# Accuracy Calculator

## Accuracy

Understanding statistical metrics is crucial when evaluating the performance of algorithms or systems. Whether it's gauging the precision of a prediction or understanding the sensitivity of a model, these metrics provide valuable insights. This guide demystifies terms such as `Recall,` `Precision,` `Accuracy,` and more. Dive in to grasp these concepts and learn how to adeptly use the Accuracy Calculator.

## How to use the Accuracy Calculator?

The Accuracy Calculator is intuitive and user-friendly:

**Input Data:**Start by entering the values for True Positives, True Negatives, False Positives, and False Negatives.**Calculate:**After entering your data, all the calculations would be done automatically.**Interpret Results:**The calculator will instantly display various metrics. To comprehend these results, refer to the definitions and formulas provided below.

## Defining Key Statistical Metrics

Let's delve into the significance of each metric:

**Accuracy:**Represents the overall correctness of predictions.**Precision:**Showcases the proportion of true positive predictions to the total predicted positives.**Recall (Sensitivity):**Highlights the proportion of true positive predictions to all actual positives.**F1-Score:**Harmonic mean of Precision and Recall, providing a balance between them.**Specificity:**Indicates the proportion of true negative predictions to all actual negatives.**False Positive Rate:**Represents the proportion of false positives to all actual negatives.**Negative Predictive Value:**Depicts the proportion of true negative predictions to total predicted negatives.**Matthews Correlation Coefficient (MCC):**A metric that provides insights into the quality of binary classifications.**Prevalence:**Indicates the actual occurrence of the positive class in the dataset.**Percent Error:**Shows the percentage of predictions that were incorrect.**Prevalence-Based Accuracy:**Accuracy adjusted based on the prevalence of classes.**Balanced Accuracy:**Arithmetic mean of sensitivity and specificity.

## Formulas for Calculations

Understand the mechanics of the Accuracy Calculator with these formulas:

Accuracy:\text{Accuracy} = \dfrac{TP + TN}{TP + TN + FP + FN}

Precision:\text{Precision} = \dfrac{TP}{TP + FP}

Recall:\text{Recall} = \dfrac{TP}{TP + FN}

F1-Score:\text{F1-Score} = 2 \cdot \dfrac{Precision \cdot Recall}{Precision + Recall}

Specificity:\text{Specificity} = \dfrac{TN}{TN + FP}

False Positive Rate:\text{False Positive Rate} = \dfrac{FP}{FP + TN}

Negative Predictive Value:\text{Negative Predictive Value} = \dfrac{TN}{TN + FN}

Matthews Correlation Coefficient (MCC):MCC = \dfrac{TP * TN - FP * FN}{\sqrt{(TP + FP)(TP + FN)(TN + FP)(TN + FN)}}

Prevalence:\text{Prevalence} = \dfrac{TP + FN}{\text{Total observations}}

Percent Error:\text{Percent Error} = \dfrac{FP + FN}{Total observations} \cdot 100

Prevalence-Based Accuracy:\text{Prevalence-Based Accuracy} = \text{Prevalence} \cdot \text{Sensitivity} + (1 - \text{Prevalence}) \cdot \text{Specificity}

Balanced Accuracy (continued):\text{Balanced Accuracy} = \dfrac{\text{Sensitivity} + \text{Specificity}}{2}

Each of these formulas plays a crucial role in understanding the performance of a predictive model. By using the Accuracy Calculator, users can derive these metrics effortlessly, ensuring accurate interpretations and better decision-making.

In the realm of data science, machine learning, and analytics, understanding the above metrics is pivotal. Whether you're evaluating a machine learning model's performance or assessing the results of a medical test, these statistics provide a comprehensive view of accuracy and related metrics. Dive deep, use them wisely, and ensure that your predictions and interpretations stand on solid ground.

## Tags

- Probability and Discrete Distributions
- Continuous Distributions and Data Visualization