comp_freq_prob computes current frequency information from a sufficient and valid set of 3 essential probabilities (prev, and sens or its complement mirt, and spec or its complement fart). It returns a list of 11 frequencies (freq) as its output.

comp_freq_prob(prev = prob$prev, sens = prob$sens, mirt = NA,
spec = prob$spec, fart = NA, tol = 0.01, N = freq$N,
round = TRUE)

## Arguments

prev 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). sens is optional when its complement mirt is provided. The decision's miss rate mirt (i.e., the conditional probability of a negative decision provided that the condition is TRUE). mirt is optional when its complement sens is provided. The decision's specificity value spec (i.e., the conditional probability of a negative decision provided that the condition is FALSE). spec is optional when its complement fart is provided. The decision's false alarm rate fart (i.e., the conditional probability of a positive decision provided that the condition is FALSE). fart is optional when its complement spec is provided. A numeric tolerance value for is_complement. Default: tol = .01. The number of individuals in the population. If N is unknown (NA), a suitable minimum value is computed by comp_min_N. A Boolean value that determines whether frequencies are rounded to the nearest integer. Default: round = TRUE.

## Value

A list freq containing 11 frequency values.

## Details

comp_freq_prob is a wrapper function for the more basic function comp_freq, which only accepts 3 essential probabilities (i.e., prev, sens, and spec) as inputs.

Defaults and constraints:

• Initial values:

By default, the values of prev, sens, and spec are initialized to the probability information currently contained in prob.

Similarly, the population size N uses the frequency information currently contained in freq as its default. If N is unknown (NA), a suitable minimum value is computed by comp_min_N.

• Constraints:

When using comp_freq_prob with the arguments mirt and fart, their complements sens and spec must either be valid complements (as in is_complement) or set to NA.

In addition to prev, both sens and spec are necessary arguments. If only their complements mirt or fart are known, first use comp_complement, comp_comp_pair, or comp_complete_prob_set to compute the 3 essential probabilities.

• Rounding:

By default, comp_freq_prob and its basic function comp_freq round frequencies to nearest integers to avoid decimal values in freq (i.e., round = TRUE by default).

When frequencies are rounded, probabilities computed from freq may differ from exact probabilities.

Using the option round = FALSE turns off rounding.

Key relationships between frequencies and probabilities (see documentation of comp_freq or comp_prob for details):

• Three perspectives on a population:

by condition / by decision / by accuracy.

• Defining probabilities in terms of frequencies:

Probabilities can be computed as ratios between frequencies, but beware of rounding issues.

Functions translating between representational formats: comp_prob_prob, comp_prob_freq, comp_freq_prob, comp_freq_freq (see documentation of comp_prob_prob for details).

comp_freq_freq computes current frequency information from (4 essential) frequencies; comp_prob_freq computes current probability information from (4 essential) frequencies; comp_prob_prob computes current probability information from (3 essential) probabilities; num contains basic numeric variables; init_num initializes basic numeric variables; freq contains current frequency information; comp_freq computes current frequency information; prob contains current probability information; comp_prob computes current probability information; comp_complement computes a probability's complement; comp_comp_pair computes pairs of complements; comp_complete_prob_set completes valid sets of probabilities; comp_min_N computes a suitable population size N (if missing).

Other functions computing frequencies: comp_freq_freq, comp_freq, comp_min_N, comp_popu, comp_prob_prob

Other format conversion functions: comp_freq_freq, comp_prob_freq, comp_prob_prob

