# PPV: The positive predictive value of a decision process or... In riskyr: Rendering Risk Literacy more Transparent

## Description

`PPV` defines some decision's positive predictive value (PPV): The conditional probability of the condition being `TRUE` provided that the decision is positive.

## Usage

 `1` ```PPV ```

## Format

An object of class `numeric` of length 1.

## Details

Understanding or obtaining the positive predictive value `PPV`:

• Definition: `PPV` is the conditional probability for the condition being `TRUE` given a positive decision:

`PPV = p(condition = TRUE | decision = positive)`

or the probability of a positive decision being correct.

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

• Alternative names: `precision`

• Relationships:

a. `PPV` is the complement of the false discovery or false detection rate `FDR`:

`PPV = 1 - FDR`

b. `PPV` is the opposite conditional probability – but not the complement – of the sensitivity `sens`:

`sens = p(decision = positive | condition = TRUE)`

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

`PPV = hi/dec.pos = hi/(hi + fa)`

• Dependencies: `PPV` is a feature of a decision process or diagnostic procedure and – similar to the sensitivity `sens` – a measure of correct decisions (positive decisions that are actually TRUE).

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

## References

`comp_PPV` computes `PPV`; `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 probability inputs.
Other probabilities: `FDR`, `FOR`, `NPV`, `fart`, `mirt`, `ppod`, `prev`, `sens`, `spec`
 ```1 2 3``` ```PPV <- .55 # => sets a positive predictive value of 55% PPV <- 55/100 # => (condition = TRUE) for 55 out of 100 people with (decision = positive) is_prob(PPV) # => TRUE (as PPV is a probability) ```