Quantifying Errors

Instructions
Table explanation
Working Table (Javascript)
Cholesterol Example
Back to Worksheet 1
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  1. Fill in Mean (Y) column with mean values from Worksheet 1.
  2. Calculate Theoretical (X) values from instructions in table below, using Mixture 3 as a true value and calculating theoretical values for remaining pools/mixtures using the known relationship between the dilutions. Note: If Pool 1 is not zero or close to zero, the actual value of Pool 1 must be taken into account.
  3. Plot the theoretical values on the X axis and calculated means on the Y axis. Calculate the slope and intercept. Ideally, slope should be close to 1.00 and intercept close to 0.0.
  4. The bias for each level is calculated by subtracting the calculated mean (Y values) from the theoretical values. Percent error is calculated by dividing the bias by the theoretical value and multiplying by 100. Note: If Pool 1 is zero, the percent error calculation is not applicable.
  5. Compare the calculated slope and intercept to the desired slope and intercept of 1.00 and 0.0.
    Compare the bias and/or percent error for each pool/mixture to the allowable error for the test. Bias and percent error should be less than the allowable error. Make a decision on acceptability.

Table Explanation

Pool or Mixture Mean (Y) Theoretical (X) Bias % Error
Pool 1: 0 (enter mean value) (mean of Mix 3 x 0) (Y1 - X1) N/A
Pool 2: 25% (enter mean value) (mean of Mix 3 x 0.5) (Y2 - X2) ((bias2/X2) x 100)
Pool 3: 50% (enter mean value) (mean of Mix 3) 0 0
Pool 4: 75% (enter mean value) (mean of Mix 3 x 1.5) (Y4 - X4) ((bias4/X4) x 100)
Pool 5: 100% (enter mean value) (mean of Mix 3 x 2.0) (Y5 - X5) ((bias5/X5) x 100)

The Working Table (Javascript-automated calculations)

Simply enter the mean values in the blanks provided and the calculator will perform the rest of the calculations.

 

Pool or Mixture Mean (Y) Theoretical (X) Bias % Error

Cholesterol Example: Validation of Reportable Range Worksheet 2 1

Pool or Mixture Mean (Y) Theoretical (X) Bias % Error
Pool 1: 0 6 0 + 6 N/A
Pool 2: 25% 138 139 - 1 - 0.7 %
Pool 3: 50% 278 278 0 0
Pool 4: 75% 411 417 - 6 - 1.4 %
Pool 5: 100% 545 556 - 11 - 2.0 %

When the above points are plotted, the following graph results: