Youden Analysis

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Youden Analysis
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Youden Analysis

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

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W. J. Youden 1900-1971

• Born in Australia
• 1921 B.S. in Chemical Engineering
• 1924 Ph.D. Analytical Chemistry
• 1924-1948 Plant Research
• 1942-1945 World War II
• 1948 NBS Statistical Consultant

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Components of Youden Graph
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Line Graphs to Youden Graphs
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Systematic and Random Components
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Systematic and Random Components
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Fitting the Ratio of Systematic Random Errors
to the Total Error
Systematic Component -6.364 (negative or
positive) Random Component 3.536 (always
positive) Sum Random Systematic 9.900 Total
Error 7.280
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Where do we get the Circle?
Each Point will have a Random Error
Random Error 2.60
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(Youdens) Calculating the radius of the Circle
Each participants 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.)
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(modified) Calculating the radius of the Circle
Each participants 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.)
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Getting the Circle on the Graph

• Formula of a Circle

• Formula rewritten in terms of y

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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
• Dont Over-Analyze
• A point that lies outside the circle doesnt
  necessarily mean that there is a problem
  (although it is never a good thing)

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Lets take a look at the Spreadsheet