Estimating the linearity of a measurement procedure

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 check box, and then in the Assigned values grid, under the Value column alongside each level, type the value.
    • If the values are relative dilutions made by mixing high and low pools, select the Relative values check box, and then in the Assigned values grid, under the Value column for the first and 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 check box.
    Note: Computation of linearity only requires the relative values, 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.