with the following rides, wilI enable the reader to determine approximate relative standard errors from the charts for estimates presented in this re-port.
Rule 1. Estimates
of aggregates: Approximaterelative standard errors for estimates of aggregates such as the number of persons with a #ven characteristic are obtained from appropriate curves on page 48. The number of persons in the total U.S. pop-ulation or in an age-sex-color class of the total population is adjusted to official Bureau of the Census figures and is not subject to sampling error.
Rule 2.
Rule 3.
Rule 4.
Estimates of percentages in a percent dis-tribution:
Relative standard errors for percentages in a percent distribution of a tot al are obtained from appropriate curves on page 50.. For values which do not fall on one of the curves presented in the chart, visual interpolation wilI pro-vide a satisfactory approximation.
Estimates of rates where the numerator is a subclass of the denominator: This rule
applies for prevalence rates or where a unit of the numerator occurs, with few exceptions, only once in the year for any one unit in the denominator. For examp-le, in computing the rate of visual im-pairments per 1,000 population, the numerator consisting of persons with the impairment is a subclass of the denomi-nator which includes all persons in the population. Such rates if converted to rates per 100 may be treated as though they were percentages and the relative standard errors obtained from the chart P4AN-M. Rates per 1,000, or on any other base, must first be converted to rates per 100; then the percentage chart wilI provide the relative standard error per 100.
Estimates of rates where the numerator is not a subclass of the denominator: This
rule appIies where a unit of the numera-tor often occurs more t.lmnonce for any one unit m the denominator. For exam-ple, in the computation of the number of persons injured per 100 currently em-ployed persons per year, it is possible that a person in the denominator could have sustained more than one of the in-juries included in the numerator. Ap-proximate relative standard errors for rates of this kind may be computed as follows:
(a) Where the denominator is the total
U.S. population or includes all
per-sons in one or more of the
age-sex-color groups of the total population,
the relative error of the rate is
equiv-alent to the relative error of the nu-merator which can be obtained di-rectly from the appropriate chart.
(b) In other cases the relative standard error of the numerator and of the de-nominator can be obtained from the appropriate curve. Square each of these relative errors, add the re-sulting values, and extract the square root of the sum. This procedure will r e suit in an upper bound on the standard error and often will over-state the error.
Rule 5. Estimates of difference between two sta-tistics (mean, rate, total, etc.): The standard error of a difference is approxi-mately the square root of the sum of the squares of each standard error considered
separately. A formula for the standard er-ror of a difference d = X1- X2 is
J(
‘d
=
xl Vxl)2+ (X2 VX2)2
where Xl is the estimate for cIass 1, X2 is the estimate for class 2, and VX~ and Vx z are the relative errors of Xl and X2 respectively. This formula repre-sents the actual standard error quite accurately for the difference between separate and uncorrelated characteris-tics although it is only a rough approxi-mation in most other cases. The relative standard error of each estimate involved in such a difference can be determined by one of the four n.des above, which-ever is appropriate.
Guide to Use of Relative Standard Error Charts
The code shown below identifies the ap- (1) A = aggregate, P = percentages; (2) the number propriate curve to be use in estimating the relative of czdendar quarters of data collection; (3) the standard error of the statistics described. The four type of statistics as described on page 44. and (4) components of each code describe the statistic as the range of the statistics as described on
follo-ws: page 44.
Statistic
Number of:
Persons in the U.S. population or total number of persons in any age-sex-color category . . . . . . . . . . Persons in any other population group . . . . . . . Physician visits in a year . . . . . . . . . . . . .
Percent distribution of:
Physician visits . . . . . . . . . . . . . . . . Persons by interval or frequency of visits . . . . . .
Number of physician visits:
Per person in total U.S. population or in any age-sex-color class per year . . . . . . . . . . . . . . . . Per person in any other population group . . . . . .
Use
Rule Code on
Not subject to sampling error 1
1
2 2
4(a) 4(b)
A4AN A4BM
P4BN-M P4AN-M
A4BM
{
Numer.: A4BM Denom.: A4AN
]age
48 48
49 50
48 48 48
-tiVO BtUidard -OI?Q fCLT 8gg133gSteS b&3edon fOIU? ~S Of diiiti ~CtiOZL fordata ofalltyps!s and.ranges
Size of estimate (in thousands)
Example of use of chart: An aggregate of 2,000,000 (on scale at bottom of chart) for a Narrow range Type A statistic (code: A4AN) has a relative standard error of 3.6 percent,
(read from scale at left side of chart), or a standard 2,000,000).
error of 72,000 (3.6 percent of For a Wide range Type B statistic (code: A4BW), an aggregate of 6,000,000 has a relative error of 16.0 percent or a standard error of 960,000 (16 ~,~ent of 6,000,000).
1
1
Relative dxmdard errors far percentages based on four quarters of 13J3tacolJ.ectim for t= B data, Narrow and Ms@m range
(Ease of percentage shown on curves in millions)
10 100
Estimated percentage
Example of use of chart: An estimate of 20 percent (on scale at bottom of chart) based on tinestimate ~f 10,000,000 hae a relative standard error of 17.0 percent (read from scale at the left side of the chart), the point at which the curve for a base of 10,000,000 in-tersects the vertical line for 20 percent. The standard error in percentage points %s equal to 20 percent X 17.0 percent or 3.4 percentage points.
ReJstivestandarderrorafor prcentagas based on four quarters of data colJ.eetion for typeA data, Narrow and Medium range
(Bu3e of percentage shown on curves In miUlons) 1
Estimatedpercentage