MedCalc  # Youden plot

 Command: Graphs Youden plot

## Description

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.

In medical literature you may encounter different graphs referred to as "Youden plot".

## Youden plots

### 1. The original Youden plot

For the original Youden plot (Youden, 1959) (see Figure 1) 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. Far out values are not used in determining the position of the median lines. A far out value is defined as a value that is smaller than the lower quartile minus 3 times the interquartile range, or larger than the upper quartile plus 3 times the interquartile range.

The intersection of the two median lines is called the Manhattan median.

A circle is drawn that should include 95 % of the laboratories if individual constant errors could be eliminated.

A 45-degree reference line is drawn through the Manhattan median.

Interpretation

Points that lie near the 45-degree reference line but far from the Manhattan median, indicate large systematic error.

Points that lie far from the 45-degree line indicate large random error.

Points outside the circle indicate large total error.

### 2. The Youden plot adapted for non-comparable samples

If two different products are being tested, MedCalc draws a Youden plot as described above, but the axes of the plot are not drawn on the same scale, but in this case, one standard deviation on the X-axis has the same length as one standard deviation on the y-axis (see Figure 2).

Analogous to the 45-degree reference line in the original Youden plot, a reference line is drawn which in this case represents a constant ratio of the two samples.

The interpretation is the same as for the original Youden plot.

### 3. Other variations of the Youden plot

A common variation of the Youden plot is a scatter diagram as described above, but the circle is replaced with one or more rectangles representing 1, 2 or 3SD on both the x-axis and y-axis (see Figure 3).

## The Youden plot dialog box Sample A and Sample B: select the variables for the first and second sample.

Filter: an (optional) filter to include only a selected subgroup of cases in the graph.

Options

• Areas - Circles:
90%, 95% or 99% Coverage probability: circles can be drawn that include 90%, 95% or 99% of the laboratories if individual constant errors could be eliminated.
Samples are similar: select this option if the samples similar and reasonably close in the magnitude of the property evaluated (this will give you the original Youden plot).
• Areas - Rectangles:
1 SD, 2SD or 3SD: draws rectangles representing 1, 2 or 3 SD on both the x-axis and y-axis.
• Outlier detection: MedCalc will detect outliers automatically and exclude them for calculations.
• Diagonal line: draws a diagonal reference line
• Subgroups: use the Subgroups button if you want to identify subgroups in the plot. A new dialog box is displayed in which you can select a categorical variable. The graph will use different markers for the different categories in this variable.

## Examples

 Fig. 1. The original youden plot. PR_A and PR_B represent similar samples. Notice the two outliers in the upper right corner of the graph. Circle represents 95% coverage probability. Fig. 2. Example of a Youden plot adapted for samples that are not similar. Circle represents 95% coverage probability. Fig. 3. Variation of Youden plot. The data are the same as in Figure 2. Rectangles represent 1 and 2 SD. ## Print all

To print multiple copies of the Youden plot, with each copy highlighting one laboratory:

• right-click in the Youden plot
• click Print all on the context menu To print the name of each laboratory on the graph, use the Select variable for case identification tool.

## Literature

• Youden WJ (1959) Graphical diagnosis of interlaboratory test results. Industrial Quality Control, 15, 24-28.