What's the Difference Between Accuracy and Precision?
Accuracy and precision are two fundamental concepts in measurement, signal processing, statistics, and engineering.
Although they are often used interchangeably in everyday conversation, they describe completely different characteristics of a measurement system.
Accuracy
Accuracy describes how close a measured value is to the true value.
If measurements are close to the actual target value, the system is considered accurate.
For example
| True Value | Measured Value | Accuracy |
|---|
| 100 | 99.9 | High |
| 100 | 70 | Low |
Thus accuracy is related to correctness.
Precision
Precision describes how consistently repeated measurements agree with each other.
If repeated measurements produce nearly the same result, the system is considered precise.
For example
| Measurement Set | Precision |
|---|
| 99.1, 99.2, 99.1 | High |
| 80, 95, 110 | Low |
Thus precision is related to repeatability or consistency.
Accuracy vs. Precision
These concepts are independent.
High Accuracy + High Precision → Ideal measurement system
Measurements: 100.1, 99.9, 100.0
- close to true value
- tightly grouped
High Precision + Low Accuracy → Calibration error, Systematic bias
Measurements: 80.1, 80.2, 80.1
- tightly grouped
- far from true value
Low Precision + High Accuracy (on average) → High random noise, Unstable measurement system
Measurements: 80, 100, 120
- average may be near true value
- measurements fluctuate heavily
Low Accuracy + Low Precision → Worst case
Measurements: 50, 120, 80
- scattered
- far from true value
Statistical Interpretation
Accuracy is mainly related to bias and systematic error.
Precision is mainly related to variance and random error.
In statistics,
Measurement = True Value + Bias + Random Noise
MSE (Mean Squared Error) = Bias2 + Variance
Signal Processing Perspective
In signal processing
- noise reduction techniques improve precision,
- calibration improves accuracy.
Averaging
Averaging multiple noisy measurements reduces variance.
Thus averaging improves repeatability, stability, and precision. However averaging does not automatically remove bias. So a system may become very precise but still inaccurate.
FFT and Spectral Analysis
In FFT measurements
Accuracy
FFT amplitude scaling must also be correct. Errors in sensor calibration, window scaling, reference values, and anti-aliasing filters can reduce accuracy.
Therefore, stable spectra do not necessarily mean accurate spectra.
Precision
Repeated FFT measurements showing nearly identical spectra indicate high precision and good statistical stability.
Welch averaging improves precision by reducing PSD variance.
Conclusions
Accuracy and precision describe different aspects of measurement quality.
- Accuracy refers to closeness to the true value
- Precision refers to repeatability and consistency
A good engineering system requires both accurate measurements and precise measurements.
In signal processing, calibration improves accuracy, while averaging and noise reduction improve precision. Understanding the distinction is essential for interpreting FFTs, PSD estimates, sensor measurements, and statistical analysis correctly.
Suggested Further Reading
You may also find these topics helpful:
What's the Difference Between Accuracy and Precision?
Accuracy and precision are two fundamental concepts in measurement, signal processing, statistics, and engineering.
Although they are often used interchangeably in everyday conversation, they describe completely different characteristics of a measurement system.
Accuracy
Accuracy describes how close a measured value is to the true value.
If measurements are close to the actual target value, the system is considered accurate.
For example
Thus accuracy is related to correctness.
Precision
Precision describes how consistently repeated measurements agree with each other.
If repeated measurements produce nearly the same result, the system is considered precise.
For example
Thus precision is related to repeatability or consistency.
Accuracy vs. Precision
These concepts are independent.
High Accuracy + High Precision → Ideal measurement system
Measurements: 100.1, 99.9, 100.0
High Precision + Low Accuracy → Calibration error, Systematic bias
Measurements: 80.1, 80.2, 80.1
Low Precision + High Accuracy (on average) → High random noise, Unstable measurement system
Measurements: 80, 100, 120
Low Accuracy + Low Precision → Worst case
Measurements: 50, 120, 80
Statistical Interpretation
Accuracy is mainly related to bias and systematic error.
Precision is mainly related to variance and random error.
In statistics,
Measurement = True Value + Bias + Random Noise
MSE (Mean Squared Error) = Bias2 + Variance
Signal Processing Perspective
In signal processing
Averaging
Averaging multiple noisy measurements reduces variance.
Thus averaging improves repeatability, stability, and precision. However averaging does not automatically remove bias. So a system may become very precise but still inaccurate.
FFT and Spectral Analysis
In FFT measurements
Accuracy
FFT amplitude scaling must also be correct. Errors in sensor calibration, window scaling, reference values, and anti-aliasing filters can reduce accuracy.
Therefore, stable spectra do not necessarily mean accurate spectra.
Precision
Repeated FFT measurements showing nearly identical spectra indicate high precision and good statistical stability.
Welch averaging improves precision by reducing PSD variance.
Conclusions
Accuracy and precision describe different aspects of measurement quality.
A good engineering system requires both accurate measurements and precise measurements.
In signal processing, calibration improves accuracy, while averaging and noise reduction improve precision. Understanding the distinction is essential for interpreting FFTs, PSD estimates, sensor measurements, and statistical analysis correctly.
Suggested Further Reading
You may also find these topics helpful: