The 1995/1996 Household Income, Expenditure - (PDF, 101 mb ...

Appendix LA Comparing Estimates from Interpenetrating Samples
To illustrate the use of half sample comparison, consider the number of
persons per household in the first half versus the number of persons per
household in the second half. The null hypothesis is a significant difference
between these means, and the t values for a paired difference experiment
allows us to draw confidence bounds around the alternative.
Average Household Size Estimates:
1. First half-sample: 5.04954, N = 7347, STD = 2.53449
2. Second half-sample: 4.93966, N = 7458, STO = 2.45973
t =
(5.04954 - 4.93966)
(2.53449)2 + (2.45973)2
7347 7458
The calculated t value is 2.68 and we may reject the null hypothesis of
equality of the two means at a 95% level of confidence. The inference is that
average household size in the second half sample is statistically smaller, but
not by much, because the difference between the two means is very small.
A different point to note, not merely illustrative of the use of
interpenetrating samples to test hypotheses, is in the use of the standard
deviation for the means, as created by SAS. SAS assumes that the estimate
comes from a simple random sample design. For the full sample of 14805
households from the recent survey, SAS produces an estimate of 4.9942 as the
mean household size, with standard deviation 2.4976. The implied 95%
confidence interval is therefore ± .0402. However, as mentioned, the HIECS
households are sampled under a stratified, two stage sampling scheme with
probability proportional to size without replacement in the first stage and
simple random sampling without replacement in the second stage. Technically,
this means that the between- and within-PSU components of the variance of
any estimate must be accounted for. In most cases, then, estimates which
account for this component of the total variance will be higher than those
which assume a simple random sample design. CENVAR software (see below),
which does take into account both variance components, produces an
(unweighted) estimate of 4.963 for the mean household size ± .055. Cochran
(1977) is a good source for this issue. In cases of critical household
estimates. where possible, the asymptotic measures reported here will be the
more conservative ones produced by CENVAR.
Appendix LB Functions of IMPS Components
1) CENTRACK handled the movement and transmittal of survey forms
between the various processing phases - receipt, entry, verification (or
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