comp_acc: Compute overall accuracy (acc) from probabilities.

Description

comp_acc computes overall accuracy acc from 3 essential probabilities prev, sens, and spec.

Usage

comp_acc(prev, sens, spec)

Value

Overall accuracy acc as a probability (proportion). A warning is provided for NaN values.

See acc for definition and accu for other accuracy metrics. comp_accu_freq and comp_accu_prob

compute accuracy metrics from frequencies and probabilities.

Arguments

prev: The condition's prevalence prev (i.e., the probability of condition being TRUE).
sens: The decision's sensitivity sens (i.e., the conditional probability of a positive decision provided that the condition is TRUE).
spec: The decision's specificity value spec (i.e., the conditional probability of a negative decision provided that the condition is FALSE).

Details

comp_acc uses probabilities (not frequencies) as inputs and returns an exact probability (proportion) without rounding.

Understanding the probability acc:

Definition: acc is the (non-conditional) probability:

acc = p(dec_cor) = dec_cor/N

or the base rate (or baseline probability) of a decision being correct, but not necessarily positive.

acc values range from 0 (no correct decision/prediction) to 1 (perfect decision/prediction).
Computation: acc can be computed in 2 ways:

(a) from prob: acc = (prev x sens) + [(1 - prev) x spec]

(b) from freq: acc = dec_cor/N = (hi + cr)/(hi + mi + fa + cr)

When frequencies in freq are not rounded, (b) coincides with (a).
Perspective: acc classifies a population of N individuals by accuracy/correspondence (acc = dec_cor/N).

acc is the "by accuracy" or "by correspondence" counterpart to prev (which adopts a "by condition" perspective) and to ppod (which adopts a "by decision" perspective).
Alternative names of acc: base rate of correct decisions, non-erroneous cases
In terms of frequencies, acc is the ratio of dec_cor (i.e., hi + cr) divided by N (i.e., hi + mi + fa + cr):

acc = dec_cor/N = (hi + cr)/(hi + mi + fa + cr)
Dependencies: acc is a feature of both the environment (true condition) and of the decision process or diagnostic procedure. It reflects the correspondence of decisions to conditions.

See accu for other accuracy metrics and several possible interpretations of accuracy.

acc defines accuracy as a probability; accu lists all accuracy metrics; comp_accu_prob computes exact accuracy metrics from probabilities; comp_accu_freq computes accuracy metrics from frequencies; comp_sens and comp_PPV compute related probabilities; is_extreme_prob_set verifies extreme cases; comp_complement computes a probability's complement; is_complement verifies probability complements; comp_prob computes current probability information; prob contains current probability information; is_prob verifies probabilities.

Other functions computing probabilities: comp_FDR(), comp_FOR(), comp_NPV(), comp_PPV(), comp_accu_freq(), comp_accu_prob(), comp_comp_pair(), comp_complement(), comp_complete_prob_set(), comp_err(), comp_fart(), comp_mirt(), comp_ppod(), comp_prob_freq(), comp_prob(), comp_sens(), comp_spec()

Other metrics: accu, acc, comp_accu_freq(), comp_accu_prob(), comp_err(), err

Examples

Run this code

# ways to work:
comp_acc(.10, .200, .300)  # => acc = 0.29
comp_acc(.50, .333, .666)  # => acc = 0.4995

# watch out for vectors:
prev.range <- seq(0, 1, by = .1)
comp_acc(prev.range, .5, .5)  # => 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5

# watch out for extreme values:
comp_acc(1, 1, 1)  #  => 1
comp_acc(1, 1, 0)  #  => 1

comp_acc(1, 0, 1)  #  => 0
comp_acc(1, 0, 0)  #  => 0

comp_acc(0, 1, 1)  #  => 1
comp_acc(0, 1, 0)  #  => 0

comp_acc(0, 0, 1)  #  => 1
comp_acc(0, 0, 0)  #  => 0