Trouble standardizing regression slopes

#1
Dear readers,

Hopefully you can help me with the following problem.

I am using meta-analytic software to perform a meta-analysis. When I perform meta-regression in this program, results only show unstandardized slopes (B). To allow comparison of my predictor X (in days) with others (from literature), I would like to standardize my B's.

As a standardized slope (Beta) reflects the change in Y per SD X, I thought to standardize B by multiplying it with SD (X). Rationale:

B = d(Y) / per day X
B * SD(X) = d(Y) / SD(X) in days = Beta.

To check whether my method is right, I performed two regressions in SPSS.
regression 1: X as independent and Y as dependent variable
regression 2: standardized X (SD=1, I checked it using descriptives) as independent and Y as dependent variable.

My idea was, if my method is right, that the following would be true:

B (regression 1) * SD(X) = B (regression 2)
This turned out to be true indeed

and

B (regression 2) = Beta (regression 2) because Beta = B*SD = B*1 = B
This turned out to be not true, moreover: Beta (regression 1) equaled Beta (regression 2).

Can someone explain to me why SPSS evidently uses another method to standardise B's than I used (and what method this is)? Does this explain that Beta (regression 1) equals Beta (regression 2)?

Thank you very much

p.s. the reason that I don't use SPSS in the first place is because it does not allow to perform a meta-regression using a random aproach (Method of Moments)
 
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