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Youden Plot

NIST/SEMATECH Section 1.3.3.31 Youden Plot

44 46 48 50 52 54 56 Run 2 Measurement 44 46 48 50 52 54 56 Run 1 Measurement Youden Plot1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
A Youden plot is a scatter plot used in interlaboratory studies that plots the result from one run or product against the result from a second run or product for each laboratory, with the lab identifier as the plot symbol. A 45-degree reference line is sometimes drawn to highlight departures from consistency between the two runs.

What It Is

A Youden plot is a scatter plot used in interlaboratory studies that plots the result from one run or product against the result from a second run or product for each laboratory, with the lab identifier as the plot symbol. A 45-degree reference line is sometimes drawn to highlight departures from consistency between the two runs.

Each laboratory is plotted as a single point with vertical coordinate = result from run/sample 1 and horizontal coordinate = result from run/sample 2. The plot symbol is the lab identifier (typically an integer from 1 to k). A 45-degree reference line is sometimes drawn: for two runs of the same product, labs producing consistent results should lie near this line. For two different products, the points should lie near some fitted straight line if the labs are consistent. Departures from the reference line indicate lab inconsistency.

Questions This Plot Answers

  • Are all labs equivalent?
  • What labs have between-lab problems (reproducibility)?
  • What labs have within-lab problems (repeatability)?
  • What labs are outliers?

Why It Matters

In interlaboratory studies or in comparing two runs from the same lab, it is useful to know if consistent results are generated. The Youden plot should be a routine plot for analyzing this type of data, as it separates between-lab systematic bias (points along the diagonal) from within-lab random variability (scatter perpendicular to the diagonal).

When to Use a Youden Plot

Use a Youden plot when analyzing data from interlaboratory comparisons, proficiency testing, or paired-sample studies where each laboratory or instrument produces two measurements under different conditions. The plot reveals whether laboratories that score high on one measurement also score high on the other, which would indicate a systematic between-laboratory bias. It is a standard tool in metrology and quality assurance for identifying laboratories whose measurement systems are consistently biased.

How to Interpret a Youden Plot

The horizontal axis shows the result from one run or product and the vertical axis shows the result from the other. Each point is labeled with its lab identifier. When two runs of the same product are being compared, a 45-degree reference line indicates where labs that produce identical results on both runs would fall — departures from this line indicate within-lab inconsistency. If two different products are being tested, the 45-degree line may not be appropriate, but consistent labs should still cluster near some fitted straight line. A tight cluster of points along the diagonal indicates that between-laboratory variability dominates, while a diffuse cloud with no diagonal trend indicates that within-laboratory variability dominates.

Assumptions and Limitations

The Youden plot requires paired measurements from each laboratory, typically two runs or two samples. It assumes that the two conditions are measured on comparable scales. The plot is most informative when the number of laboratories is moderate to large, typically 10 or more. When runs are on the same product, a 45-degree reference line is the natural baseline; when runs are on different products, a fitted straight line is more appropriate.

Reference: NIST/SEMATECH e-Handbook of Statistical Methods, Section 1.3.3.31

Python Example

import numpy as np
import matplotlib.pyplot as plt


# Generate paired lab comparison data (15 labs, 2 runs on same product)
rng = np.random.default_rng(42)
n_labs = 15
lab_bias = rng.normal(0, 2, n_labs)  # between-lab systematic bias
run1 = 50 + lab_bias + rng.normal(0, 0.8, n_labs)
run2 = 50 + lab_bias + rng.normal(0, 0.8, n_labs)


fig, ax = plt.subplots(figsize=(7, 7))


# Plot each lab with its identifier as the marker
for i in range(n_labs):
    ax.text(run2[i], run1[i], str(i + 1), ha='center', va='center',
            fontsize=10, fontweight='bold', color='steelblue')


# 45-degree reference line (NIST convention for same-product comparisons)
lims = [min(run1.min(), run2.min()) - 1,
        max(run1.max(), run2.max()) + 1]
ax.plot(lims, lims, 'r-', alpha=0.5, label='45-degree line')
ax.set_xlim(lims)
ax.set_ylim(lims)
ax.set_xlabel("Run 2 Result")
ax.set_ylabel("Run 1 Result")
ax.set_title("Youden Plot — Interlaboratory Comparison")
ax.legend(fontsize=9)
ax.set_aspect('equal')
ax.grid(True, alpha=0.3)
plt.tight_layout()
plt.show()