# FDR: The false detection rate of a decision process or diagnostic... In riskyr: Rendering Risk Literacy more Transparent

## Description

`FDR` defines a decision's false detection (or false discovery) rate (`FDR`): The conditional probability of the condition being `FALSE` provided that the decision is positive.

## Usage

 `1` ```FDR ```

## Format

An object of class `numeric` of length 1.

## Details

Understanding or obtaining the false detection fate or false discovery rate (`FDR`):

• Definition: `FDR` is the conditional probability for the condition being `FALSE` given a positive decision:

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

• Perspective: `FDR` further classifies the subset of `dec_pos` individuals by condition (`FDR = fa/dec_pos = fa/(hi + fa)`).

• Alternative names: false discovery rate

• Relationships:

a. `FDR` is the complement of the positive predictive value `PPV`:

`FDR = 1 - PPV`

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

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

• In terms of frequencies, `FDR` is the ratio of `fa` divided by `dec_pos` (i.e., `hi + fa`):

`FDR = fa/dec_pos = fa/(hi + fa)`

• Dependencies: `FDR` is a feature of a decision process or diagnostic procedure and a measure of incorrect decisions (positive decisions that are actually `FALSE`).

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

## References

Consult Wikipedia for additional information.

`prob` contains current probability information; `comp_prob` computes current probability information; `num` contains basic numeric parameters; `init_num` initializes basic numeric parameters; `freq` contains current frequency information; `comp_freq` computes current frequency information; `is_prob` verifies probabilities.
Other probabilities: `FOR`, `NPV`, `PPV`, `acc`, `err`, `fart`, `mirt`, `ppod`, `prev`, `sens`, `spec`
 ```1 2 3``` ```FDR <- .45 # sets a false detection rate (FDR) of 45% FDR <- 45/100 # (condition = FALSE) for 45 out of 100 people with (decision = positive) is_prob(FDR) # TRUE ```