Caution 1 · Vertical axis
Same data, two stories
A 4-point gap looks huge when the axis starts at 90. Starting above zero exaggerates variation, although it can be useful for showing small-scale trends.
Module 7: Graphics and Correlation
Chapter 5, Sections D and E · Read graphs without being fooled, and know when a correlation means cause.
- Homework 7 Sun, Oct 11
- Quiz 7 Mon, Oct 12
- Project 2 Fri, Oct 16
Part 1 · Reading and building graphs
Caution 2 · Perception
Length vs. area
The eye reads area. Doubling both the width and height of a picture makes it look four times as large. Pictographs and 3-D bars add decoration, not information.
Caution 3 · Scale choice
When to use an exponential scale
Each step multiplies by 10. Use it when the data span a very large range, so small and large values both remain visible.
Graphic type
Reading a stack plot
- Group A
- Group B
Two bands are equal when they are equally thick. The total grew most where the top edge climbs most steeply. A double bar graph makes group-to-group comparison easier.
Caution 4 · Uncertainty
Reading error bars
Each bar shows where a value probably lies. If one flat line passes through every bar, the data do not show a significant difference.
Infographics and surveys
Percent of a group
40% of 500 = 0.40 × 500 = 200
Each square is 10 students. Two similar percentages from one survey need not describe the same students.
Calculations
Formulas from graphs
Difference over a career
(A − B) × years
($60k − $40k) × 30 = $600,000
Percentage difference (B is the reference)
(A − B) ÷ B × 100%
(60k − 50k) ÷ 50k = 20% more
Rate per 1,000 (Project 2)
deaths ÷ population × 1000
Construct it yourself
Graph-building checklist
- Double bar graph: keep the requested bar order and axis range.
- One category from a stacked bar: use that segment only.
- Scatterplot: first-named variable on the horizontal axis.
- Label axes with units; use evenly spaced scales.
- Excel: select both columns, Insert → Scatter.
- Judging media graphics: check the source, date, labels, and scales.
Part 2 · Correlation and causation
Correlation · type and strength
What scatterplots tell you
Positive: both rise (or fall) together. Negative: one rises as the other falls. Strength: the closer the points hug a straight line, the stronger the correlation. State a conclusion cautiously: “higher X may be likely to go with lower Y.”
Correlation is not causation
Why do X and Y move together?
Example of a common cause: better health care both lowers infant mortality and raises life expectancy. Growth in overall population or time can raise two unrelated counts together.
Confidence in causality
How sure can we be?
“Beyond reasonable doubt” is not “beyond all doubt.”
Establishing causality · six guidelines
Building the case that X causes Y
- Effect tracks the cause even while other factors vary.
- Groups differing only in the cause differ in the effect.
- More of the cause gives more of the effect.
- Effect remains after ruling out other causes.
- Test with an experiment (animals, cells, or models if needed).
- Find the physical mechanism.
← Back to Module 7 lesson · Text version: Module 7 one-page summary · Lecture slides · © Andrew H. Volk 2026