# fart: The false alarm rate (or false positive rate) of a decision... In riskyr: Rendering Risk Literacy more Transparent

## Description

`fart` defines a decision's false alarm rate (or the rate of false positives): The conditional probability of the decision being positive if the condition is FALSE.

## Usage

 `1` ```fart ```

## Format

An object of class `numeric` of length 1.

## Details

Understanding or obtaining the false alarm rate `fart`:

• Definition: `fart` is the conditional probability for an incorrect positive decision given that the condition is `FALSE`:

`fart = p(decision = positive | condition = FALSE)`

or the probability of a false alarm.

• Perspective: `fart` further classifies the subset of `cond_false` individuals by decision (`fart = fa/cond_false`).

• Alternative names: false positive rate (`FPR`), rate of type-I errors (`alpha`), statistical significance level, `fallout`

• Relationships:

a. `fart` is the complement of the specificity `spec`:

`fart = 1 - spec`

b. `fart` is the opposite conditional probability – but not the complement – of the false discovery rate or false detection rate `FDR`:

`FDR = p(condition = FALSE | decision = positive)`

• In terms of frequencies, `fart` is the ratio of `fa` divided by `cond_false` (i.e., `fa + cr`):

`fart = fa/cond_false = fa/(fa + cr)`

• Dependencies: `fart` is a feature of a decision process or diagnostic procedure and a measure of incorrect decisions (false positives).

However, due to being a conditional probability, the value of `fart` is not intrinsic to the decision process, but also depends on the condition's prevalence value `prev`.

## References

`comp_fart` computes `fart` as the complement of `spec` `prob` contains current probability information; `comp_prob` computes current probability information; `num` contains basic numeric parameters; `init_num` initializes basic numeric parameters; `comp_freq` computes current frequency information; `is_prob` verifies probabilities.
Other probabilities: `FDR`, `FOR`, `NPV`, `PPV`, `acc`, `err`, `mirt`, `ppod`, `prev`, `sens`, `spec`
 ```1 2 3``` ```fart <- .25 # sets a false alarm rate of 25% fart <- 25/100 # (decision = positive) for 25 out of 100 people with (condition = FALSE) is_prob(fart) # TRUE ```