Scatter Graphs & Correlation

Activities to try

1. 1

   Scatter sandbox: tighten the cloud, then toggle a confounder

   Why it works: Strength of correlation is how closely points hug the line, not how steep the line is; and a real, strong correlation can exist between two variables when a hidden third variable drives both — so correlation alone never proves causation.

   1. Drag points on a scatter graph and watch a live 'strength' read-out and a best-fit line update as you move them.
   2. Stretch the whole cloud vertically (scale every y-value by the same factor) so the trend line gets steeper and the spread around it grows in proportion, and notice that the strength read-out stays the same; then pull the points closer to the line without changing its steepness and watch the strength increase.
   3. Move a single 'temperature' slider and watch it simultaneously push ice-cream sales UP and beach-swimming/drownings UP, so a strong positive correlation appears between ice cream and drownings even though neither causes the other.
   4. Turn the temperature slider back down and watch both variables fall together, showing that in this model, where temperature is built in as the common cause, the hidden variable drives both.
   5. For fresh correlated pairs, use a 'what else could explain this?' prompt to name any plausible confounder, and decide which of four explanations seems most plausible for each pair, giving a reason: direct cause, common cause, reverse cause, coincidence.
2. 2

   Argue it out with a sceptical scientist

   Why it works: Correlation-vs-causation is an argument you can make: a real link can be explained by a confounder, reverse cause, or coincidence, so you must give a reason rather than accept the causal story.

   1. Respond to a character who presents tempting causal claims drawn from correlations, e.g. 'Towns with more churches have more crime — so do churches cause crime?' or 'More firefighters are sent to bigger fires and there is more damage — so should we send fewer firefighters?'
   2. For each claim, explain in your own words what ELSE could account for the link besides one variable causing the other, and try to name the confounding common cause (e.g. town population; fire size).
   3. When pressed, state whether the correlation is real, and separately whether the causal claim follows from it.
3. 3

   Predict-observe-explain: the firefighters data

   Why it works: A correlation can be fully real yet not show the effect of one variable on the other, because a confounding variable (fire size; hot weather) drives both measured quantities — so changing one variable need not change the other in the way the correlation suggests (sending fewer firefighters would likely mean more damage, not less).

   1. Study data in which the number of firefighters sent to a fire is strongly positively correlated with the amount of damage caused.
   2. Before any discussion, WRITE your prediction and your REASON for this question: 'If the fire service sent FEWER firefighters to each fire, would there be less damage?' Commit to both prediction and reason first.
   3. Then observe the lurking variable — the SIZE of the fire — which drives both the firefighters sent and the damage, and compare it against your written reason.
   4. Finally, transfer the reasoning to a fresh pair: explain what could cause BOTH ice-cream sales and drownings to rise and fall together.