Continuous improvement
Scatter diagram: read a process relationship
Read a scatter diagram using 36 published NIST calibration pairs. Inspect individual observations, the relationship and limits of the conclusion.
A scatter diagram plots paired numerical observations: one variable on the horizontal axis and another on the vertical axis. Each point must join values that belong to the same observation.
The plot can reveal shape, spread and unusual pairs. It cannot establish the effect of changing a process variable by itself.
NIST's scatter-plot guidance describes the relationship view. The pairing matters as much as the choice of axes.
Inspect published calibration observations
NIST's Norris dataset contains 36 observed pairs from ozone-monitor calibration. It names the variables x and y but does not state physical units in the data file. The figure keeps x and y as supplied.
The records range from x = 0.2 to x = 999.0. Readings near the high end can dominate the visual scale, so the figure also lets you inspect y − x.
NIST Norris calibration dataset / 36 observed pairs
Inspect each paired observation
The second view exposes y − x on a different, clearly labelled scale. Neither view establishes a process tolerance.
Observation 1: x = 0.2, y = 0.1. y − x = -0.1.
Inspect all 36 source pairs
| Observation | x | y | y − x |
|---|---|---|---|
| 1 | 0.2 | 0.1 | -0.1 |
| 2 | 337.4 | 338.8 | 1.4 |
| 3 | 118.2 | 118.1 | -0.1 |
| 4 | 884.6 | 888 | 3.4 |
| 5 | 10.1 | 9.2 | -0.9 |
| 6 | 226.5 | 228.1 | 1.6 |
| 7 | 666.3 | 668.5 | 2.2 |
| 8 | 996.3 | 998.5 | 2.2 |
| 9 | 448.6 | 449.1 | 0.5 |
| 10 | 777 | 778.9 | 1.9 |
| 11 | 558.2 | 559.2 | 1 |
| 12 | 0.4 | 0.3 | -0.1 |
| 13 | 0.6 | 0.1 | -0.5 |
| 14 | 775.5 | 778.1 | 2.6 |
| 15 | 666.9 | 668.8 | 1.9 |
| 16 | 338 | 339.3 | 1.3 |
| 17 | 447.5 | 448.9 | 1.4 |
| 18 | 11.6 | 10.8 | -0.8 |
| 19 | 556 | 557.7 | 1.7 |
| 20 | 228.1 | 228.3 | 0.2 |
| 21 | 995.8 | 998 | 2.2 |
| 22 | 887.6 | 888.8 | 1.2 |
| 23 | 120.2 | 119.6 | -0.6 |
| 24 | 0.3 | 0.3 | 0 |
| 25 | 0.3 | 0.6 | 0.3 |
| 26 | 556.8 | 557.6 | 0.8 |
| 27 | 339.1 | 339.3 | 0.2 |
| 28 | 887.2 | 888 | 0.8 |
| 29 | 999 | 998.5 | -0.5 |
| 30 | 779 | 778.9 | -0.1 |
| 31 | 11.1 | 10.2 | -0.9 |
| 32 | 118.3 | 117.6 | -0.7 |
| 33 | 229.2 | 228.9 | -0.3 |
| 34 | 669.1 | 668.4 | -0.7 |
| 35 | 448.9 | 449.2 | 0.3 |
| 36 | 0.5 | 0.2 | -0.3 |
NIST source observations and certified statistics
For the pair x = 884.6 and y = 888.0, the difference is 3.4 in the source variable scale. For x = 999.0 and y = 998.5, it is −0.5. A strong overall relationship can coexist with differences that deserve examination against the measurement decision.
Keep the meaning of the pair intact
| Check | Why it matters |
|---|---|
| Observation identity | Avoid joining one item's x value to another item's y value |
| Units and transformation | Prevent an apparent relationship caused by inconsistent scales |
| Operating group | Keep equipment, product or other recorded conditions available |
| Range | Avoid generalising beyond the conditions actually observed |
| Reference status | Establish whether either variable is a reference or simply another observation |
The Norris file supports inspecting the supplied pairs. It does not provide a modern operating tolerance or a complete measurement-system study. The Gage R&R guide explains the additional repeat and reference questions.
Examine patterns before adding a line
Look for curvature, changes in spread, separate groups and individual points that need a data check. Do not remove an inconvenient point merely because it weakens a relationship.
ASQ's scatter-diagram guidance warns that a third factor can affect both variables. A relationship can guide investigation without settling a causal explanation.
The regression Note fits the same published dataset and examines residuals. That adds a model with assumptions; it does not turn the scatter plot into evidence of a process intervention.
Use the plot to choose the next check
For a paired-measurement review, verify the join and units first. Then inspect where the differences matter to the intended decision and identify the reference evidence or repeat study needed to assess them.
Keep the point identities with the chart. They let someone return to the original record when the visual reveals a question worth investigating.