Lecture slides
The Module 7 slides on graphics and correlation.
Open slidesLearn the Concepts
1 · Reading graphics critically
A graph can be technically accurate and still mislead. Watch for:
- A vertical axis that doesn't start at zero — small differences look dramatic.
- Inconsistent or missing scales — unequal spacing distorts trends.
- Pictographs that scale area — doubling a value but drawing an image twice as tall and wide quadruples the apparent size.
- Missing labels or sources — you can't judge what you can't see.
Always ask: what are the axes, where do they start, and what is being compared?
Learn the Concepts
2 · Correlation vs. causation
Two variables are correlated when they tend to change together. On a scatterplot:
- Positive correlation — both rise together (points trend up).
- Negative correlation — one rises as the other falls (points trend down).
- No correlation — no clear pattern.
Correlation does not prove causation. A strong relationship can come from coincidence or, more often, a confounding variable that influences both. Establishing real causation requires ruling out other explanations — ideally with a controlled study.
Worked Examples
See it done, step by step
Example 1 — A bar chart's y-axis starts at 90 instead of 0. What's the effect?
Think about how the bar heights compare to the real values.
Values of 92 and 96 look like one bar is roughly twice the other, when the real difference is only about 4%. Truncating the axis exaggerates small differences.
Example 2 — Hours studied vs. exam score. What correlation would you expect?
Positive correlation — more study time generally goes with higher scores, so the scatterplot trends upward.
Example 3 — Ice cream sales and drownings both rise together. Does ice cream cause drowning?
Look for a confounding variable.
No. Both rise in hot summer weather — the confounding variable. The correlation is real, but neither causes the other.
Watch & Review
Resources for this module
Calculators
Check Yourself
Quick self-check
1. Towns with more firefighters tend to have more fire damage. Do firefighters cause damage?
No — the confounding variable is the size of the fire (or town): bigger fires bring both more firefighters and more damage.
2. Height vs. shoe size across many people: which type of correlation?
Positive correlation — taller people tend to have larger feet.
3. What's the quickest way a chart can exaggerate a difference?
Starting the vertical axis somewhere other than zero.
Ready to turn it in?
When you're confident reading graphs and relationships, complete the Module 7 homework and quiz in Canvas. This wraps up the material for Test 2.
Submit in Canvas