Youden Analysis

Introduction to W. J. Youden Components of the Youden Graph Calculations Getting the “Circle” What to do with the results.

W. J. Youden Born in Australia 1921 – B.S. in Chemical Engineering 1924 – Ph.D. Analytical Chemistry – Plant Research – World War II 1948 – NBS Statistical Consultant

Components of Youden Graph X Axis Y Axis2sd limit of the random components 45 degree Origin (0,0) Median(x,y) Known(x,y)

Line Graphs to Youden Graphs

Systematic and Random Components Plot the Point (-2,-7) X-axis = -2 Y- axis = -7 Total magnitude of Error = 7.28 Calculated by using the formula for the distance between two points (x1,y1) and (x2,y2): Draw a line from the Point to the 45 degree line (Perpendicular) Intercept Point

Systematic and Random Components Systematic Distance from Origin to Intercept Calculated by using a variation of the Pythagorean formula for 45 o right triangles: Origin=(x 1,y 1 ) Point = (x 2,y 2 ) Random Distance from Point to Intercept Calculated using the formula for the distance between two points:

Fitting the Ratio of Systematic & Random Errors to the Total Error Systematic Component = (negative or positive) Random Component = (always positive) Sum Random & Systematic = Total Error = 7.280

Where do we get the Circle? Random Error =2.60 Each Point will have a “Random Error”

Each participant’s point provides a perpendicular. Each perpendicular is squared. These squares are then summed and divided by n-1. The square root of this result is an indication of the standard deviation based only on the random components of each point. Multiplying the standard deviation by 2.45 gives the value for the radius of the circle. (95% of the points should fall within this circle if all systematic errors could be eliminated.) (Youden’s) Calculating the radius of the Circle

Each participant’s point provides a random error (ran). Each random error is squared. These squares are then summed and divided by n-1. The square root of this result is an indication of the standard deviation based only on the random components of each point. Multiplying the standard deviation by 2.45 gives the value for the radius of the circle. (95% of the points should fall within this circle if all systematic errors could be eliminated.) (modified) Calculating the radius of the Circle

Getting the Circle on the Graph Formula of a Circle Formula rewritten in terms of y

Rules of Youden Analysis Requires Two Artifacts –Must have two values to plot a point Artifacts must be same Nominal Value –“Cannot compare Apples & Oranges” Same procedure must be used to test both Artifacts –SOP - Restraint - Equipment - Metrologist Artifacts should not be Tested at Same Time –Random errors appear to become more systematic when tested at the same time Participants should be working at the same precision level Don’t Over-Analyze –A point that lies outside the circle doesn’t necessarily mean that there is a problem (although it is never a good thing)

Let’s take a look at the Spreadsheet Spreadsheet