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st: svy:tab why standard error and confidence intervals for count are different than for percentages [SEC=UNCLASSIFIED]


From   "Adhikari, Pramod" <pramod.adhikari@aihw.gov.au>
To   statalist@hsphsun2.harvard.edu
Subject   st: svy:tab why standard error and confidence intervals for count are different than for percentages [SEC=UNCLASSIFIED]
Date   Thu, 4 Feb 2010 10:00:35 +1100

Dear Listers
I am using svy:tab to generate estimate for a variable; one in terms of
percentages and another in terms of weighted numbers. The results in the
first table show that 95.3% said yes to H1, with a standard error of
0.51896%. Given the size of the population (weighted population size of
9577.258); I should be able to estimated the weighted population with
the estimated percentage. In terms of weighted counts, 95.3196% of
9577.258=9129.0 said yes to H1. This weighted number is available in the
second table.  
Since the standard error of the estimated prevalence is 0.51896%, I
would have thought that I can convert this percent to count. In terms of
weighted count it should be 0.51896%*9577.258=49.70. However, the
results in the second table show that the standard error of the weighted
count is whooping 390.4 compared to 49.7. 
Are the variance estimation methods different for counts and
percentages? I would appreciate any pointer to the literature or any
explanation to this anomaly.
Thanks in advance.

. svy: tab B1 AGE,  col  per se ci format(%8.0g);
(running tabulate on estimation sample)

Number of strata   =        4             Number of obs      =      4728
Number of PSUs     =      854             Population size    =  9577.258
                                          Design df          =       850
-------------------------------------------------------------------
B1.       |     AGE    
          |             18-64                65+              Total
----------+--------------------------------------------------------
      Yes |           95.4283            94.8244            95.3196
          |         (.629407)          (.519357)           (.51896)
          | [94.0213,96.5164]  [93.7049,95.7539]   [94.1889,96.239]
          | 
 No, Resp |           3.84734            3.94298            3.86456
          |         (.566421)          (.466178)          (.467171)
          | [2.87742,5.12696]  [3.12318,4.96693]  [3.04508,4.89344]
          | 
 No, Resp |           .551012            .848229            .604518
          |         (.196268)          (.215967)          (.165789)
          | [.273566,1.10672]  [.514144,1.39635]  [.352625,1.03448]
          | 
 Don't Kn |           .173358            .280251            .192601
          |         (.130816)          (.114265)          (.109104)
          | [.039371,.759864]  [.125804,.623127]  [.063302,.584459]
          | 
  Refused |                 0            .104101            .018741
          |               (0)          (.080389)          (.014434)
          |                     [.022849,.47292]  [.004133,.084943]
          | 
    Total |               100                100                100
-------------------------------------------------------------------

. svy: tab B1 AGE,  count se ci format(%8.0g);
(running tabulate on estimation sample)

Number of strata   =      4              Number of obs      =      4728
Number of PSUs     =    854              Population size    =  9577.258
                                         Design df          =       850
----------------------------------------------------------------------
B1.       |       AGE    
          |              18-64                 65+               Total
----------+-----------------------------------------------------------
      Yes |            7494.11              1634.9                9129
          |          (312.169)           (63.6021)           (350.389)
          |  [6881.39,8106.82]   [1510.06,1759.73]   [8441.27,9816.73]
          | 
 No, Resp |            302.137             67.9821             370.119
          |          (47.2943)           (8.40981)            (48.005)
          |   [209.31,394.964]   [51.4757,84.4885]   [275.897,464.341]
          | 
 No, Resp |            43.2717             14.6246             57.8963
          |          (15.5448)            (3.7955)           (16.0738)
          |   [12.761,73.7824]   [7.17493,22.0742]   [26.3472,89.4453]
          | 
 Don't Kn |             13.614             4.83189             18.4459
          |           (10.295)           (1.96964)           (10.4707)
          | [-6.59256,33.8206]   [.965959,8.69783]  [-2.10556,38.9974]
          | 
  Refused |                  0             1.79483             1.79483
          |                (0)           (1.38913)           (1.38913)
          |              [0,0]  [-.931702,4.52137]  [-.931702,4.52137]
          | 
    Total |            7853.13             1724.13             9577.26
          |          (327.514)           (66.3948)                    
          |   [7210.3,8495.96]   [1593.81,1854.45]                    
----------------------------------------------------------------------
  Key:  weighted counts
        (linearized standard errors of weighted counts)
        [95% confidence intervals for weighted counts] 

Cheers

Pramod
--------------------------------
Pramod Adhikari
Australian Institute of Health and Welfare
Phone: 02-6249 5111
Fax: 02-6244 1299


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