If you have any material or mathematical formula regarding this please let me know
While standardizing performance areas I have computed two new z scores and further results need to standardize
For example, customer relation as an indicator, "After this initial standardization, a weighted average of the two new z scores was computed, which was standardized again, the obtained denominator is 0.87
My query is how to standardized two z-scores?
It's not clear what you are asking. Please rephrase the question in a way that will be comprehensible for anyone who is not familiar with your project.
Just a conjecture, assuming that the original scores are independent:
If Z1 and Z2 are:the two z-scores, Z=(Z1+Z2)/sqrt(2).
More generally, Z=(w1*Z1+w2*Z2)/sqrt(w1**2 + w2**2) is a standardized Z.
If Z1 and Z2 are not independent, then the correlation needs to be incorporated
As David states, if the standard scores Z1 and Z2 are not independent, then the correlation has to be incorporated.
More precisely, the covariance; however, it equals the correlation in your case:
r *sZ1*sZ2 = cov (and sZ1 = sZ2 = 1 as you have standard scores).
Z = (w1*Z1 + w2*Z2) / (sqrt(w12 + w22 + w1*w2*cov(Z1, Z2) ) )
where you estimate the covariance from your data on the standard scores Z1 and Z2.
Sorry, I forgot the factor 2 for the mixed term with the covariance.
Manfred's approach should be used as it is more general. The approach assuming independence may have been used in the example you originally cited.
@ David R Bristol Can you please clarify about denominator.What does " ** " indicate?
Waiting for your reply
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