$$T_n$$ True negative
$$T_p$$ True positive
$$F_n$$ False negative
$$F_p$$ False positive
$$S_p$$ Specificity $$\equiv \frac{T_n}{T_n+F_p}$$
$$S_n$$ Sensitivity $$\equiv \frac{T_P}{T_p+F_n}$$
$$P_\text{prev}$$ Prevalence $$\equiv T_p+F_n$$
$$\text{PPV}$$ Positive predictive value $$\equiv \frac{T_P}{T_p+F_p}$$
$$\text{NPV}$$ Negative predictive value $$\equiv \frac{T_n}{T_n+F_n}$$
$$\text{LR}{+}$$ Positive likelihood ratio $$\equiv\frac{S_n}{1- S_p}$$
$$\text{LR}{-}$$ Negative likelihood ratio $$\equiv\frac{ 1 - S_n }{S_p}$$

# Visualizing problems in binary classification

Photo credit to Icons8 Team

## Origins of the math behind this utility

This grapher implements equations from Test that lie, the article on STD testing shortcomings.

Recall that a binary classification test is any test which returns a pos/neg or yes/no result. This is in contrast to a quantitative test which returns a numerical measurement. This is the difference between a test that says "You are pregnant" and a test that says "The concentration of human chorionic gonadotropin in your urine is 20 ng/mL." A binary classification provides one of two results each time it is run and therefore the test has four possible outcomes: true positive (TP), true negative (TN), false positive (FP), and false negative (FN).

[Caption] Binary classification outcome chart otherwise known as a confusion matrix. From four outcomes (true positive, true negative, false positive, false negative), there are four conditional probabilities (positive predictive value, negative predictive value, sensitivity, and specificity).

## Inputs

All values must be greater than 0.00001 and less than 0.99999. When using the mirror-log scale, areas will not be proportional to probabilities; they will accentuate low probability spaces.

Show as
Prevalence $$P_\text{prev} =$$
Sensitivity $$S_n =$$
Specificity $$S_p =$$

## Outputs

$$T_p =$$ NvN
$$F_p =$$ NvN
$$T_n =$$ NvN
$$F_n =$$ NvN
$$\text{LR}{-} =$$ NvN
$$\text{LR}{+} =$$ NvN
$$\text{PPV} =$$ NvN
$$\text{NPV} =$$ NvN