Begg and Mazumdar's rank correlation test for publication bias

The effects are standardised so that under the null they are independent of their variances: \(w_i = 1/v_i\), \(\theta = \sum w_i y_i / \sum w_i\), \(v_b = 1/\sum w_i\), \(v_i^* = v_i - v_b\), \(y_i^* = (y_i - \theta)/\sqrt{v_i^*}\); the statistic is Kendall's tau between \(y^*\) and \(v\), with the two-sided normal-approximation p-value. Subtracting \(v_b\) is what makes the null hold; without it the test over-rejects.

Usage

Beggtest(yi, vi)

Arguments

yi

Observed effect sizes.

vi

Their sampling variances (not standard errors).

Value

List with tau, statistic (z), p_value, n, method.

References

Begg and Mazumdar (1994), Biometrics 50:1088-1101. Paywalled; the coded form was read from Viechtbauer's metafor, R/ranktest.r, the reference implementation.

Examples

V <- c(1, 2, 3, 4, 5, 6, 7, 8)
Beggtest(V, V)
#> $tau
#> [1] 1
#> 
#> $statistic
#> [1] 3.464102
#> 
#> $p_value
#> [1] 0.0005320055
#> 
#> $n
#> [1] 8
#> 
#> $method
#> [1] "Begg-Mazumdar rank correlation test"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"