Investigating bivariate measurement data (internal)
Internal 4 credits PPDAC Scatter plots Regression Correlation Prediction ContextA full statistical enquiry cycle on a relationship between two measurement variables. Every rung of the grade ladder is about context: Achieved covers the cycle, Merit links each stage to the context with evidence, and Excellence integrates contextual knowledge throughout — including what the model cannot do.
1 Reading the notation
What NZQA explicitly rules in and out for this standard.📖 Terms and boundaries the schedule grades you on
4 terms- y-variable (response)
- Must be CONTINUOUS — a discrete or categorical response cannot be modelled here.
- x-variable (explanatory)
- Can be EITHER discrete or continuous.
- R²
- Explicitly NOT expected at this level (explanatory note 5) — do not spend report time on it.
- Non-linear relationships
- Explicitly allowed (note 4) — a curved relationship is a legitimate, gradeable finding, not a failure to find a line.
2 The cycle, and where each grade is won
Achieved covers the stages; Merit links them to context; Excellence integrates context throughout.| Stage | Achieved | Merit adds | Excellence adds |
|---|---|---|---|
| Problem | A relationship question | Both variables, units, population named | Why the relationship matters in this context |
| Plan | Data source described | Collection method and limitations | How the method shapes what can be concluded |
| Data | Scatter plot drawn and labelled | Description with data values as evidence | Unusual features explained from context knowledge |
| Analysis | Line fitted, r stated | Gradient interpreted in context and units | Model adequacy evaluated; other variables considered |
| Conclusion | Question answered | Evidence cited for the answer | Limitations, confounders, and what it cannot support |
The pattern down every column is the same: Achieved does it, Merit evidences it, Excellence reflects on it.
✕A perfect analysis with no context in it
The single most common ceiling. Correct plot, correct line, correct r — and not one sentence about what the variables actually are. NZQA's Merit criterion is "linking components of the statistical enquiry cycle to the context", so a report that could describe any two variables at all cannot pass Achieved.3 Describing the scatter: all five features, each with evidence
Trend, association, form, unusual features, scatter.A description that scores
- TREND: "as wingspan increases, body mass tends to increase" — direction, in context.
- ASSOCIATION: strong / moderate / weak, backed by r and by how tightly points cluster.
- FORM: linear, or curved — and say which, because it decides whether a straight line is even appropriate.
- UNUSUAL FEATURES: name the outlier by its coordinates, and say what it might be in context.
- SCATTER: does the spread about the line stay constant, or widen at one end? Widening scatter is itself a finding.
4 Evaluating the model: the route to statistical insight
Residual patterns, confounders and reflection — the most reliable Excellence route.What to check
- Curvature in the scatter that a straight line does not capture.
- Residuals: randomly scattered (good fit) or patterned (structure missed)?
- Where specifically does the model predict poorly?
- A plausible confounding variable, named and explained.
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.