The MUAC sub-sample nobody weighted

A multi-sector household survey measured MUAC on one child under five per household. Somebody has computed acute malnutrition from it — 13.3% — and put it in a draft beside the SMART survey’s 14.9%, as though the two were comparable.

They are not comparable, for three separate reasons, and quantifying each is this lab.

The files

household-survey-2025.v1.csv — 996 household interviews from a stratified two-stage cluster survey, of which 653 measured a child under five. household-survey-frame-2025.v1.csv — the 470-area sampling frame.

The survey course built the household weights from that frame. This lab needs them again, and then needs one more multiplication.

Set up first

A project folder, both files read-only, an outputs/ directory, and a script that runs top to bottom from a clean interpreter.

Part one: the child weight

Reconstruct the household weights from the frame, then derive the weight for a measured child.

One child was selected per household from among the eligible children, so a measured child in a household with three under-fives stands for three children. Work out the multiplication, apply it, and prove it: the child weights should sum to a plausible under-five population for this frame.

State what the sum comes to and whether you believe it.

Part two: the estimate

Compute acute malnutrition by MUAC, four ways, and put them in one table:

• unweighted, on measured children
• household-weighted only
• child-weighted, which is the correct one
• child-weighted with a design-adjusted confidence interval

Report the design effect and the effective sample size. The survey course’s machinery applies unchanged; the only new thing is the weight.

Handle the five MUAC values recorded in centimetres before any of this. They are in the dataset’s known issues and they will not fix themselves.

Part three: the three reasons it is not the SMART figure

The SMART survey reports GAM of 14.9% by weight-for-height. This survey reports something near 11.4% by MUAC. Decompose the difference into its three causes and quantify what you can:

• Measure. MUAC and weight-for-height identify overlapping but different children, as lesson 4 established. Say which direction this pushes and why you cannot quantify it from these two files alone.
• Population. Both are population samples, so this one should contribute little. Say how you would check.
• Precision. Put both estimates beside their intervals and say whether the difference is larger than the intervals support.

Part four: what it can be read against

The IPC acute malnutrition phases are defined against weight-for-height GAM. Say plainly whether your MUAC-based estimate can be read against them, and write the two sentences you would put in the report.

Then say what this survey is good for that the SMART survey is not, and use its strata to demonstrate it.

What to hand in

A Python script, run from a clean interpreter, producing:

• the weight construction with its proof, and the child weights saved to outputs/
• the four-way estimate table with denominators and n
• the design-adjusted interval, design effect and effective sample size
• the decomposition table from part three
• a short reporting block, in the shape lesson 6 uses

Check your numbers

	Expected
Households interviewed	996
Households with a measured child	653
MUAC values in centimetres	5
Household weights sum to	56,428
Acute malnutrition, unweighted	about 13.3%
Acute malnutrition, child-weighted	about 11.4%

If your household weights do not sum to 56,428, fix that before anything else. If your child-weighted figure equals your household-weighted one, the sub-sample multiplication is missing.

The questions to answer in prose

Three sentences each.

1. The child weight is the household weight times something. Say what, why, and which direction the estimate moves if you omit it — using the fact that larger households are systematically poorer.

2. Your estimate and the SMART survey’s differ by about three points. Say how much of that difference the confidence intervals can rule out as chance, and what remains to be explained by measure.

3. A colleague wants to put your figure in an IPC evidence table. Give the two sentences you would write in reply, and name the one thing that would make the figure usable there.

How to know you are done

Delete outputs/, restart the interpreter, run once, and every table regenerates identically. Every estimate in your output carries a denominator, an interval and the name of the measure — and no figure anywhere in it is called “GAM” without a qualifier.

What this lab is not

It is not survey methodology; the survey course covers weights, design effects and intervals, and this lab reuses them. It is not CMAM analysis either. This is the join between the two: a nutrition indicator estimated from a survey that was not designed for nutrition, with an honest account of what that costs and what it still supports.