SiliciumHex FieldKit

Problem Solving & Quality · Quality Tools

Scatter Diagram

Plot pairs of values — temperature against viscosity, speed against scrap — to see whether two variables move together before claiming a link.

  • Time30 min
  • FormatSolo
  • StageQuality Tools

Scatter Diagram: what it is and why it works

A scatter diagram plots pairs of measurements, a suspected input X on the horizontal axis and an output Y on the vertical, to show whether they move together. Each point is one unit, batch or time period on which both were measured. The pattern reveals direction (positive or negative), shape (straight, curved, threshold), strength (tight or loose) and any clusters or outliers. Coloring the points by line, shift or supplier often exposes groups that behave differently. A pattern is treated as a lead to confirm, never as proof of cause.

Teams often have both variables in their records but never put them on the same graph, so arguments about whether temperature or speed matters can run for months. A scatter plot answers the first question, whether there is any relationship in the range where we operate, in minutes. The correlation coefficient r summarizes the strength of a linear relationship, but the plot should always come first, because curves, clusters and outliers can make r misleading. A narrow range of X can hide a real effect, and a third factor can create a relationship with no direct causal link. Stratification separates groups, and on/off cause verification or a designed experiment establishes causation. Once a link is confirmed, a control chart can track X as a leading indicator.

What you need

  • A suspected input X and an output Y
  • At least 30 paired measurements taken on the same units or batches
  • Data covering the normal operating range of X
  • Labels for stratification: line, shift, supplier, source
  • A spreadsheet or statistics tool

What you get

  • A scatter plot with both axes labeled in units
  • A description of the pattern: direction, shape, strength, outliers
  • A stratified view if groups exist
  • Optionally, a correlation coefficient or fitted line
  • A decision on whether to confirm the link with a trial

When to use it

When a suspected cause and an effect are both measured but never compared.

How to do it, step by step

  1. Pick the suspected input (X) and the output (Y), measured on the same units or batches.
  2. Collect at least 30 pairs covering the normal operating range of X.
  3. Plot X on the horizontal axis and Y on the vertical; look for slope, curve, clusters or outliers.
  4. Stratify the points by color — line, shift, supplier — to reveal hidden groups.
  5. Treat a pattern as a lead, not proof: confirm the link with a controlled trial before acting.

Worked example: Filter cake moisture at a zinc concentrator

Illustrative scenario — figures are realistic but not from a real company.

A zinc concentrator must keep filter cake moisture below 9% to meet shipping and contract requirements. Moisture ranges from 7.5% to 10.5%. Operators believe it depends on filter-press cycle time, and the plant has been lengthening cycles, at the cost of filter capacity.

  1. The metallurgist chose two candidate Xs, press cycle time and the percentage of feed finer than 20 µm from the particle-size analyzer, with cake moisture from shift composite samples as Y.
  2. She compiled 64 pairs from eight weeks of shift data, covering the normal range of both variables and allowing for the lag between the analyzer and the press.
  3. Cycle time against moisture gave a loose cloud with almost no slope across the operating range of 11 to 16 minutes.
  4. Fines against moisture showed a clear upward trend; cakes from feed above 30% fines were over 9% moisture almost every time. Colored by ore source, the high-fines points came mostly from one pit area.
  5. Treating this as a lead, the team ran a controlled trial, blending ore to change the fines content while holding cycle time fixed.

Result. The trial confirmed that moisture followed fines content, not cycle time, within the operating range. The plant returned to shorter cycles, recovering about a tenth of its filter capacity, and began blending ore from the high-fines pit area. One afternoon of plotting existing records had shown what months of adjusting cycle time had not.

Open it in the FieldKit Problem Solving app → Get the Problem Solving template pack — join the waitlist

Common pitfalls and how to avoid them

  • Treating correlation as proof.Confirm the link with a controlled trial, and ask what third factor could be driving both variables.
  • Too narrow a range of X.Collect data across the full operating range; a small range can hide a real relationship.
  • Mismatched pairs.Make sure X and Y refer to the same unit, batch or time window, allowing for process lag.
  • Relying on r without looking at the plot.Always inspect the chart first; a single outlier or a curve can make the correlation coefficient misleading.

Frequently asked questions

What does a scatter diagram show?

It shows whether two measured variables are related: whether Y tends to rise or fall as X changes, how strongly and in what shape. It also reveals clusters, outliers and thresholds that summary statistics hide. In quality work, it is used to check whether a suspected cause varies with the effect before investing time and money in a controlled trial.

How many data points do you need for a scatter diagram?

A common rule of thumb is at least 30 pairs, spread across the normal operating range of X. Fewer points can show a strong relationship but make weaker ones hard to judge. Coverage matters more than the count: points bunched in a narrow band of X say little about what happens outside that band.

What is a good correlation coefficient?

It depends on the process and the purpose. The coefficient r ranges from −1 to +1: values near zero mean no linear relationship, values near ±1 a strong one. r² gives the share of the variation in Y associated with X in a linear fit. Interpret r only after looking at the plot, and remember that even a high r does not prove causation.

Origin

Scatter diagram — one of the seven basic quality tools (Ishikawa, JUSE); correlation after Francis Galton and Karl Pearson, 1880s–1890s.

Related methods

More in “Quality Tools”

The statistical and risk tools of industrial quality: Pareto, SPC, capability, measurement, FMEA.