Test scores calculator

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Explanation

Sensitivity (True Positive Rate)

Definition: Sensitivity measures the proportion of actual positives that are correctly identified by the test. It reflects how good the test is at detecting positive cases.

Formula:

$$\text{Sensitivity} = \frac{\text{True Positives (TP)}}{\text{True Positives (TP)} + \text{False Negatives (FN)}}$$

Specificity (True Negative Rate)

Definition: Specificity measures the proportion of actual negatives that are correctly identified by the test. It reflects how good the test is at detecting negative cases.

Formula:

$$\text{Specificity} = \frac{\text{True Negatives (TN)}}{\text{True Negatives (TN)} + \text{False Positives (FP)}}$$

Positive Predictive Value (PPV)

Definition: PPV, or Precision, is the proportion of positive results that are true positives. It shows how often a positive test result is correct.

Formula:

$$\text{PPV} = \frac{\text{True Positives (TP)}}{\text{True Positives (TP)} + \text{False Positives (FP)}}$$

Negative Predictive Value (NPV)

Definition: NPV is the proportion of negative results that are true negatives. It shows how often a negative test result is correct.

Formula:

$$\text{NPV} = \frac{\text{True Negatives (TN)}}{\text{True Negatives (TN)} + \text{False Negatives (FN)}}$$

Positive Predictive Value (PPV) with Prevalence

Definition: PPV can also be expressed in terms of the prevalence of the disease, sensitivity, and specificity. Prevalence refers to the proportion of the population that has the disease. This formula incorporates the underlying prevalence to estimate how likely a positive result is truly positive.

Formula:

$$\text{PPV} = \frac{\text{Prevalence} \times \text{Sensitivity}}{\text{Prevalence} \times \text{Sensitivity} + (1 - \text{Prevalence}) \times (1 - \text{Specificity})}$$

Negative Predictive Value (NPV) with Prevalence

Definition: NPV can similarly be expressed using the prevalence of the disease. It represents the likelihood that a person with a negative test result truly does not have the disease, considering the disease's prevalence in the population.

Formula:

$$\text{NPV} = \frac{(1 - \text{Prevalence}) \times \text{Specificity}}{(1 - \text{Prevalence}) \times \text{Specificity} + \text{Prevalence} \times (1 - \text{Sensitivity})}$$

This allows PPV and NPV to be adjusted for the actual prevalence of the disease in the population, which provides more accurate interpretations when the disease is rare or common.

Accuracy

Definition: Accuracy measures the proportion of all correct test results (both true positives and true negatives) out of the total number of tests. It indicates the overall effectiveness of the test.

Formula:

$$\text{Accuracy} = \frac{\text{True Positives (TP)} + \text{True Negatives (TN)}}{\text{Grand Total}}$$

Accuracy with Prevalence

Definition: Accuracy can also be expressed using the prevalence of the disease, sensitivity, and specificity. This formula gives the overall probability that the test result (positive or negative) is correct, accounting for the prevalence of the disease in the population.

Formula:

$$\text{Accuracy} = (\text{Prevalence} \times \text{Sensitivity}) + ( (1 - \text{Prevalence}) \times \text{Specificity})$$

This formula combines both correct positive and correct negative classifications, weighted by how common the disease is in the population (prevalence). It's useful in situations where the disease prevalence is skewed, as it gives a more realistic overall performance measure of the test.