Census of Population and Housing, 1960 Public Use Sample ...

-7o-
d= +ciJ j
2 (b - a2
wher& 8 is the statistic of interest canputed from the full sample;
I~J is the statistic computed from the jth random group; and
t is the number of randaa groups.
The statistic emay be an index, a regression or correlation coefficient,
or other measure for hich the following approximate relationship holds:
,
Esj = Ee
where EeJ and E&indicate the expected values of the measure for the jth
random group and the full sample respectively. Thus, for example, the
formula does not apply for &defined as an estimated total number of persons
or housing units in e category.
The procedure specified by the formula ford; requires the following
steps:
1. Use t = 50 when dealing with the l-in-100 sample or t = 10 with the
l-in-l,%0 sample. (See note below for use of other values of t.)
2. Assign each oh the recorda to one of the t random groups based on
the subsample nunbe* (item H93-94).
a. To construct 50 random groups, assign all records in which
the subsample number is 01 or 51 to the first random group;
all records in which the subsample number is 02 or 52 to the
second random group; etc. Finally, assign all records in tiich
the subsample number is 50 or CO to random group number 59.
b. To construct 10 random groups of the l-in-l,000 sample, assign
all records with a 1 in the tens digit to random group 1;
those with 8 2 in the tens digit to random group 2; etc.
3. Independently within each random group, calculate the desired
measure (@J) as if the recorda for that randan griup were the
entire sample.
4. Compute the desired measure (a) on the entire sample.
5. Compute the t values (BJ - e)' and apply in the above formula.
'3. The square root of the result is'the desired standard error.
-7l-
Note: Ihe user is cautioned that the standard error given by this
procedure is itself subject to sampling error. Some control can be put
on the reliability of the estimated 6 $ by the number of random groups
used. The total sample can be separated into different numbers of
random groups by different schemes involving the subsample numbers which
for the l-in-100 sample range frCT0 OCl to 99. Ideally, each random group
should represent the total sample.
The number of rando? groups should be chosen to maximize the reliability
of the estimate 0' The reliability of the estimated 6 6 will depend
on the number of degrees of freedom in the estimate (i.e., by the choice
of t, the number of random groups), and the number of units in each ofi
the re,sulting random groups. As a general rule, when estimating d 8
using the l-in-100 sample choosing t = 50 would produce reasonably
reliable estimates of 6 i,for most statistics. One might choose a
smaller value for t to es Imate the sampling errors for statistics for a
given State. The considerations leading to the proper choice of t are
described in several statistical texts (for example, Hansen, HurWitz,
Madow, Sample Survey Methods and Theory, Vol. I, Chapter 10, Section 16,
page 440 ff).
For the l-in-l,000 sample, the tens digits of the subsample number ranges
from 0 to 9 and can be used to define 10 random groups (the units digit
is fixed). When this sample is being used, the choice of t is limited to
a maximum of t = 10.