# 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.

 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.