Bias vs Linearity vs Detection Limit (LOD / LOQ)
These three parameters are critical in method validation under ISO 17025 and determine the reliability and performance of laboratory analyzers.
1. Bias (Systematic Error)
Bias represents the difference between the measured value and the true value.
Bias = Measured Value − True Value
% Bias = (Bias / True Value) × 100
Example:
True value = 1.00 %
Measured value = 1.03 %
Bias = +0.03 %
% Bias = 3 %
- Caused by calibration drift
- Improper standard preparation
- Detector misalignment
- Systematic temperature effects
2. Linearity
Linearity indicates how well the instrument response corresponds to concentration across a specified range.
Linear regression: y = mx + c
Coefficient of determination: R² ≥ 0.995 (typical lab requirement)
- Evaluate minimum 5 calibration levels
- Check residual plots
- Verify no curvature
- Ensure detector not saturated
Poor linearity leads to inaccurate quantification even if precision is good.
3. Detection Limit (LOD)
LOD is the lowest concentration that can be reliably detected but not necessarily quantified.
LOD = 3.3 × (σ / S)
σ = Standard deviation of response
S = Slope of calibration curve
- Based on signal-to-noise ratio (~3:1)
- Below this level → result unreliable
- Used in environmental & trace analysis
4. Limit of Quantification (LOQ)
LOQ is the lowest concentration that can be quantified with acceptable precision and accuracy.
LOQ = 10 × (σ / S)
- Signal-to-noise ratio ~10:1
- Ensures acceptable RSD%
- Must be validated experimentally
Comparison Summary
Bias
Systematic deviation from true value.
Linearity
Consistency of response across concentration range.
LOD / LOQ
Lowest detectable and quantifiable limits.
Common Validation Mistakes
- Confusing precision with bias
- Accepting high R² without residual analysis
- Estimating LOD without statistical basis
- Using outdated calibration slope
Proper method validation ensures defensible laboratory results during audits.