Scatter Diagram

A scatter diagram is the simplest tool for answering one of the most common shop-floor questions: do these two things actually move together? Most quality investigations have a moment where the team suspects that one variable, coolant temperature, ambient humidity, supplier lot number, is driving a problem in another variable, dimension, hardness, color. Theories pile up. A scatter diagram is the fastest way to test them. Forty paired measurements and twenty minutes of drawing is usually enough to separate the suspects worth investigating from the dead ends.

"Two variables, forty pairs, twenty minutes. The dots will tell you which theories are worth chasing."

How a scatter diagram works

A scatter diagram is built one paired observation at a time. The team picks two variables they suspect are related and collects matched measurements from the same moment or batch. Forty pairs is a reasonable minimum; below that, the pattern is mostly noise. Above sixty or eighty, patterns become clear if they exist.

Each pair becomes a single dot on the chart. One variable goes on the X axis, the other on the Y. As the dots accumulate, a pattern emerges or fails to emerge:

• A rising cloud from lower-left to upper-right means the two variables move together. Higher X, higher Y. Positive correlation.
• A falling cloud from upper-left to lower-right means the two variables move oppositely. Higher X, lower Y. Negative correlation.
• A formless blob with no clear direction means the variables are not related, at least within the range of the data collected.
• A curved or U-shaped pattern means there is a relationship, but not a simple linear one. Common with temperature variables that have an optimum range.

The diagnostic value of the scatter diagram is that it cheaply confirms or denies a theory. A theory the team had assumed for months can be falsified in twenty minutes of plotting. A theory nobody had considered can become visible when an unexpected correlation appears.

The trap is causation. A correlation on a scatter diagram tells you the variables move together. It does not tell you that one causes the other. A third variable may be driving both. The scatter diagram is the start of an investigation, not the end.

Where a scatter diagram fits on the shop floor of a small manufacturer

Imagine a 30-person sheet metal fab shop where a critical weld profile has been drifting. The team has three theories: the gas regulator is creeping, the operator's technique varies, or the ambient humidity in the shop is the issue. Without data, the loudest theory tends to win arguments. With a scatter diagram, the team can test all three in a week.

The inspector measures weld penetration and pairs it with humidity, regulator pressure, and operator on each shot. Forty pairs collected over a week. Three scatter diagrams drawn on grid paper at the inspection station. The humidity diagram shows a formless cloud. The operator-vs-penetration diagram shows minimal pattern. The regulator pressure diagram shows a clear positive cloud climbing from lower-left to upper-right. Pressure is the suspect.

The shop installs a small regulator-stability check at the start of each shift and continues to log measurements for the next two weeks. The drift stops. The other two theories, both confidently held before the experiment, were dead ends. That is what a scatter diagram does. It lets a small team test theories cheaply rather than committing to changes based on the loudest voice.

Common mistakes with scatter diagrams

• Treating correlation as causation. A clear pattern means the variables move together. It does not prove that one causes the other. A confirmed correlation is the start of an investigation, not the end.
• Too few data points. Fewer than thirty pairs and the pattern is noise. Aim for forty to sixty.
• Mismatched time scales. A once-a-day measurement plotted against an hourly one produces meaningless dots. Match the sampling interval.
• Plotting without a hypothesis. The diagram tests a specific theory. Plotting random pairs of available data and hunting for patterns is fishing, and it will find false positives.
• Stopping at the diagram. Confirm the suspected cause with a follow-up experiment or by intervening on the variable and seeing if the dependent variable responds.

Scatter diagram and related Lean tools

A scatter diagram is one of the seven basic quality tools and complements a control chart, which monitors a single variable over time. The shape of an individual variable's distribution is captured by a histogram. The paired data that feeds a scatter diagram usually comes from a check sheet where two variables are logged side by side.