Trueness

Trueness is the closeness of agreement between the average of an infinite number of replicate measured quantity values and a reference quantity value.

Trueness is not a quantity and therefore cannot be expressed numerically. Rather it is expressed as bias.

• Bias
  Bias is a measure of a systematic measurement error, the component of measurement error that remains constant in replicate measurements.
• Linearity
  Nonlinear bias is a component of bias that cannot be represented by a linear relationship between the measured and true values.
• Interferences
  Interference bias is a component of bias caused by nonspecificity attributable to the presence of a specific interfering substance.

Bias is a measure of a systematic measurement error, the component of measurement error that remains constant in replicate measurements.

The bias can be expressed in absolute measurement units or as a percentage relative to the known value. A point estimate is a single value that is the best estimate of the true unknown parameter; a confidence interval is a range of values and indicates the uncertainty of the estimate.

The bias is an estimate of the true unknown bias in a single study. If the study were repeated, the estimate would be expected to vary from study to study. Therefore, if a single estimate is compared directly to 0 or compared to the allowable bias the statement is only applicable to the single study. To make inferences about the true unknown bias you must perform a hypothesis test:

Estimate the trueness of a measurement system or measurement procedure.

1. Select a cell in the dataset.
2. On the Analyse-it ribbon tab, in the Statistical Analyses group, click Trueness.
   The analysis task pane opens.
3. In the Y drop-down list, select the measured quantity variable.
4. If there are multiple levels of measurement, in the By drop-down list, select the level variable, and then:
   • If the values are identifiers, select the Identifier, and then in the Assigned values grid, under the Value column alongside each level, type the value.
   • If the values are dilutions made by diluting a high pool or mixing high and low pools, select the Relationship, and then select Mixture, Dilution, or Addition based on how the levels were prepared. In the Assigned values grid, under the Value column for the first and/or last level, type the value (intermediate values are automatically calculated using relative values).
   • If the values are known/expected/assigned values, select the Known values.
5. If the reference materials package insert includes an estimate of the uncertainty of the assigned values, select the Uncertainty in assigned values check box, and then in the Assigned values grid, under the SE column for each level, type the value:
   • If the estimate is expressed as standard uncertainty or combined standard uncertainty, use the value.
   • If the estimate is expressed as a 95% confidence interval (CI) use the value CI/2, or if the confidence interval is expressed as upper and lower limits use the value (CI upper limit- CI lower limit)/2.
   • If the estimate is expressed as expanded uncertainty (U) with a coverage factor (% or k) use the value U/k. If coverage is 95%, use the value U/2; if coverage is 99%, use the value U/3.
6. Optional: To compare the bias against performance requirements:
   • If the allowable bias is a constant or proportional value across the measuring interval, select Across measuring interval, and then in the Absolute edit box, type the bias in measurement units, and/or in the Relative edit box, type the bias as a percentage (suffix with % symbol).
     Note: The allowable bias is the greater of the absolute bias and the relative bias for each level. Therefore, with a absolute bias of 5mg/dL and a relative bias of 10%, the allowable bias will be set at 5mg/dL for all values 0 mg/dL up to 50mg/dL and then at 10% of assigned value for values above 50mg/dL.
   • If the allowable bias varies for each level, select Each level and then in the Allowable bias grid, under the Absolute / Relative column alongside each level, type the bias in measurement units, or the bias as a percentage (suffix with % symbol).
   Note: To compare if the value of the reference material is equal to the assigned value, see Testing against an assigned value.
7. Click Calculate.

Test if the value of the reference material is equal to the assigned value; that is the bias is zero.

1. Activate the analysis report worksheet.
2. On the Analyse-it ribbon tab, in the Bias group, click Test Equality.
   The analysis task pane Trueness panel opens.
3. Optional: In the Significance level edit box, type the maximum probability of rejecting the null hypothesis when in fact it is true (typically 5% or 1%) and if required select the Familywise error rate check box.
   Note: CLSI EP15 uses a 5% familywise significance level so the overall significance level is a maximum of 5% regardless of the number of comparisons (for example, for 1 level the significance level is 5%, for 2 levels the significance level is 5%/2 = 2.5% for each level, for 3 levels the significance level is 5%/3 = 1.6% for each level).
4. Click Recalculate.

