ETF5922 Chap.9 Exploring Patterns and Uncertainty
Exploring Patterns and Uncertainty
Patterns need support and spread
Exploration looks for distribution, association, clusters, unusual observations and gaps. A visible association is not evidence that one variable causes another.
Missingness changes confidence
Missingness can differ by group, so completeness belongs beside a summary.
Intervals and sensitivity views show how estimates vary across samples or analytical choices.
Qualify the visible difference
A mean can look stable even when many observations are absent.
Showing the observed count or missing proportion reveals whether groups have comparable support and prevents precision from being inferred from incomplete data.
Qualify the visible difference in context
Exploration should hold several evidence dimensions together.
Centre without spread can hide heterogeneous groups; association without raw points can conceal clusters; an outlier removed without investigation can reverse a conclusion; a summary without completeness can overstate support. Uncertainty displays help only when their meaning and assumptions are clear.
Sensitivity checks provide a practical discipline: vary a defensible treatment, retain unusual observations while investigating them, and note which patterns persist. The written claim should scale with observed support, separating a description of this dataset from a population statement or causal explanation the design cannot establish.
What this chapter covers
- 01
Exploration looks for distribution, association, clusters, unusual observations and gaps.
- 02
A visible association is not evidence that one variable causes another.
- 03
Missingness can differ by group, so completeness belongs beside a summary.
- 04
Intervals and sensitivity views show how estimates vary across samples or analytical choices.
- 05
Use distribution and association to frame the reader's task
- 06
Check cluster against outlier before styling
- 07
Explain how missingness changes the visible comparison
- 08
Audit interval without removing necessary context
Report pattern, support and missingness together
- 3Compute both group means from observed values.
- 1Report complete and incomplete observation rates beside those means.
- 2Show raw points because Group B rests on only two observations.
- 2Describe difference and uncertainty without claiming a population effect.
Key terms
- Distribution
- The shape, centre and spread of values considered together rather than as a lone average.
- Association
- The way two variables vary together, described without automatically implying causation.
- Outlier
- An unusual observation retained for investigation rather than deleted because it disrupts a story.
- Completeness
- The proportion and count of expected observations that are actually available for analysis.
Exploring Patterns and Uncertainty FAQ
Why should completeness sit beside a group mean?
A mean can look stable even when many observations are absent. Showing the observed count or missing proportion reveals whether groups have comparable support and prevents precision from being inferred from incomplete data.
How should an unusual observation be handled?
Retain it while checking measurement, context and influence. Compare summaries with the point present and flagged, not silently removed. If the conclusion changes materially, report that sensitivity. Distance from the main group alone does not establish that an observation is erroneous.
What can an uncertainty display legitimately claim?
It can communicate the variability, interval or support represented by its construction, provided assumptions and group completeness are clear. It cannot automatically establish a causal effect or population difference. Pair the visual with raw support when small samples or missingness make precision easy to overread.
Why show raw points with small groups?
Raw points expose sample size, overlap, clusters and unusual values that a mean can conceal. With unequal completeness, they also show that summaries rest on different amounts of evidence. Jitter or transparency may improve visibility, but the plot should not imply more observations or precision than the underlying groups contain.
Exam move
Construct two groups with different sample sizes, missingness and one unusual value. Compare raw points, summaries and an uncertainty display, then recompute results with the unusual value retained and separately flagged. Write a claim that reports centre, spread and completeness together. The goal is sensitivity reasoning, not finding a view that makes the groups appear maximally different.
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