## Examples

# Basics:
comp_freq_prob(prev = .1, sens = .9, spec = .8, N = 100)  # => ok: hi = 9, ... cr = 72.#> $N #> [1] 100 #> #>$cond_true
#> [1] 10
#>
#> $cond_false #> [1] 90 #> #>$dec_pos
#> [1] 27
#>
#> $dec_neg #> [1] 73 #> #>$dec_cor
#> [1] 81
#>
#> $dec_err #> [1] 19 #> #>$hi
#> [1] 9
#>
#> $mi #> [1] 1 #> #>$fa
#> [1] 18
#>
#> $cr #> [1] 72 #> # Same case with complements (using NAs to prevent defaults): comp_freq_prob(prev = .1, sens = NA, mirt = .1, spec = NA, fart = .2, N = 100) # => same result#>$N
#> [1] 100
#>
#> $cond_true #> [1] 10 #> #>$cond_false
#> [1] 90
#>
#> $dec_pos #> [1] 27 #> #>$dec_neg
#> [1] 73
#>
#> $dec_cor #> [1] 81 #> #>$dec_err
#> [1] 19
#>
#> $hi #> [1] 9 #> #>$mi
#> [1] 1
#>
#> $fa #> [1] 18 #> #>$cr
#> [1] 72
#>
comp_freq_prob()                   # => ok, using probability info currently contained in prob#> $N #> [1] 1000 #> #>$cond_true
#> [1] 250
#>
#> $cond_false #> [1] 750 #> #>$dec_pos
#> [1] 400
#>
#> $dec_neg #> [1] 600 #> #>$dec_cor
#> [1] 774
#>
#> $dec_err #> [1] 226 #> #>$hi
#> [1] 212
#>
#> $mi #> [1] 38 #> #>$fa
#> [1] 188
#>
#> $cr #> [1] 562 #> length(comp_freq_prob()) # => a list containing 9 frequencies#> [1] 11all.equal(freq, comp_freq_prob()) # => TRUE, unless prob has been changed after computing freq#> [1] TRUEfreq <- comp_freq_prob() # => computes frequencies and stores them in freq # Ways to work: comp_freq_prob(prev = 1, sens = 1, spec = 1, N = 101) # => ok + warning: N hits (TP)#> Warning: Extreme case (prev = 1 & sens = 1): #> N hi (TP) cases; 0 cond_false or dec_false cases; NPV = NaN.#>$N
#> [1] 101
#>
#> $cond_true #> [1] 101 #> #>$cond_false
#> [1] 0
#>
#> $dec_pos #> [1] 101 #> #>$dec_neg
#> [1] 0
#>
#> $dec_cor #> [1] 101 #> #>$dec_err
#> [1] 0
#>
#> $hi #> [1] 101 #> #>$mi
#> [1] 0
#>
#> $fa #> [1] 0 #> #>$cr
#> [1] 0
#>
# Same case with complements (using NAs to prevent defaults):
comp_freq_prob(prev = 1, sens = NA, mirt = 0, spec = NA, fart = 0, N = 101)#> Warning: Extreme case (prev = 1 & sens = 1):
#>   N hi (TP) cases; 0 cond_false or dec_false cases; NPV = NaN.#> $N #> [1] 101 #> #>$cond_true
#> [1] 101
#>
#> $cond_false #> [1] 0 #> #>$dec_pos
#> [1] 101
#>
#> $dec_neg #> [1] 0 #> #>$dec_cor
#> [1] 101
#>
#> $dec_err #> [1] 0 #> #>$hi
#> [1] 101
#>
#> $mi #> [1] 0 #> #>$fa
#> [1] 0
#>
#> $cr #> [1] 0 #> comp_freq_prob(prev = 1, sens = 1, spec = 0, N = 102) # => ok + warning: N hits (TP)#> Warning: Extreme case (prev = 1 & sens = 1): #> N hi (TP) cases; 0 cond_false or dec_false cases; NPV = NaN.#>$N
#> [1] 102
#>
