Stouffer

Stouffer's Z-score method

stouffer_zscore(pvals, weights = rep(1, seq_along(pvals)), side = "two")

Arguments

pvals	A vector of p-values
weights	A vector of weights
side	How the p-values were generated. One of 'right', 'left' or 'two'.

Value

A list containing the following components:

• statistic the value of the test statistic.

• p.value the p-value of the test.

Details

Given a set of i.i.d p-values and associated weights, it combines the p-values \(p_i\). Letting \(\phi\) be the standard normal cumulative distribution function and \(Z_i =\phi^{-1} (1-p_i)\), the meta-analysis Z-score is

$$Z = (\sum w_i Z_i) * (\sum (w_i)^2)^(-1/2)$$

References

Samuel Andrew Stouffer. Adjustment during army life. Princeton University Press, 1949.

Examples

 pvals <- runif(100, 0, 1)
 weights <- runif(100, 0, 1)
 stouffer_zscore(pvals, weights)
#> $statistic
#> [1] 6.729832
#> 
#> $p.value
#> [1] 8.492959e-12
#>