Folktables ACSIncome Result Interpretation

This worked example asks:

If we only report people by age band, education band, and sex, is that coarse grouping enough to know the overall ACSIncome target rate? Or could the answer change if the hidden mix inside those groups changed?

The short answer:

The coarse public grouping is not perfectly adequate, but the instability is fairly small in this sample.

What Was Estimated

The observed target rate is 0.1237, meaning about 12.37% of the sampled people exceed the ACSIncome income threshold.

The stress test keeps the public distribution fixed. In other words, it keeps the same proportions of people in each:

AGE_BAND x EDU_BAND x SEX

group, but allows the hidden composition inside those public groups to change. The hidden composition includes:

  • occupation major group

  • class of worker

  • weekly-hours band

  • race

  • marital status

  • birthplace

  • relationship status

Under that stress test, the target rate could range from:

11.79% to 13.44%

The observed value, 12.37%, is inside that possible range.

Transport Ambiguity

The width of the range is:

13.44% - 11.79% = 1.65 percentage points

That width is the transport ambiguity. It means:

Even if age, education, and sex proportions stayed exactly the same, hidden composition changes could move the aggregate income-threshold rate by up to about 1.65 percentage points.

This is not a confidence interval. It is not saying that the estimate is statistically uncertain by this much. It is saying:

Given this coarse public representation, here is how much the answer could change if hidden subgroups inside the public cells were rearranged.

So when the report says:

Public adequate: no

it means:

Age band, education band, and sex alone do not fully determine the target rate under the chosen stress test.

At least one public group contains hidden subgroups with different income-threshold rates.

Worst Public Fibers

A public fiber is one coarse group, such as:

under_25 x hs_or_some_college x SEX=1

Inside that public group, there are 7 retained hidden cells. Those hidden cells differ by occupation, class of worker, weekly hours, race, marital status, birthplace, and relationship status.

For that group:

mass = 0.3019
range = 0.0385
contribution = 0.0116

Plain English:

About 30.19% of the retained sample is in this public group. Inside it, hidden subgroups have target rates ranging from 0.00% to 3.85%. Because the group is large, this hidden variation contributes about 1.16 percentage points of the total 1.65 percentage-point ambiguity.

That first public group explains most of the instability.

The second meaningful contributor is:

AGE_BAND=45_54, EDU_BAND=hs_or_some_college, SEX=2

It has:

mass = 0.0450
range = 0.1096
contribution = 0.0049

Plain English:

This group is smaller, only about 4.5% of the retained sample, but its hidden cells differ more sharply: the target rate ranges from 37.04% to 48.00%. That contributes about 0.49 percentage points of ambiguity.

Together, those two groups account for essentially all the transport ambiguity. The remaining listed groups have only one retained hidden cell each, so their range is zero. They do not add ambiguity under this stress test.

Refinement Table

The refinement table asks:

If we were allowed to add one hidden variable to the public representation, which one would make the public grouping more stable?

The best answer is:

add OCC_MAJOR

Adding occupation major group reduces ambiguity from:

0.0165 to 0.0090

So it removes about:

0.0075 = 0.75 percentage points

of ambiguity.

Plain English:

Occupation is the most valuable extra public variable. It explains the largest part of the hidden instability that age, education, and sex leave unresolved.

The next best refinements are:

RELP        relationship status
WKHP_BAND   weekly-hours band
RAC1P       race

while COW, MAR, and POBP do not help in this particular retained state space.

Takeaway

With only age band, education band, and sex, the public categories are not fully stable for estimating the ACSIncome target rate. But in this sampled, filtered demo, the residual ambiguity is modest: about 1.65 percentage points. Most of that ambiguity comes from one large young / less-educated public group, and adding occupation would reduce the instability the most.

A concise README interpretation:

In this ACSIncome sample, coarse demographic categories almost determine the aggregate income-threshold rate, but not quite: hidden occupational and household-composition differences can move the result by up to 1.65 percentage points even when the public demographic mix is held fixed.