#> $cond_true #> [1] 102 #> #>$cond_false
#> [1] 0
#>
#> $dec_pos #> [1] 102 #> #>$dec_neg
#> [1] 0
#>
#> $dec_cor #> [1] 102 #> #>$dec_err
#> [1] 0
#>
#> $hi #> [1] 102 #> #>$mi
#> [1] 0
#>
#> $fa #> [1] 0 #> #>$cr
#> [1] 0
#> comp_freq_prob(prev = 1, sens = 0, spec = 1, N = 103)  # => ok + warning: N misses (FN)#> Warning: Extreme case (prev = 1 & sens = 0):
#>   N mi (FN) cases; 0 cond_false or dec_true cases; PPV = NaN.#> $N #> [1] 103 #> #>$cond_true
#> [1] 103
#>
#> $cond_false #> [1] 0 #> #>$dec_pos
#> [1] 0
#>
#> $dec_neg #> [1] 103 #> #>$dec_cor
#> [1] 0
#>
#> $dec_err #> [1] 103 #> #>$hi
#> [1] 0
#>
#> $mi #> [1] 103 #> #>$fa
#> [1] 0
#>
#> $cr #> [1] 0 #> comp_freq_prob(prev = 1, sens = 0, spec = 0, N = 104) # => ok + warning: N misses (FN)#> Warning: Extreme case (prev = 1 & sens = 0): #> N mi (FN) cases; 0 cond_false or dec_true cases; PPV = NaN.#>$N
#> [1] 104
#>
#> $cond_true #> [1] 104 #> #>$cond_false
#> [1] 0
#>
#> $dec_pos #> [1] 0 #> #>$dec_neg
#> [1] 104
#>
#> $dec_cor #> [1] 0 #> #>$dec_err
#> [1] 104
#>
#> $hi #> [1] 0 #> #>$mi
#> [1] 104
#>
#> $fa #> [1] 0 #> #>$cr
#> [1] 0
#> comp_freq_prob(prev = 0, sens = 1, spec = 1, N = 105)  # => ok + warning: N correct rejections (TN)#> Warning: Extreme case (prev = 0 & spec = 1):
#>   N cr (TN) cases; 0 cond_true or dec_false cases; NPV = NaN.#> $N #> [1] 105 #> #>$cond_true
#> [1] 0
#>
#> $cond_false #> [1] 105 #> #>$dec_pos
#> [1] 0
#>
#> $dec_neg #> [1] 105 #> #>$dec_cor
#> [1] 105
#>
#> $dec_err #> [1] 0 #> #>$hi
#> [1] 0
#>
#> $mi #> [1] 0 #> #>$fa
#> [1] 0
#>
#> $cr #> [1] 105 #> comp_freq_prob(prev = 0, sens = 1, spec = 0, N = 106) # => ok + warning: N false alarms (FP)#> Warning: Extreme case (prev = 0 & spec = 0): #> N fa (FP) cases; 0 cond_true or dec_true cases; PPV = NaN.#>$N
#> [1] 106
#>
#> $cond_true #> [1] 0 #> #>$cond_false
#> [1] 106
#>
#> $dec_pos #> [1] 106 #> #>$dec_neg
#> [1] 0
#>
#> $dec_cor #> [1] 0 #> #>$dec_err
#> [1] 106
#>
#> $hi #> [1] 0 #> #>$mi
#> [1] 0
#>
#> $fa #> [1] 106 #> #>$cr
#> [1] 0
#>
# Same case with complements (using NAs to prevent defaults):
comp_freq_prob(prev = 0, sens = NA, mirt = 0,
spec = NA, fart = 1, N = 106)  # => ok + warning: N false alarms (FP)#> Warning: Extreme case (prev = 0 & spec = 0):
#>   N fa (FP) cases; 0 cond_true or dec_true cases; PPV = NaN.#> $N #> [1] 106 #> #>$cond_true
#> [1] 0
#>
#> $cond_false #> [1] 106 #> #>$dec_pos
#> [1] 106
#>
#> $dec_neg #> [1] 0 #> #>$dec_cor
#> [1] 0
#>
#> $dec_err #> [1] 106 #> #>$hi
#> [1] 0
#>
#> $mi #> [1] 0 #> #>$fa
#> [1] 106
#>
