4.4 KiB
| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Design effect | 5/12 | https://en.wikipedia.org/wiki/Design_effect | reference | science, encyclopedia | 2026-05-05T09:49:56.844427+00:00 | kb-cron |
Alternatively, when the sampling design is fully known (leading to some
p
h
{\displaystyle p_{h}}
probability of selection for some element from stratum h), and the non-response is measurable (i.e., we know that only
r
h
{\displaystyle r_{h}}
observations answered in stratum h), then an exactly known inverse probability weight can be calculated for each element i from stratum h using:
w
i
=
1
p
h
r
h
{\displaystyle w_{i}={\frac {1}{p_{h}r_{h}}}}
. Sometimes a statistical adjustment, such as post-stratification or raking, is used for estimating the selection probability. E.g., when comparing the sample we have with same target population, also known as matching to controls. The estimation process may be focused only on adjusting the existing population to an alternative population (for example, if trying to extrapolate from a panel drawn from several regions to an entire country). In such a case, the adjustment might be focused on some calibration factor
c
i
{\displaystyle c_{i}}
and the weights be calculated as
w
i
=
c
i
p
h
r
h
{\displaystyle w_{i}={\frac {c_{i}}{p_{h}r_{h}}}}
. However, in other cases, both the under-coverage and non-response are all modeled as part of the statistical adjustment, which leads to an estimation of the overall sampling probability (lets say
p
i
′
{\displaystyle p_{i}'}
). In such a case, the weights are simply:
w
i
=
1
p
i
′
{\displaystyle w_{i}={\frac {1}{p_{i}'}}}
. Notice that when statistical adjustments are used,
w
i
{\displaystyle w_{i}}
is often estimated based on some model. The formulation in the following sections assume this
w
i
{\displaystyle w_{i}}
is known, which is not true for statistical adjustments (since we only have
w
^
i
{\displaystyle {\widehat {w}}_{i}}
). However, if it is assumed that the estimation error of
w
^
i
{\displaystyle {\widehat {w}}_{i}}
is very small then the following sections can be used as if it was known. Having this assumption be true depends on the size of the sample used for modeling, and is worth keeping in mind during analysis. When the selection probabilities may be different, the sample size is random, and the pairwise selection probabilities are independent, we call this Poisson sampling.