comp_acc(prev, sens, spec)The condition's prevalence prev
(i.e., the probability of condition being TRUE).
The decision's sensitivity sens
(i.e., the conditional probability of a positive decision
provided that the condition is TRUE).
The decision's specificity value spec
(i.e., the conditional probability
of a negative decision provided that the condition is FALSE).
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.
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
# ways to work:
comp_acc(.10, .200, .300) # => acc = 0.29
#> [1] 0.29
comp_acc(.50, .333, .666) # => acc = 0.4995
#> [1] 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
#> [1] 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
#> [1] 1
comp_acc(1, 1, 0) # => 1
#> [1] 1
comp_acc(1, 0, 1) # => 0
#> [1] 0
comp_acc(1, 0, 0) # => 0
#> [1] 0
comp_acc(0, 1, 1) # => 1
#> [1] 1
comp_acc(0, 1, 0) # => 0
#> [1] 0
comp_acc(0, 0, 1) # => 1
#> [1] 1
comp_acc(0, 0, 0) # => 0
#> [1] 0