Sensitivity analysis and bounds
Sensitivity analysis asks “What if the missing values were different?” Bounds show the smallest and largest results allowed by the known scale.
Let N be all eligible people, n the observed count, T the observed sum, and m an assumed mean among the N-n missing people. A hypothetical full-population mean is [T+(N-n)*m]/N. Evaluate several plausible m values without modifying the final observed dataset.
W3 pp. 33-34: N=20, n=12, observed mean=4, so T=48 and eight ratings are missing. Assuming m=1 gives 2.8; m=3 gives 3.6; m=4 gives 4.0; m=5 gives 4.4. On a 1-5 scale, full-population bounds are 2.8 to 4.4. A 3.5 target could be met or missed. These are logical bounds under the scale and roster assumptions, not confidence intervals.
Your earlier 30-student survey uses a different seed-dependent n. Recalculate using its actual output; do not copy 2.8-4.4 or the 100-student class example into that notebook.
Source: W3 PDF pp. 4-55. The 14-row registry example below comes from the Week 3 lab code you previously pasted in this conversation; it is separate from the lecture's smaller examples.
The lecture separates recovered observations from assumed replacements. The mean-fill demonstration and sensitivity table show different consequences of assumptions.
Practice problems
Supplementary study questions on the lecture concepts — not verbatim exam questions. Each answer counts toward spaced review.
1. Conceptual understanding
Definitions and distinctions.
What does a sensitivity analysis do?
Twelve of 20 people answer with mean 4 on a 1–5 scale. What are full-group bounds?
2. Application
Apply the concept to a case or calculation.
Twelve observed ratings have mean 4. What is their observed total?
There are 8 missing ratings among 20 people. If their mean is assumed 1 and observed total is 48, what is the full mean?
3. Interpretation and limitations
Evaluate assumptions and justify conclusions.
For the same case, assume the 8 missing ratings average 5. What is the full mean?
Bounds are 2.8 to 4.4 and the target is at least 3.5. What conclusion fits?
Explain it in writing
Self-checked, not marked. Write a few sentences, then compare with the example answer. Your writing is saved as you type.
Show an example answer
No. Some allowed missing-value scenarios meet the target and others do not. The current observations alone do not settle the all-person target.
Check: did you answer the question, use evidence or working, and avoid claiming more than the evidence supports?
Show an example answer
Recovering additional reliable responses reduces the unknown total. Credible evidence about nonrespondents can also support narrower assumptions, which should remain explicit.
Check: did you answer the question, use evidence or working, and avoid claiming more than the evidence supports?