Precision vs Approximation: Difference and Comparison

Key Takeaways

1. Precision refers to exact, accurate results with minimal error, approximation provides estimated results that are “close enough”.
2. Precision requires more care, time, and effort to minimize uncertainty, approximation is faster and easier but less exact.
3. Precision is needed for sensitive measurements, approximation works for general estimates within an acceptable margin.

What is Precision?

In various fields such as statistics, machine learning, and engineering, precision refers to the measure of exactness or accuracy of a measurement, calculation, or estimate. It is commonly used in the context of evaluating the performance of classification models.

In the context of binary classification, precision is defined as the number of true positive results divided by the sum of true positive and false positive results. It quantifies the proportion of correctly predicted positive instances out of the total instances predicted as positive.

What is Approximation?

Approximation refers to the process of estimating or approaching a value, quantity, or result that may not be known exactly. It involves finding an approximate value that is close to the true value or within a certain range of it. Approximations are used when the exact calculation or measurement is difficult, time-consuming, or impractical.

The accuracy of an approximation depends on the specific method used and the assumptions made during the process. The level of approximation required will vary depending on the application or problem at hand, and it is essential to assess the trade-off between accuracy and computational complexity or feasibility.

Difference Between Precision and Approximation

1. Precision primarily refers to the accuracy and exactness of a measurement, calculation, or estimate. It involves obtaining the correct result or value without significant errors or variations. On the other hand, approximation refers to the process of estimating or approaching a value that may not be known exactly. It involves finding a close or reasonable value that is within a certain range of the true value.
2. Precision is a concept commonly used in various fields, such as statistics, machine learning, and engineering, to evaluate the accuracy of models or measurements. It focuses on the correctness of results. Approximation, on the other hand, is a broader concept used in different domains, including mathematics, physics, and everyday life, whenever an exact value is not readily available or practical to obtain.
3. The purpose of precision is to assess the exactness or correctness of a measurement or model’s predictions. It is used to quantify the accuracy of positive predictions compared to both true and false positives. Approximation, on the other hand, aims to provide an estimate or close approximation of a value when the exact value is unknown or difficult to obtain. It focuses on finding a value that is within a certain range of the true value.
4. Precision is evaluated through mathematical formulas, such as true positive divided by the sum of true positive and false positive results in binary classification. It is a quantifiable measure based on specific criteria. Approximation, on the other hand, involves various methods and techniques depending on the context, such as rounding, truncation, interpolation, or numerical methods. These methods provide an approximation of a value based on specific assumptions or simplifications.
5. Precision is commonly used in assessing the performance of classification models, evaluating the accuracy of measurements or experiments, or determining the correctness of calculations. It is particularly relevant in situations where false positives need to be minimized. Approximation, on the other hand, finds application in a wide range of scenarios where exact values are challenging to obtain, such as numerical calculations, scientific modeling, data analysis, or even everyday situations like estimating distances or quantities.

Comparison Between Precision and Approximation

Parameters of Comparison	Precision	Approximation
Focus	Accuracy and correctness of results	Estimating or approaching a value
Purpose	Assess the exactness of measurements/models	Provide an estimate when the exact value is unknown or impractical
Evaluation	Quantifiable measures based on specific criteria	Varied methods and techniques based on context
Application	Performance evaluation, measurements, calculations	Numerical calculations, modeling, data analysis
Criteria	Minimize false positives, maximize true positives	Close approximation within a certain range

References

1. https://www.aanda.org/articles/aa/abs/2020/03/aa37202-19/aa37202-19.html
2. https://ieeexplore.ieee.org/abstract/document/5363547/