Accuracy and precision are two distinct but related concepts in the context of measurements and data analysis. They describe different aspects of the quality of a measurement process or system.

 

1. Accuracy:

   • Accuracy refers to how close a measured or observed value is to the true or accepted value. It is an indication of the correctness of the measurement.
   • Inaccuracy implies a systematic error, meaning there is a consistent deviation from the true value in the same direction.
   • Example: If a scale consistently reads 1 kg higher than the true weight, it is accurate but not precise.

2. Precision:

   • Precision, on the other hand, refers to the degree of repeatability or reproducibility of a set of measurements. It measures the consistency or variability of measurements.
   • Precision is not concerned with how close the measurements are to the true value, but rather with how close repeated measurements are to each other.
   • Lack of precision implies random errors, where measurements vary widely even if their average is close to the true value.
   • Example: If a scale consistently reads weights with slight variations (e.g., 1.000 kg, 1.002 kg, 0.998 kg), it is precise but not necessarily accurate.

3. Visualization with Targets:

   • The blue dots represent accurate and precise measurements, as they are close to the center (target or true value) and clustered together.
   • The red dots represent accurate but not precise measurements, as they are close to the center but scattered.
   • The green dots represent precise but not accurate measurements, as they are clustered but not close to the center.

4. Mathematical Representation:

   • Accuracy can be quantified using metrics such as bias or percent error, which indicate the deviation of measurements from the true value.
   • Precision is often quantified using measures of variability, such as standard deviation or coefficient of variation, which indicate the spread of measurements.

 

In summary, accuracy relates to the correctness of measurements, indicating how close they are to the true value. Precision relates to the consistency or reproducibility of measurements, indicating how closely repeated measurements agree with each other. A measurement system can be accurate, precise, both, or neither, depending on the characteristics of systematic and random errors in the measurements.

 

Thank you.