Youden's plot

plot a Youden's Plot

The Youden plot is a graphical method to analyse inter-laboratory data, where all laboratories have analysed 2 samples. The plot visualises within-laboratory variability as well as between-laboratory variability.
For the original Youden plot (Youden WJ (1959) Graphical diagnosis of interlaboratory test results. Industrial Quality Control, 15, 24-28.) the two samples must be similar and reasonably close in the magnitude of the property evaluated. The axes in this plot are drawn on the same scale: one unit on the x-axis has the same length as one unit on the y-axis. Each point in the plot corresponds to the results of one laboratory and is defined by a first response variable on the horizontal axis (i.e. run 1 or product 1 response value) and a second response variable 2 (i.e., run 2 or product 2 response value) on the vertical axis. A horizontal median line is drawn parallel to the x-axis so that there are as many points above the line as there are below it. A second median line is drawn parallel to the y-axis so that there are as many points on the left as there are on the right of this line. Outliers are not used in determining the position of the median lines. The intersection of the two median lines is called the Manhattan median.
A circle is drawn that should include a percent (usually 95%) of the laboratories if individual constant errors could be eliminated. A 45-degree reference line is drawn through the Manhattan median. Moreover, there are two tangents to the circle and parallel to the 45° line.
Interpretation
Points that lie into the circle: only random error
Points that lie outside the circle but inside the tangents: systematic error
Points that lie near the 45-degree reference: very precise results
Points that lie near the 45-degree reference but outside the circle: very precise results but systematic error
Points that lie outside the tangents: gross errors