Scatter Plot Maker

How the Scatter Plot Maker works

A scatter plot is the first chart to draw whenever you suspect two measurements are related. Each row becomes one point, x across and y up, and the shape of the cloud tells you more than any single statistic can: whether the relationship is a line or a curve, whether it holds for every group, and whether one odd value is doing all the work. It is the chart statisticians reach for before they fit anything, because a summary number computed without looking can be badly wrong.

Why looking beats summarising

In 1973 the statistician Francis Anscombe published four small data sets, now called Anscombe's quartet, that share the same means, the same variances, the same correlation (r = 0.816) and the same fitted line, y = 0.5x + 3. Plotted, they look nothing alike: one is a clean linear trend, one is a smooth curve, one is a perfect line spoiled by a single outlier, and one is a vertical stack with one far point creating the whole correlation. A 2017 follow-up, the "Datasaurus Dozen", made the same point with thirteen sets that share their statistics, one of which is shaped like a dinosaur. The lesson for everyday work is simple: plot first, quote numbers second.

Where scatter plots are used

Scientists plot dose against response, height against weight, or temperature against reaction rate. Economists plot income against life expectancy, the chart Hans Rosling made famous. Marketers plot ad spend against sales by month, and engineers plot load against deflection to find where a material stops behaving linearly. In quality control, a scatter plot of two machine settings often shows the interaction a table hides. Anywhere you have two numeric columns for the same rows, it is worth a look.

Preparing data for the scatter plot maker

The first numeric column is x and the second is y; the header row supplies the axis names unless you type your own. Any column that is not numeric is used to group the points: each distinct value gets a palette colour and a legend entry, so a Group or Region column can sit before, between or after the numbers. Rows missing an x or y value are skipped. Put the variable you control or that comes first in time on x, and the outcome on y; the trend line is fitted to predict y from x, and swapping the columns gives a different line.

Expert tips and pitfalls

Correlation is not causation. Ice cream sales and drownings rise together because both follow summer, not because one causes the other. A strong r tells you the points line up, never why.

Check for outliers before quoting r. One point far from the rest can turn r = 0.1 into r = 0.8. If removing a single row changes the story, say so, or report both figures.

r only measures straight-line relationships. Points on a perfect U-shaped curve can give r close to zero. If the cloud bends, the linear trend line is the wrong summary and the plot itself is the finding.

Watch for hidden groups. Two groups that each trend upwards can combine into a cloud that trends down, an effect known as Simpson's paradox. Adding a group column colours the points so you can see whether the pattern holds within each group or only across them.

Choose axes deliberately. Fit to data zooms each axis to the range of the values, which is what a scatter plot usually wants. From zero includes the origin, which is right when absolute size matters. Forcing zero on data clustered between 950 and 1,000 squashes the pattern into a line.

Match point size to the count. Small suits hundreds of points where overlap would hide density; Large suits a dozen on a slide. Points are drawn slightly translucent so clusters read darker where they overlap. For thousands of rows, a histogram of each column or a bubble chart that aggregates the points may read better.

How to read the result

Points is the number of rows plotted after skipping incomplete ones. Correlation r runs from −1 to 1: roughly, 0.1 to 0.3 is weak, 0.3 to 0.7 moderate and above 0.7 strong, with the sign giving the direction. Squaring it gives the share of the variation in y that a straight line explains, so r = 0.7 means about 49%. The trend line is the ordinary least-squares fit, the same line a spreadsheet's linear trendline draws, shown as y = mx + c. The slope m is how much y changes for each unit of x, in the units of your data; c is where the line crosses x = 0, which may be meaningless if zero lies far outside your data. Use the line to describe the data you have, and be cautious about extending it beyond the range you measured.

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