Calculates identities Z1 to Z18 as defined in (Costello and Watts 2016; Zhu et al. 2020) . Probability theory predicts that these will all equal 0.
Z_identities(
a = NULL,
b = NULL,
a_and_b = NULL,
a_or_b = NULL,
a_given_b = NULL,
b_given_a = NULL,
a_given_not_b = NULL,
b_given_not_a = NULL,
a_and_not_b = NULL,
b_and_not_a = NULL,
not_a = NULL,
not_b = NULL
)Probability estimates given by participants
Probability estimates given by participants. If not given, they'll default to 1-a and 1-b respectively
Dataframe with identities Z1 to Z18
If some of the probability estimates are not given, calculation will proceed and equalities that cannot be calculated will be coded as NA.
Costello F, Watts P (2016).
“People's Conditional Probability Judgments Follow Probability Theory (plus Noise).”
Cognitive Psychology, 89, 106--133.
doi:10.1016/j.cogpsych.2016.06.006
.
Zhu J, Sanborn AN, Chater N (2020).
“The Bayesian Sampler: Generic Bayesian Inference Causes Incoherence in Human Probability Judgments.”
Psychological Review, 127(5), 719--748.
doi:10.1037/rev0000190
.
Z_identities(
a=.5,
b=.1,
a_and_b=.05,
a_or_b=.55,
a_given_b=.5,
b_given_a=.1,
a_given_not_b=.5,
b_given_not_a=.1,
a_and_not_b=.45,
b_and_not_a=.05,
)
#> z1 z2 z3 z4 z5 z6 z7 z8 z9 z10 z11 z12 z13 z14 z15 z16 z17 z18
#> 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
#Get identities for a set of participants
library(magrittr)
library(dplyr)
library(tidyr)
data.frame(
ID = LETTERS[1:20],
a=runif(20),
b=runif(20),
a_and_b=runif(20),
a_or_b=runif(20),
a_given_b=runif(20),
b_given_a=runif(20),
a_given_not_b=runif(20),
b_given_not_a=runif(20),
a_and_not_b=runif(20),
b_and_not_a=runif(20),
not_a=runif(20),
not_b=runif(20)
) %>%
group_by(ID) %>%
do(
Z_identities(
.$a,
.$b,
.$a_and_b,
.$a_or_b,
.$a_given_b,
.$b_given_a,
.$a_given_not_b,
.$b_given_not_a,
.$a_and_not_b,
.$b_and_not_a,
.$not_a,
.$not_b
)
)
#> # A tibble: 20 × 19
#> # Groups: ID [20]
#> ID z1 z2 z3 z4 z5 z6 z7 z8 z9
#> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 A -0.162 -0.426 0.272 0.697 0.859 0.433 1.13 1.29 0.300
#> 2 B -0.489 0.486 0.710 0.224 0.712 1.20 1.42 1.91 -0.564
#> 3 C 0.124 0.00307 -0.0132 -0.0163 -0.141 -0.138 -0.154 -0.278 -0.447
#> 4 D -0.242 0.0264 0.596 0.570 0.811 0.838 1.41 1.65 0.0323
#> 5 E 0.250 -0.0649 1.02 1.08 0.832 0.767 1.85 1.60 -0.296
#> 6 F -0.348 0.246 -0.387 -0.633 -0.285 -0.0391 -0.672 -0.324 -0.270
#> 7 G 1.10 0.146 1.49 1.35 0.245 0.391 1.74 0.636 0.0453
#> 8 H -0.342 1.30 1.16 -0.136 0.206 1.50 1.37 1.71 0.0114
#> 9 I -0.593 0.798 0.938 0.140 0.733 1.53 1.67 2.26 -0.449
#> 10 J 0.633 0.115 1.35 1.24 0.603 0.719 1.95 1.32 0.561
#> 11 K 0.843 -0.824 0.654 1.48 0.635 -0.189 1.29 0.446 0.364
#> 12 L 0.108 0.604 0.745 0.141 0.0330 0.637 0.778 0.670 -0.268
#> 13 M 0.182 -0.0559 0.520 0.576 0.394 0.338 0.914 0.732 0.458
#> 14 N -0.390 1.56 0.878 -0.678 -0.288 1.27 0.591 0.981 -0.632
#> 15 O -0.0527 0.893 1.04 0.146 0.198 1.09 1.24 1.29 -0.276
#> 16 P 0.573 0.784 1.25 0.466 -0.106 0.678 1.14 0.572 -0.279
#> 17 Q 0.603 -0.663 0.572 1.24 0.632 -0.0314 1.20 0.600 0.161
#> 18 R 0.841 -0.847 0.230 1.08 0.235 -0.612 0.465 -0.377 0.0552
#> 19 S 1.08 0.147 1.29 1.14 0.0666 0.214 1.36 0.280 -0.438
#> 20 T -0.524 -0.615 -0.161 0.454 0.978 0.364 0.818 1.34 0.264
#> # ℹ 9 more variables: z10 <dbl>, z11 <dbl>, z12 <dbl>, z13 <dbl>, z14 <dbl>,
#> # z15 <dbl>, z16 <dbl>, z17 <dbl>, z18 <dbl>