# Presentation: 713840

## Youden Analysis

## 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 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

**Notes:**
Interesting – Youden was a statistician for bombing accuracy during World War II.

## Components of Youden Graph

**Notes:**
Youden’s analysis is directed toward interlaboratory comparisons of chemical testing.  These types of tests are more procedure dependent than that of mass measurements.  Youden’s main objective was to determine the precision of a procedure and expect all labs to meet this level of precision.  He also expected lab’s systematic errors to be small compared to the precision (random error).  However this type of analysis can be used effectively to evaluate mass measurements.  Remembering that in mass measurements it is usually the random errors that are small as compared to the systematic errors.
Also, note that the “origin” is not always (0,0).  In fact, the origin is only at (0,0) when ‘differences’ are used.  In most cases, the origin will be determined by the “best value” for the artifact, such as the NIST value (if available), the mean (average) value, or the median value.  The median value is most commonly used because it is not as vulnerable to ‘outliers’.
The advantage of using Youden Analysis is its unique ability to separate random & systematic errors.  An Error that is purely systematic will fall on the 45 degree line.  For example, if a lab’s mass standard is off by 2 mg, both artifacts will have a 2 mg error from the true value and will fall on the 45 degree line.

## Line Graphs to Youden Graphs

**Line Graphs to Youden Graphs**

**Notes:**
Lne Graphs have been the most common method of graphing round robin results.  However, when the data allows, Youden Graphs can provide valuable information to the participants concerning possible systematic errors.
This slide illustrates how data can be taken from line graphs and used to create a Youden Graph (must meet certain criteria first).
Data from one artifact is graphed on the X-axis and data from the another artifact is graphed on the Y-axis.

## Systematic and Random Components

**Notes:**
Youden’s method of determining vector lengths were approximations and were designed for ease of use.  In the early 1960’s all calculations were done by hand with the use of a slide rule (slip-stick).  Now, with the availability of calculators and computers the vectors can be easily defined.  Modifications to Youden’s original methods have been made and the vectors and their associated intercept points are now calculated by using formulas for the “distance between two points” , the Law of Sines”, and Pythagorean formulas for right triangles.

## Systematic and Random Components

**Systematic and Random Components**

**Notes:**
There are many different methods to calculate the vectors we need, the methods used here are just the ones that came to mind first.

***This portion of the training needs to be refined and redefined in future presentations to show the “actual” random & systematic components that comprise the total error as shown in the calculations and graph on the next two slides.

## 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**

**Notes:**
The absolute value of the “systematic component” added to the “random component” must be fitted to the Error Vector.
Using the Law of Sines for triangles, it can be verified that this “ratio method” is valid.
The next slide shows the “actual” random error.

## Where do we get the Circle?

**Random Error**
**=2.60**

- Each Point will have a “Random Error”

**Notes:**
A horizontal line drawn from the “45 degree intercept point” to the error vector shows the proper random and systematic components.

A Circle is defined by its origin (or center) and by its radius.  The origin is determined by the “true” values of artifact#1 and artifact#2.  The radius of the circle is based on the standard deviation of the lab random errors.  This standard deviation of the random errors is then multiplied by a confidence factor that should make the circle contain 95% of all points IF the systematic errors were eliminated.
The next slide shows the calculations for determining the standard deviation of the random errors and the radius of the circle.

## (Youden’s) Calculating the radius of the Circle

- 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**

**Notes:**
THIS SLIDE IS CURRENTLY HIDDEN.

FORMULA NEEDS TO BE CHECKED.

THE FORMULA LOOKS LIKE A ‘STANDARD DEVIATION’ FORMULA BUT IT DOES NOT USE RESIDUALS.

## (modified) Calculating the radius of the Circle

- 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**

**Notes:**
(This slide is self-explanatory)

## Getting the Circle on the Graph

- Formula of a Circle

- Formula rewritten in terms of  y

**Notes:**
We use the “Formula for a Circle” to calculate points on the circle.  X and Y will be offset by the value for artifact#1 and artifact#2.

(The bottom formula is a hyperlink to a spreadsheet to show the layout of data used to draw the circle on the graph)

## 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)

**Notes:**
(Self-explanatory)

(Don’t over-analyze:  This should be expanded when more training time is allowed.)

## Let’s take a look at the Spreadsheet

**Notes:**
We will now take a look at a Youden Spreadsheet.  And we will attempt to perform a file transfer so each of you may have a copy.  The Spreadsheet is still being developed, so if you have any suggestions (after you have time to explore) let me know and I will try to incorporate the changes and keep the spreadsheet updated.  Maybe we could have it as a “downloadable” on the OWM website.

(“Spreadsheet” is a hyperlink to the Youden Spreadsheet)