Making a statistical inference (internal)
Internal 4 credits PPDAC Comparison Box plots Confidence interval Making the callAS 91264, 4 credits — the largest Level 2 statistics internal. A full enquiry cycle comparing two groups from an existing data set, ending in an inference about the populations with an informal confidence interval.
1 Reading the notation
The data is GIVEN — this standard samples from an existing population, unlike 91265's own-collected experiment.📖 Terms the schedule grades you on
3 terms- Make an inference (Achieved)
- Evidence of using EACH component of the statistical enquiry cycle.
- With justification (Merit)
- Link components to context/populations; refer to sample statistics, data values, trends, display features.
- With statistical insight (Excellence)
- Integrate statistical and contextual knowledge throughout — may involve reflecting on process or considering other explanations.
2 Posing the comparison question
Both groups, the variable, its units, and the population — named precisely.What a strong comparison question names
- Both groups being compared.
- The variable, and its units.
- The population the data comes from.
- The summary measure — usually the median.
3 Box plots and sample distributions
Shape, centre, spread, overlap — described in context, with values.The one calculation
Informal confidence interval median ± 1.5 × IQR / √n Per group, separately Making the call Intervals do NOT overlap → make the call They overlap → say you cannot Internal-style Group A: median 148, IQR 24, n = 36. Group B: median 139, IQR 21, n = 25 Can you make the call? A: 1.5 × 24 / √36 = 1.5 × 24 / 6 = 6.0 → interval 142.0 to 154.0 B: 1.5 × 21 / √25 = 1.5 × 21 / 5 = 6.3 → interval 132.7 to 145.3 The intervals OVERLAP between 142.0 and 145.3. CONCLUSION: I cannot make the call that the population median of A is larger than B, because the intervals overlap. The sample difference of 9 may be explained by sampling variability. ✓ Overlap → no call. Declining is the correct answer here, and it earns more than forcing a claim the data cannot support.4 Making the call
The interval decides — not intuition about which sample looked bigger. ✕Comparing sample medians directly, without intervals
Sample A having a higher median than sample B does NOT by itself mean the population median is higher — that is exactly what sampling variability could produce by chance. The interval overlap check is what turns a sample observation into a defensible population inference.5 What lifts this to statistical insight
Confounding variables and process reflection — integrated throughout, not tacked on.| Grade | What it takes | The half people drop |
|---|---|---|
| Achieved | Evidence of using EACH component of the process | Missing one component entirely — every one needs visible evidence |
| Merit ("with justification") | Link components to the context; support findings with evidence from the work | Asserting a decision instead of explaining WHY, for this context |
| Excellence ("with statistical insight") | Integrate statistical and contextual knowledge THROUGHOUT | Treating it as one closing paragraph rather than woven through every component |
"With statistical insight" often means reflecting on the process itself, or naming another variable/explanation the data cannot rule out.
Practice
Recall it first, then use it — testing yourself builds the memory, where rereading the notes above only feels easier.
Recall and application shuffled together — you have to work out what each item wants before you can answer it, which is the part the exam actually tests. Both kinds feed the same spacing schedule, so anything you miss comes back sooner.
Say the answer out loud before flipping — that attempt is where the learning happens, even when you get it wrong.
Exam-style only. Instant feedback, shuffled each attempt, best score saved on this device.