#> $cr #> [1] 0 #> # Watch out for: comp_freq_prob(prev = 1, sens = 1, spec = 1, N = NA) # => ok + warning: N = 1 computed#> Warning: Extreme case (prev = 1 & sens = 1): #> N hi (TP) cases; 0 cond_false or dec_false cases; NPV = NaN.#> Warning: Extreme case (prev = 1 & sens = 1): #> N hi (TP) cases; 0 cond_false or dec_false cases; NPV = NaN.#> Warning: Unknown population size N. A suitable minimum value of N = 1 was computed.#>$N
#> [1] 1
#>
#> $cond_true #> [1] 1 #> #>$cond_false
#> [1] 0
#>
#> $dec_pos #> [1] 1 #> #>$dec_neg
#> [1] 0
#>
#> $dec_cor #> [1] 1 #> #>$dec_err
#> [1] 0
#>
#> $hi #> [1] 1 #> #>$mi
#> [1] 0
#>
#> $fa #> [1] 0 #> #>$cr
#> [1] 0
#> comp_freq_prob(prev = 1, sens = 1, spec = 1, N =  0)  # => ok, but all 0 + warning (NPV = NaN)#> Warning: Extreme case (prev = 1 & sens = 1):
#>   N hi (TP) cases; 0 cond_false or dec_false cases; NPV = NaN.#> $N #> [1] 0 #> #>$cond_true
#> [1] 0
#>
#> $cond_false #> [1] 0 #> #>$dec_pos
#> [1] 0
#>
#> $dec_neg #> [1] 0 #> #>$dec_cor
#> [1] 0
#>
#> $dec_err #> [1] 0 #> #>$hi
#> [1] 0
#>
#> $mi #> [1] 0 #> #>$fa
#> [1] 0
#>
#> $cr #> [1] 0 #> comp_freq_prob(prev = .5, sens = .5, spec = .5, N = 10, round = TRUE) # => ok, but all rounded#>$N
#> [1] 10
#>
#> $cond_true #> [1] 5 #> #>$cond_false
#> [1] 5
#>
#> $dec_pos #> [1] 5 #> #>$dec_neg
#> [1] 5
#>
#> $dec_cor #> [1] 4 #> #>$dec_err
#> [1] 6
#>
#> $hi #> [1] 2 #> #>$mi
#> [1] 3
#>
#> $fa #> [1] 3 #> #>$cr
#> [1] 2
#> comp_freq_prob(prev = .5, sens = .5, spec = .5, N = 10, round = FALSE) # => ok, but not rounded#> $N #> [1] 10 #> #>$cond_true
#> [1] 5
#>
#> $cond_false #> [1] 5 #> #>$dec_pos
#> [1] 5
#>
#> $dec_neg #> [1] 5 #> #>$dec_cor
#> [1] 5
#>
#> $dec_err #> [1] 5 #> #>$hi
#> [1] 2.5
#>
#> $mi #> [1] 2.5 #> #>$fa
#> [1] 2.5
#>
#> \$cr
#> [1] 2.5
#>
# Ways to fail:
comp_freq_prob(prev = NA, sens = 1, spec = 1, 100)  # => NAs + no warning (prev NA)#> Warning: Please enter a valid set of essential probabilities.comp_freq_prob(prev = 1, sens = NA, spec = 1, 100)  # => NAs + no warning (sens NA)#> Warning: Please enter a valid set of essential probabilities.comp_freq_prob(prev = 1, sens = 1, spec = NA, 100)  # => NAs + no warning (spec NA)#> Warning: Please enter a valid set of essential probabilities.comp_freq_prob(prev = 8, sens = 1, spec = 1,  100)  # => NAs + warning (prev beyond range)#> Warning: Please enter a valid set of essential probabilities.comp_freq_prob(prev = 1, sens = 8, spec = 1,  100)  # => NAs + warning (sens & spec beyond range)#> Warning: Please enter a valid set of essential probabilities.