Test if the bias meets performance requirements; that is the bias is less than allowable bias.

1. Activate the analysis report worksheet.
2. On the Analyse-it ribbon tab, in the Bias group, click Test Equivalence.
   The analysis task pane Trueness panel opens.
3. Optional: In the Significance level edit box, type the maximum probability of rejecting the null hypothesis when in fact it is true (typically 5% or 1%) and if required select the Familywise error rate check box.
   Note: CLSI EP15 uses a 5% familywise significance level so the overall significance level is a maximum of 5% regardless of the number of comparisons (for example, for 1 level the significance level is 5%, for 2 levels the significance level is 5%/2 = 2.5% for each level, for 3 levels the significance level is 5%/3 = 1.6% for each level).
4. Enter the performance requirements:
   • If the allowable bias is a constant or proportional value across the measuring interval, select Across measuring interval, and then in the Absolute edit box, type the bias in measurement units, and/or in the Relative edit box, type the bias as a percentage (suffix with % symbol).
     Note: The allowable bias is the greater of the absolute bias and the relative bias for each level. Therefore, with a absolute bias of 5mg/dL and a relative bias of 10%, the allowable bias will be set at 5mg/dL for all values 0 mg/dL up to 50mg/dL and then at 10% of assigned value for values above 50mg/dL.
   • If the allowable bias varies for each level, select Each level and then in the Allowable bias grid, under the Absolute / Relative column, alongside each level, type the absolute bias in measurement units, or the relative bias as a percentage (suffix with % symbol).
5. Click Recalculate.

Nonlinear bias is a component of bias that cannot be represented by a linear relationship between the measured and true values.

A measurement procedure is linear when there is a mathematically verified straight-line relationship between the measured and true values. It is an important parameter as it allows linear interpolation of results between points.

Bias due to nonlinearity is measured as the difference between the linear fit and the best fitting polynomial fit.

Determine whether a measurement system or procedure provides measured quantity values (within a measuring interval) that are directly proportional to the true value.

1. Select a cell in the dataset.
2. On the Analyse-it ribbon tab, in the Statistical Analyses group, click Linearity.
3. In the Y drop-down list, select the measured variable.
4. In the By drop-down list, select the level variable, and then:
   • If the values are identifiers, select the Identifier, and then in the Assigned values grid, under the Value column alongside each level, type the value.
   • If the values are dilutions made by diluting a high pool or mixing high and low pools, select the Relationship, and then select Mixture, Dilution, or Addition based on how the levels were prepared. In the Assigned values grid, under the Value column for the first and/or last level, type the value (intermediate values are automatically calculated using relative values).
   • If the values are known/expected/assigned values, select the Known values.
   Note: Computation of linearity only requires the relationship between the levels, you do not need to enter the assigned values if they are unknown.
5. Optional: To compare the nonlinearity bias against performance requirements:
   • If the allowable nonlinearity bias is a constant or proportional value across the measuring interval, select Across measuring interval, and then in the Absolute edit box, type the bias in measurement units, and/or in the Relative edit box, type the bias as a percentage (suffix with % symbol).
     Note: The allowable bias is the greater of the absolute bias and the relative bias for each level. Therefore, with a absolute bias of 5mg/dL and a relative bias of 10%, the allowable bias will be set at 5mg/dL for all values 0 mg/dL up to 50mg/dL and then at 10% of assigned value for values above 50mg/dL.
   • If the allowable nonlinearity bias varies for each level, select Each level and then in the Allowable nonlinearity grid, under the Absolute / Relative column alongside each level, type the bias in measurement units, or the bias as a percentage (suffix with % symbol).
6. Optional: To change the polynomial fit, on the Fit Model panel, in the Fit drop-down list, select:

