In the SPSS Statistics Algorithm Manual Version 29 (p.132 in the pdf) the computation of the two-sided p-value for the bootstrap procedure is described as follows:
Sadly, because of different RNGs, I cannot verify the computation via R and have to rely on the manual in order to recreate SPSS's computation.
What is unclear to me is what standard errors are used to compute the test statistics $z_0$ and $z_b^*$.
$SE_b^*$ is never explicitly described in the manual as far as I can tell, but since the manual writes that the standard error is estimated "from the standard error calculated within the procedure" one could interpret this as $SE_b^*$ being the standard error of the bth parameter estimate $T_b^*$ of the bth bootstrap sample and $SE$ being the standard error for the original parameter estimate $T$, where $SE$ estimated via the bootstrap procedure is (SPSS manual p. 131):
Does anyone happen to have any knowledge about this particular approach described in SPSS? I know that there is a variety of ways to compute the p-values for bootstrap tests (e.g. see this post) but I am specifically interested in the SPSS two-sided p-value.
