The course-registration example
The lecture's part-time group has a higher pooled pass rate even though full-time leads in both broad course groups. Different course mixes help explain this.
| Course group | Full-time passes/registrations | Part-time passes/registrations |
|---|---|---|
| Quantitative service: MA110, CH110, ST110 | 305/1,027 = 29.7% | 7/38 = 18.4% |
| Other nine courses | 2,754/3,081 = 89.4% | 422/519 = 81.3% |
| Pooled | 3,059/4,108 = 74.5% | 429/557 = 77.0% |
Full-time leads in both broad course groups. Part-time registrations put much more weight on the higher-pass group:519/557 about 93.2%, compared with 3,081/4,108=75% for full-time. That composition explains how the pooled ranking can reverse.
Broad groups can still conceal differences. The slides report that part-time has lower observed rates in 11 of 12 individual courses, not all 12. EC102 is an exception. A1/9 small cell is unstable: one extra pass changes 11.1% to 22.2%. Always keep counts beside percentages.
The source's pass definition is final grade at least 50. Different pass thresholds, missing outcomes or eligibility definitions would change the comparison. Re-check these before comparing another dataset.
Source: W5 PDF pp. 3-51, 53. The lecture uses both a constructed 200-student support example and a synthetic 4,665-registration course dataset. They are different tables with different units.
Changing groupby changes the comparison, not its causal strength. Course mix and preparation can still differ between programmes.
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 chiefly explains the course example's pooled part-time advantage?
Why report counts beside small-cell percentages?
2. Application
Apply the concept to a case or calculation.
The course example's pooled rates use which denominator unit?
Which group has the greater share in the higher-pass broad course group?
3. Interpretation and limitations
Evaluate assumptions and justify conclusions.
One pass among nine becomes two passes among nine. What happens to the percentage?
Why is the lecture's 2.6-point gap not reproduced by subtracting displayed 77.0 and 74.5?
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
The part-time group places much more weight on the higher-pass course group. Pooled rates combine within-group rates with these different weights.
Check: did you answer the question, use evidence or working, and avoid claiming more than the evidence supports?
Show an example answer
It comes from only nine registrations. One additional pass changes it from 11.1% to 22.2%, so a single outcome has a large effect on the percentage.
Check: did you answer the question, use evidence or working, and avoid claiming more than the evidence supports?