The document you attached talks about computing weighted variance estimates. Is what you're asking for how to compute the weighted variance so you can use it for z-test (which you already know how to do in Tableau)?
If so weighted variance can be written as an LOD expression. If you're doing it for the entire table it can be written in the following form.
First calculated field is weighted mean, let's call it Wmean
Then the variance calculation SPSS uses (relies on the Wmean calculation)
Note that this uses a fixed LOD expression for Wmean that computes the mean of x over the entire table
You can learn more about level of detail (LOD) expressions here