An A function

This function allows you to calculate A from from a vector hits and a vector a false alarms.

A(data, h, f)

Arguments

data	A data frame.
h	A vector of hits (0 = miss, 1 = hit).
f	A vector of false alarms (0 = correct rejection, 1 = false alarm).

Examples

# Create some data
set.seed(1); library(dplyr)
#> 
#> Attaching package: ‘dplyr’
#> The following objects are masked from ‘package:stats’:
#> 
#>     filter, lag
#> The following objects are masked from ‘package:base’:
#> 
#>     intersect, setdiff, setequal, union
axb <- data.frame(subj = sort(rep(1:10, each = 20, times = 10)),
                  group = gl(2, 1000, labels = c("g1", "g2")),
                  hit = c(rbinom(1000, size = c(0, 1), prob = .8), 
                          rbinom(1000, size = c(0, 1), prob = .6)),
                  fa =  c(rbinom(1000, size = c(0, 1), prob = .3), 
                          rbinom(1000, size = c(0, 1), prob = .4))
)

# Calculate A on entire data frame
A(axb, hit, fa)
#> [1] 0.6703768

# Calculate A for each subject
# by group, plot it, and run a 
# linear model
axb %>%
  group_by(subj, group) %>%
  summarize(A = A(., hit, fa)) %T>%
 {
  plot(A ~ as.numeric(group), data = ., 
       main = "A as a function of group", xaxt = "n", 
       xlab = "Group", ylab = "A")
  axis(1, at = 1:2, labels = c("g1", "g2"))
  abline(lm(A ~ as.numeric(group), data = .), col = "red")
 } %>%
 lm(A ~ group, data = .) %>%
 summary()
#> `summarise()` has grouped output by 'subj'. You can override using the `.groups` argument.
#> Warning: essentially perfect fit: summary may be unreliable
#> 
#> Call:
#> lm(formula = A ~ group, data = .)
#> 
#> Residuals:
#>        Min         1Q     Median         3Q        Max 
#> -7.022e-17 -7.022e-17  0.000e+00  0.000e+00  2.809e-16 
#> 
#> Coefficients:
#>               Estimate Std. Error   t value Pr(>|t|)    
#> (Intercept)  6.704e-01  4.965e-17  1.35e+16   <2e-16 ***
#> groupg2     -7.022e-17  7.022e-17 -1.00e+00    0.347    
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Residual standard error: 1.11e-16 on 8 degrees of freedom
#> Multiple R-squared:  0.619,	Adjusted R-squared:  0.5714 
#> F-statistic:    13 on 1 and 8 DF,  p-value: 0.006926
#>