26134 · Responsible Evidence-based Decisions
Communicating Insights from Data
Week 2 completes Module 1 by pairing description with honest communication: which chart suits which data, the principles of good visual design, and the classic ways graphs mislead. It also picks up skewness and correlation from Week 1. This is examinable short-answer territory that students often under-prepare — expect an exam item that asks you to spot a truncated axis or explain percentage points vs percent change.
What this chapter covers
- 01Choosing a chart: bar chart (categorical), histogram (grouped numerical), scatterplot (two numerical), and why pie charts are often a poor choice
- 02Correlation: Pearson r = cov(x,y)/(sₓs_y), range −1 to +1, measures LINEAR association only
- 03Correlation ≠ causation and spurious correlation
- 04The truncated-axis fallacy: bar charts must start the y-axis at zero
- 05Percentage points vs percent (relative) change; absolute vs relative risk
- 06Exploratory vs explanatory messaging; knowing your data before you present
- 07Principles of visual design: pre-attentive attributes, reducing chart junk, visual hierarchy
Reading a misleading bar chart
- +1Name the flaw. The y-axis is truncated (starts at 34% instead of 0). Because a bar's LENGTH encodes magnitude, cutting the baseline exaggerates a small change into a large visual jump — the reader over-reads the difference.
- +1Absolute change. 38.5% − 34% = 4.5 percentage points. This is the honest 'size' of the move on the original scale.
- +1Relative change. (38.5 − 34)/34 × 100 = 4.5/34 × 100 = 13.2%. So the correct reading is 'up 4.5 percentage points, about a 13% relative rise' — not a 'surge'. Redrawing with the axis from 0 shows the bars are nearly the same height.
Key terms
- Pearson correlation coefficient (r)
- A unitless measure of LINEAR association between two numerical variables, r = cov(x,y)/(sₓs_y), ranging from −1 (perfect negative) through 0 (no linear relationship) to +1 (perfect positive). An r near 0 does not rule out a strong non-linear relationship.
- Correlation vs causation
- A correlation between two variables does not prove one causes the other; both may be driven by a third factor, or the link may be coincidental (a spurious correlation). Establishing causation needs more than an observed association.
- Truncated-axis fallacy
- Starting a bar chart's value axis above zero so that small differences in bar length look large. Because bar length encodes magnitude, the baseline must be zero; truncating it visually exaggerates the change.
- Percentage points vs percent change
- A change from 34% to 38.5% is 4.5 percentage points in absolute terms but (4.5/34) ≈ 13% in relative terms. Percentage points measure the raw gap; percent change measures the gap relative to the starting value.
- Pre-attentive attributes
- Visual features the eye processes almost instantly — colour, size, position, length, orientation. Used deliberately, they direct a reader's attention to the key message; overused, they add clutter (chart junk).
- Exploratory vs explanatory analysis
- Exploratory work is for the analyst still discovering what the data say; explanatory communication presents a specific, known finding to an audience. The audience and purpose change which chart and how much annotation you use.
Communicating Insights from Data FAQ
Why are pie charts often a bad choice?
Humans compare angles and areas poorly, so it is hard to judge which slice is larger, especially with many similar slices. A bar chart, where length is easy to compare on a common baseline, usually communicates the same categorical data more clearly. Reserve pie charts for a few slices with very different sizes, if at all.
Does a correlation of zero mean the variables are unrelated?
No — it means no LINEAR relationship. Two variables can have r near 0 yet be strongly related in a curved (non-linear) way, for example a U-shaped pattern. Always look at the scatterplot, not just r, before concluding there is no association.
How do I present a statistic responsibly?
Attach the context a reader needs: is it a sample or the whole population, mean or median (use the median for skewed data like income), the time period, the units, and the source and any limitations. Distinguish absolute from relative change, and avoid design choices like a truncated axis that overstate the finding.
Can AI help me with data communication in 26134?
Yes, as a study aid. Sia can explain when to use a bar chart versus a histogram or scatterplot, walk you through spotting a misleading axis, and check your percentage-points-versus-percent reasoning on practice items. Use it to rehearse the concepts; it does not complete your graded assignment, and the UTS academic-integrity policy applies.
Exam move
This week is conceptual but fully examinable, so build a short checklist rather than memorising slides. For every chart, ask: right chart for the data type? Does the bar axis start at zero? Is the change reported in percentage points AND relative percent? Is a correlation being treated as causation? Practise writing one-sentence critiques of misleading graphics and one-sentence 'responsible' rewrites, because that is exactly the exam's short-answer form. Keep the correlation formula and the percentage-points-vs-percent distinction on your printed notes. When a concept feels vague, ask Sia to generate a fresh misleading-chart example and talk you through the fix; confirm assessment details on Canvas.
Working through Communicating Insights from Data in 26134? Sia is AskSia’s AI Statistics tutor — ask any 26134 Communicating Insights from Data question and get a clear, step-by-step explanation grounded in how 26134 is taught and assessed. Read this chapter free, then take your hardest questions to Sia.
