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directly standardized rate for Miami 6.92
SRR = ——————————————— = ——— = 1.03
directly standardized rate for Alaska 6.71
Similarly, the difference of the two rates would be a "standardized rate difference" (SRD = 6.92–
6.71=0.21 [per 1,000 – the ratio has no need for the scaling factor, but the difference does). Since
the rates are virtually identical, the SRR is close to 1.0, and the SRD is close to zero, all give the same
message: the mortality experience in Alaska, Miami, and the total U.S. are all about the same when
the differences due to age structure are eliminated.
In addition, a directly standardized rate can be compared to the crude rate in the population from
which the weights were taken (the "standard population"). The reason that this works is that, as
noted above, the crude rate for a population can be expressed as a weighted average of the
population's stratum-specific death rates (Rk) weighted by its own age distribution. Therefore the
crude rate and the directly standardized rates are all weighted averages based on the same set of
weights (the proportional age distribution in the standard population). So the following SRR is
legitimate:
directly standardized rate for Alaska 6.92
SRR = ——————————————— = ——— = 0.852
directly standardized rate for total U.S. 8.13
Standardized ratios and differences are also weighted averages [optional]
It may or may not be of interest to know that the standardized ratios and differences obtained by
taking the ratios and differences of directly-standardized rates are also weighted averages. For
example, the SRR can be written as:
∑ (rkWk) ∑ (rk/r'k)( r'k Wk) ∑[(RR k)( r'k Wk)]
SRR = ———— = —————— = ———————
∑ (r'jWj) ∑ (r'jWj) ∑ (r'jWj)
j j j
] = ∑ (RRk)
( r'k Wk)
——— )
= ∑ (RRkW'k)
k ∑ (r'jWj)
K
[ ( j
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www.sph.unc.edu/courses/EPID168, © Victor J. Schoenbach 1999 6. Standardization - 138
rev. 9/14/1999, 12/22/1999, 1/13/2000, 9/10/2000