Calculate representation explicitly
A group can make up a smaller share of replies than of invitations. That changes the weights in the pooled observed mean.
In the W3 lecture example, 80 Day students yield 72 replies and 20 Evening students yield 8 replies. Response rates are 72/80=90% and 8/20=40%. Missing fractions are 8/80=10% and 12/20=60%.
Evening students make up 20/100=20% of invitees but 8/80=10% of respondents. Dropping missing ratings changes group composition. Keep clear the distinction between a within-group response rate and a group's share of all replies.
With respondent means 4 for Day and 2 for Evening, the pooled observed mean is (724+82)/80 = 3.8. If responders represent nonresponders within each class, a class-size weighted estimate for all students is (804+202)/100 = 3.6. That estimate depends on an assumption; it is not a newly observed mean.
If the 12 missing Evening ratings average 1 while all Day ratings average 4, the all-student mean becomes (804+82+12*1)/100 = 3.48, below a 3.5 target. This is why the respondent mean alone cannot establish the target claim.
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 connects nonresponse with representation. The survey separates group invitation shares from reply shares and asks what MCAR/MAR/MNAR mean.
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.
Evening has 20 of 100 invitations and 8 of 80 replies. What happened to its share?
Day has 72 replies with mean 4; Evening 8 with mean 2. What is the pooled observed mean?
2. Application
Apply the concept to a case or calculation.
A group has 30 invitations and 18 replies. What is its response rate?
The same group has 30 invitations and 18 replies. What fraction is missing?
3. Interpretation and limitations
Evaluate assumptions and justify conclusions.
Evening gives 8 replies out of 80 total replies. What is its reply share?
Means 4 and 2 come from 72 and 8 replies. Why is their simple average 3 not the pooled observed mean?
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.
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Day is missing 8/80, or 10%. Evening is missing 12/20, or 60%. The denominators are each group's invited people.
Check: did you answer the question, use evidence or working, and avoid claiming more than the evidence supports?
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It uses only the 80 observed replies. Nonrespondents may have different satisfaction, and Evening is less represented among replies than among invitees.
Check: did you answer the question, use evidence or working, and avoid claiming more than the evidence supports?