Scatterplots, Correlation and Inference

A scatterplot puts one dot on the page for each thing measured, positioned by two of its values at once. Here each dot is a single pine tree, placed by how wide its trunk is and what percentage of its bark is smooth. The cloud of dots slopes downwards, which tells you that wider trees tend to have less smooth bark. Tend to is exactly the right phrase, because plenty of individual dots sit well off the trend, and an option that says all or every is usually wrong for that reason.

To read a value, go across from the number on the side axis until you meet the cloud, then drop down to the bottom axis. Here forty holes per square metre corresponds to dots sitting around forty-five per cent smooth bark. Notice you get a rough region rather than an exact point, because the dots scatter — so the honest answer is about forty-five. The options are written knowing that, and if one of them demands more precision than the cloud can give, that is a sign it is not the answer.

The hardest version gives you two graphs and asks something that neither answers on its own. Here nothing links beetle holes directly to trunk diameter — but smooth bark appears on both graphs, so it is the bridge. Forty holes per square metre corresponds to about forty-five per cent smooth bark on the first graph, and forty-five per cent smooth bark corresponds to a trunk of about twenty-five centimetres on the second. The move is always the same: find the quantity that appears on both graphs and route your answer through it.

Most consistent with the data means test each claim against the picture, one at a time. The claim that fewer beetles feed in mostly smooth-barked trees matches the downward slope, so it survives. A claim that all trees have both bark types dies the moment you find a dot at nought or a hundred per cent — one dot is enough. A claim that bark type does not affect feeding contradicts a clear slope. And watch for claims that are about the other graph entirely, which is a favourite trick when two graphs are given.

The last idea is the one that decides the hardest items. A scatterplot can show that two things move together; it can never show that one causes the other. So the claim that trees with more smooth bark tend to have fewer holes is safe, while the claim that smooth bark stops beetles feeding is not — something else could explain both, such as older trees being both wider and rougher. Prefer the weakest claim the data supports. Words like tend to, most and about tend to survive, while all, every and causes usually do not. Quiz and exercises now.