   Option	Description
   Best significant term polynomial (default)	Fits a 2nd- and 3rd-order polynomial fit, then determines if either are better than the linear fit by testing whether the nonlinear terms (polynomial fit coefficients) are statistically significant. The 3rd-order polynomial is used if it has significant nonlinear terms, the 2nd-order polynomial is used if it has significant nonlinear terms, otherwise the measurement procedure is assumed to be linear. Recommended by CLSI EP6.
   Forward stepwise polynomial LoF	Fits a linear fit and performs a lack-of-fit (LoF) significance test to determine how well the model fits the data. If the fit is significantly worse than expected, a 2nd-order polynomial is fit and the LoF test is repeated. If the 2nd-order polynomial fit is not significantly worse, it is used, otherwise a 3rd-order polynomial is fit. Recommended by Liu and others.
   Polynomial	Fits a polynomial model of given order.

   Note: If the precision of the measurement procedure is poor nonlinearity can be difficult to detect as neither of the polynomial fits will be significantly better than the linear fit, due to the amount of random error in the measurements.
7. Click Calculate.

Determine whether a measurement system or procedure provides measured quantity values (within a measuring interval) that are directly proportional.

1. Select a cell in the dataset.
2. On the Analyse-it ribbon tab, in the Statistical Analyses group, click Linearity.
3. In the Y drop-down list, select the measured variable.
4. In the By drop-down list, select the level variable, and then:
   • If the values are identifiers, select the Identifier, and then in the Assigned values grid, under the Value column alongside each level, type the value.
   • If the values are dilutions made by diluting a high pool or mixing high and low pools, select the Relationship, and then select Mixture, Dilution, or Addition based on how the levels were prepared. In the Assigned values grid, under the Value column for the first and/or last level, type the value (intermediate values are automatically calculated using relative values).
   • If the values are known/expected/assigned values, select the Known values.
   Note: Computation of linearity only requires the relationship between the levels, you do not need to enter the assigned values if they are unknown.
5. Optional: To compare the nonlinearity bias against performance requirements:
   • If the allowable nonlinearity bias is a constant or proportional value across the measuring interval, select Across measuring interval, and then in the Absolute edit box, type the bias in measurement units, and/or in the Relative edit box, type the bias as a percentage (suffix with % symbol).
     Note: The allowable bias is the greater of the absolute bias and the relative bias for each level. Therefore, with a absolute bias of 5mg/dL and a relative bias of 10%, the allowable bias will be set at 5mg/dL for all values 0 mg/dL up to 50mg/dL and then at 10% of assigned value for values above 50mg/dL.
   • If the allowable nonlinearity bias varies for each level, select Each level and then in the Allowable nonlinearity grid, under the Absolute / Relative column alongside each level, type the bias in measurement units, or the bias as a percentage (suffix with % symbol).
6. On the Fit Model panel, in the Fit drop-down list, select Linear.
7. In the X drop-down list, select Expected values and in the Y down list, select Mean.
8. In the Weights drop down list, select

   Option	Description
   None	Fit an ordinary regression. Use when measurement procedure exhibits constant SD over the measuring interval.
   Var(Y level)	Fit a weighted regression with weight based on the variance at each level. Recommended when number of replicates per level is 4 or more.
   Var(Y level pooled)	Fit a weighted regression with weight based on the pooled variance over a subinterval of levels. Recommended when number of replicates per level is 2 or 3.
   VarFn(Y)	Fit a weighted regression with weight based on the variance function at the mean of each level. Recommended when the precision can be modelled by a variance function.

9. If the levels are made by a dilution of a high level, select Force through zero check box. Otherwise, if the levels are produced by mixing a high and low level, clear the Force though origin check box.
10. Click Calculate.

Interference bias is a component of bias caused by nonspecificity attributable to the presence of a specific interfering substance.

Measurement systems analysis study requirements and dataset layout.