Pooled rates in a grouped chart
Pooled rates add counts before dividing, so they depend on group sizes. A grouped bar chart can show that one mode leads in every group yet trails overall.
W6 pp. 26-27 reuse Week 5's synthetic registrations. A registration can differ from a distinct student.
| Course group | Full-time passes/all | Part-time passes/all |
|---|---|---|
| Quantitative | 305/1,027 = 29.7% | 7/38 = 18.4% |
| Other | 2,754/3,081 = 89.4% | 422/519 = 81.3% |
| Pooled | 3,059/4,108 = 74.5% | 429/557 = 77.0% |
Pooling adds counts before dividing: (305+2,754)/(1,027+3,081). It is not the simple mean of the two percentages. That mean would be (29.7+89.4)/2 ≈ 59.5% for full-time, a hypothetical equal-mix figure, not the observed rate.
A grouped bar chart with course groups along the x-axis and study mode as a labelled colour makes the reversal visible: full-time leads within each group, but part-time leads in "All courses", because 519/557 ≈ 93% of part-time registrations sit in the high-pass group versus 3,081/4,108 = 75% of full-time registrations. A single pooled pair of bars would hide this. Good design: a 0-100 common axis, a legend with names, bar labels, and the denominators (especially the 38-registration cell) in the caption. Caption the limit too: these observations do not show cause (see 7.7-7.9).
Source: W6 PDF pp. 1-37. Most numbers in the lecture are illustrative or constructed for teaching; pp. 26-27 reuse the Week 5 synthetic registration counts. The Week 6 lab manual (L6) practises Week 5 EDA reasoning and is worked through section by section in Lab work.
The Week 5 course registrations, drawn as a grouped chart in Week 6, show full time leading in both course groups while part time leads overall.
Everything together: data checks, pooled and stratified rates, weights, a common mix, one histogram and a written conclusion that separates association from causation.
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.
How is a pooled pass rate calculated across course groups?
Full-time leads within each course group but part-time leads overall. What chiefly explains this?
2. Application
Apply the concept to a case or calculation.
Quantitative courses: full-time 305/1,027 and part-time 7/38. Which rate is higher?
What is the simple mean of full-time's 29.7% and 89.4%?
3. Interpretation and limitations
Evaluate assumptions and justify conclusions.
What should a grouped bar chart of these rates include?
Which caption is defensible?
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
Add the passes and the registrations: (305 + 2,754)/(1,027 + 3,081) = 3,059/4,108 ≈ 74.5%. Averaging 29.7% and 89.4% would wrongly give about 59.5%.
Check: did you answer the question, use evidence or working, and avoid claiming more than the evidence supports?
Show an example answer
That full-time leads within each course group while part-time leads overall because the course mix differs, with the denominators shown, and that these observations do not show that study mode causes the difference.
Check: did you answer the question, use evidence or working, and avoid claiming more than the evidence supports?