p = .678) | Lpb = 15.49 (p < .001) |
| Anagram tests: k = 12, Δuc = -0.06 (p = 0.184) | |||
| 1. | Rank correlationa | r = -.27 (p = .250) | |
| 2. | Peter et al.’s (2006) regression test | Δ = -0.01 (p = .900) | B = -9.28 (p = .095) |
| 3. | PET/PEESEb | Δ = 0.00 (p = .983) | B = -2.31 (p = .069) |
| 4. | Modified PET/PEESEc | Δ = -0.01 (p = .900) | B = -2.32 (p = .095) |
| 5. | Selection modelsd | Δ = -0.01 (p = .785) | χ2 = 2.76 (p = .331) |
| 6. | Modified selection modelsc | Δ = -0.02 (p = .678) | χ2 = 2.49 (p = .114) |
| 7. | puniform*e | Δ = -0.04 (p = .422) | Lpb = 0.13 (p = .936) |
| Reasoning tests: k = 17, Δuc = -0.34 (p = .016) | |||
| 1. | Rank correlationa | r = -.43 (p = .017) | |
| 2. | Peter et al.’s (2006) regression test | Δ = 0.17 (p = .324) | B = -23.44 (p = .021) |
| 3. | PET/PEESEb | Δ = 0.14 (p = .333) | B = -5.06 (p = .009) |
| 4. | Modified PET/PEESEc | Δ = 0.17 (p = .324) | B = -5.86 (p = .021) |
| 5. | Selection modelsd | Δ = 0.08 (p = .175) | χ2 = 29.50 (p = .033) |
| 6. | Modified selection modelsc | Δ = 0.05 (p = .444) | χ2 = 23.92 (p < .001) |
| 7. | puniform*e | Δ = 0.03 (p = .704) | Lpb = 6.78 (p = .034) |
| Knowledge tests: k = 10, Δuc = -0.04 (p = .598) | |||
| 1. | Rank correlationa | r = .29 (p = .291) | |
| 2. | Peter et al.’s (2006) regression test | Δ = -0.21 (p = .200) | B = 19.80 (p = 252) |
| 3. | PET/PEESEb | Δ = -0.17 (p = .242) | B = 3.72 (p = .308) |
| 4. | Modified PET/PEESEc | Δ = -0.21 (p = .200) | B = 4.95 (p = .252) |
| 5. | Selection modelsd | Δ = -0.02 (p = .813) | χ2 = 0.80 (p = .371) |
| 6. | Modified selection modelsc | Δ = -0.02 (p = .806) | χ2 = 0.79 (p = .375) |
| 7. | puniform*e | Δ = -0.01 (p = .850) | Lpb = 0.86 (p = .649) |
Note. All analyses are based on the within-sample averaged sample sizes (see Supplementary Online Material, Section C)
Δ indicates pooled effect adjusted for publication bias, Δuc indicates unadjusted pooled effect, k number of independent effect sizes, B unstandardized regression weight, χ2 test statistic for publication bias with 1 degree of freedom, Lpb test statistic for publication bias
aBegg and Madzumdar (1994)
bStanley (2017)
cSubstitutes the sampling variances of d with a function of the sample size (Pustejovsky & Rodner, 2019)
dVevea and Woods (2005)
evan Aert and van Assen (2020)