The data represent the results for a test for a certain disease. I assume one individual from the group is randomly selected. Find the probability of getting someone who tested negative given that here she had the disease. Probability is approximately: ____

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The data represent the results for a test for a certain disease. I assume one individual from the group is randomly selected. Find the probability of getting someone who tested negative given that here she had the disease.

Probability is approximately: ____

### Understanding Test Accuracy with Example Data

In medical diagnostics, understanding the accuracy of a test is crucial for proper diagnosis and patient care. The following table provides a summary of test results comparing the test outcome to the actual disease state of individuals.

#### Breakdown of Test Results

|                             | The Individual Actually Had the Disease |
|-----------------------------|-----------------------------------------|
|                             | Yes                                     | No                                      |
| Positive                    | 139                                     | 28                                      |
| Negative                    | 5                                       | 128                                     |

**Explanation:**

This table showcases the number of individuals who were tested for a particular disease and compares the test results (positive or negative) with the actual state of the disease (whether they truly had the disease or not).

- **True Positives (139):** This represents the number of individuals who tested positive for the disease and indeed had the disease.
- **False Positives (28):** This shows the number of individuals who tested positive for the disease but did not actually have the disease.
- **True Negatives (128):** This illustrates the number of individuals who tested negative for the disease and did not have the disease.
- **False Negatives (5):** This represents the number of individuals who tested negative for the disease but indeed had the disease.

Understanding these values is fundamental in assessing the test's sensitivity (true positive rate), specificity (true negative rate), and overall accuracy.

### Key Metrics Derived from the Table:

- **Sensitivity (True Positive Rate):** Sensitivity = (True Positives) / (True Positives + False Negatives) = 139 / (139 + 5)
- **Specificity (True Negative Rate):** Specificity = (True Negatives) / (True Negatives + False Positives) = 128 / (128 + 28)
- **Overall Accuracy:** Accuracy = (True Positives + True Negatives) / (Total Population) = (139 + 128) / (139 + 128 + 28 + 5)

By analyzing these metrics, healthcare professionals and researchers can better understand the efficacy of the diagnostic test and make informed decisions about its use in clinical practice.
Transcribed Image Text:### Understanding Test Accuracy with Example Data In medical diagnostics, understanding the accuracy of a test is crucial for proper diagnosis and patient care. The following table provides a summary of test results comparing the test outcome to the actual disease state of individuals. #### Breakdown of Test Results | | The Individual Actually Had the Disease | |-----------------------------|-----------------------------------------| | | Yes | No | | Positive | 139 | 28 | | Negative | 5 | 128 | **Explanation:** This table showcases the number of individuals who were tested for a particular disease and compares the test results (positive or negative) with the actual state of the disease (whether they truly had the disease or not). - **True Positives (139):** This represents the number of individuals who tested positive for the disease and indeed had the disease. - **False Positives (28):** This shows the number of individuals who tested positive for the disease but did not actually have the disease. - **True Negatives (128):** This illustrates the number of individuals who tested negative for the disease and did not have the disease. - **False Negatives (5):** This represents the number of individuals who tested negative for the disease but indeed had the disease. Understanding these values is fundamental in assessing the test's sensitivity (true positive rate), specificity (true negative rate), and overall accuracy. ### Key Metrics Derived from the Table: - **Sensitivity (True Positive Rate):** Sensitivity = (True Positives) / (True Positives + False Negatives) = 139 / (139 + 5) - **Specificity (True Negative Rate):** Specificity = (True Negatives) / (True Negatives + False Positives) = 128 / (128 + 28) - **Overall Accuracy:** Accuracy = (True Positives + True Negatives) / (Total Population) = (139 + 128) / (139 + 128 + 28 + 5) By analyzing these metrics, healthcare professionals and researchers can better understand the efficacy of the diagnostic test and make informed decisions about its use in clinical practice.
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