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# Annual Statistical Report on the Social Security Disability Insurance Program, 2023

# Appendix: Sampling Variability

Estimates based on sample data may differ from the figures that would have been obtained had all, rather than specified samples, of the records been used. These differences are termed sampling variability. The standard error is a measure of the sampling variability. About 68 percent of all possible probability samples selected with the same specifications will give estimates within one standard error of the figure obtained from a compilation of all records. Similarly, approximately 90 percent will give estimates within 1.645 standard errors, about 95 percent will give estimates within two standard errors, and about 99 percent will give estimates within two and one-half standard errors. The standard error of an estimate depends on the design elements such as the method of sampling, sample size, and the estimation process.

Because of the large number of data cells tabulated from the sample files, it is not practical to calculate the standard error for every possible cell. However, standard errors for a large number of cells were estimated. These estimates were used to fit regression curves to provide estimates of approximate standard errors associated with tabulated counts and proportions.

The tables showing the sampling variability provide a general order of magnitude for similar estimates from the various sample files. Table A-1 presents approximate standard errors for the estimated number of people from the 1 percent and the 10 percent files. The reliability of an estimated percentage depends on both the size of the percentage and on the size of the total on which the percentage is based. Data in Table A-2 provide approximate standard errors of the estimated percentage of people in the 1 percent and 10 percent files. The standard errors are expressed in percentage points, and the bases shown are in terms of inflated data.

Table A-1. Approximate standard errors of estimated number of people
Size of estimate (inflated) | Standard error
--- | ---
1 percent file
500 | 250
1,000 | 300
2,500 | 500
5,000 | 800
7,500 | 900
10,000 | 1,100
25,000 | 1,700
50,000 | 2,400
75,000 | 3,000
100,000 | 3,400
250,000 | 5,400
500,000 | 7,800
750,000 | 9,600
1,000,000 | 11,100
5,000,000 | 25,800
10,000,000 | 36,900
25,000,000 | 57,700
50,000,000 | 76,100
75,000,000 | 82,900
10 percent file
100 | 30
500 | 70
1,000 | 100
5,000 | 225
10,000 | 300
50,000 | 700
100,000 | 1,000
500,000 | 2,200
1,000,000 | 3,200
2,000,000 | 4,300
3,000,000 | 5,300
5,000,000 | 6,500
10,000,000 | 8,500
20,000,000 | 9,300

Table A-2. Approximate standard errors of estimated percentage of people
Size of base (inflated) | 2 or 98 | 5 or 95 | 10 or 90 | 25 or 75 | 50
--- | --- | --- | --- | --- | ---
| 1 percent file
1,000 | 4.7 | 7.3 | 10.1 | 14.5 | 16.8
10,000 | 1.5 | 2.3 | 3.2 | 4.6 | 5.3
50,000 | 0.7 | 1.0 | 1.4 | 2.1 | 2.4
100,000 | 0.5 | 0.7 | 1.0 | 1.5 | 1.7
500,000 | 0.2 | 0.3 | 0.4 | 0.7 | 0.8
1,000,000 | 0.1 | 0.2 | 0.3 | 0.5 | 0.5
5,000,000 | 0.1 | 0.1 | 0.1 | 0.2 | 0.2
10,000,000 | (L) | 0.1 | 0.1 | 0.2 | 0.2
50,000,000 | (L) | (L) | (L) | 0.1 | 0.1
100,000,000 | (L) | (L) | (L) | (L) | (L)
| 10 percent file
500 | 1.9 | 3.0 | 4.1 | 5.9 | 6.8
1,000 | 1.3 | 2.1 | 2.9 | 4.1 | 4.8
2,500 | 0.8 | 1.3 | 1.8 | 2.6 | 3.0
10,000 | 0.4 | 0.6 | 0.9 | 1.3 | 1.5
50,000 | 0.2 | 0.3 | 0.4 | 0.6 | 0.7
100,000 | 0.1 | 0.2 | 0.3 | 0.4 | 0.5
500,000 | (L) | 0.1 | 0.1 | 0.2 | 0.2
1,000,000 | (L) | 0.1 | 0.1 | 0.1 | 0.2
5,000,000 | (L) | (L) | (L) | (L) | 0.1
10,000,000 | (L) | (L) | (L) | (L) | (L)
50,000,000 | (L) | (L) | (L) | (L) | (L)
NOTE: (L) = less than 0.05 percent.