Computes empirical hit rates, false-alarm rates, sensitivity (\(d'\)), and response criteria for each participant without fitting a model. It can also calculate sampling variances, standard errors, and expected values for \(d'\).
Arguments
- data
A
usdt_dataobject or a standard trial-level data frame. When given ausdt_dataobject, the function processes both tasks and includes ataskcolumn in the output.- subject_col, condition_col, response_col
Column names for subject, condition, and response variables. Only required when
datais a plain data frame.- condition_levels, response_levels
Named vectors mapping condition and response labels, like
c(signal = "old", noise = "new"). Required for a plain data frame. Ausdt_dataobject supplies its own roles and needs neither.- coding
Criterion definition to report:
"deviation"measures the criterion from the midpoint between the signal and noise distributions, whereas"treatment"measures it from the noise distribution. Ausdt_dataobject supplies its own coding.- correction
Handling of extreme rates (0 or 1) that make \(d'\) infinite.
"hautus"adds 0.5 to all four cell counts for affected participants."none"leaves infinite values in place.- variances
Logical. If
TRUE, computes the sampling variance of \(d'\) from Gourevitch and Galanter (1967) and Miller (1996), each with its own standard error, as well as the expected value of \(d'\) under Miller's distribution.
Value
A data frame with one row per subject (or per subject and task for
usdt_data inputs) containing:
hit,miss,fa,cr: Raw response counts.hr,far: Observed hit and false-alarm rates.zhr,zfar: Probit-transformed rates.dprime,criterion: Descriptive SDT estimates.corrected: Logical flag indicating whether the participant received an edge correction.var_gg,se_gg: Asymptotic variance and standard error from Gourevitch and Galanter (1967), present whenvariances = TRUE.var_miller,se_miller,expected_dprime: Moments from Miller (1996), present whenvariances = TRUE.
Details
Edge corrections apply only to participants with extreme rates (0 or 1) rather than the whole sample, leaving well-defined rates unchanged.
When requested, the sampling variance of \(d'\) is estimated using the asymptotic approximation of Gourevitch and Galanter (1967) and the binomial-distribution approach of Miller (1996). See Suero et al. (2017) for a comparison between the two approaches.
References
Gourevitch, V., & Galanter, E. (1967). A significance test for one parameter isosensitivity functions. Psychometrika, 32(1), 25–33. doi:10.1007/BF02289402
Hautus, M. J. (1995). Corrections for extreme proportions and their biasing effects on estimated values of \(d'\). Behavior Research Methods, Instruments, & Computers, 27(1), 46–51. doi:10.3758/BF03203619
Miller, J. (1996). The sampling distribution of \(d'\). Perception & Psychophysics, 58(1), 65–72. doi:10.3758/BF03205476
Suero, M., Privado, J., & Botella, J. (2017). Methods to estimate the variance of some indices of the signal detection theory: A simulation study. Psicologica, 38(1), 77–109.
Examples
# 1. From a prepared usdt_data object (both tasks at once)
d <- usdt_data_tasks(
direct = vadillo_awareness,
indirect = vadillo_cuing,
subject_col = "subj",
condition_col = "condition",
condition_levels = c(signal = "old", noise = "new"),
response_col = list(direct = "judged.old", indirect = "rt"),
response_levels = list(direct = c(signal = 1, noise = 0),
indirect = c(signal = "faster", noise = "slower")),
dichotomize = list(direct = FALSE, indirect = TRUE)
)
head(sdt_moments(d))
#> task subj hit miss fa cr hr far zhr zfar dprime
#> 1 Direct 2001 19 13 15 17 0.59375 0.46875 0.23720211 -0.07841241 0.31561452
#> 2 Direct 2002 24 8 21 11 0.75000 0.65625 0.67448975 0.40225007 0.27223968
#> 3 Direct 2003 20 12 19 13 0.62500 0.59375 0.31863936 0.23720211 0.08143725
#> 4 Direct 2004 22 10 10 22 0.68750 0.31250 0.48877641 -0.48877641 0.97755282
#> 5 Direct 2005 17 15 23 9 0.53125 0.71875 0.07841241 0.57913216 -0.50071975
#> 6 Direct 2006 17 15 20 12 0.53125 0.62500 0.07841241 0.31863936 -0.24022695
#> criterion corrected
#> 1 -0.07939485 FALSE
#> 2 -0.53836991 FALSE
#> 3 -0.27792074 FALSE
#> 4 0.00000000 FALSE
#> 5 -0.32877229 FALSE
#> 6 -0.19852589 FALSE
# 2. From raw trials with sampling variances and standard errors
head(sdt_moments(vadillo_awareness,
subject_col = "subj",
condition_col = "condition",
condition_levels = c(signal = "old", noise = "new"),
response_col = "judged.old",
response_levels = c(signal = 1, noise = 0),
variances = TRUE))
#> subj hit miss fa cr hr far zhr zfar dprime
#> 1 2001 19 13 15 17 0.59375 0.46875 0.23720211 -0.07841241 0.31561452
#> 2 2002 24 8 21 11 0.75000 0.65625 0.67448975 0.40225007 0.27223968
#> 3 2003 20 12 19 13 0.62500 0.59375 0.31863936 0.23720211 0.08143725
#> 4 2004 22 10 10 22 0.68750 0.31250 0.48877641 -0.48877641 0.97755282
#> 5 2005 17 15 23 9 0.53125 0.71875 0.07841241 0.57913216 -0.50071975
#> 6 2006 17 15 20 12 0.53125 0.62500 0.07841241 0.31863936 -0.24022695
#> criterion corrected var_gg se_gg var_miller se_miller
#> 1 -0.07939485 FALSE 0.09930004 0.3151191 0.1049949 0.3240291
#> 2 -0.53836991 FALSE 0.11009703 0.3318087 0.1207283 0.3474598
#> 3 -0.27792074 FALSE 0.10104010 0.3178681 0.1073747 0.3276808
#> 4 0.00000000 FALSE 0.10713629 0.3273168 0.1160479 0.3406581
#> 5 -0.32877229 FALSE 0.10470577 0.3235827 0.1128152 0.3358798
#> 6 -0.19852589 FALSE 0.10013446 0.3164403 0.1061461 0.3258007
#> expected_dprime
#> 1 0.32409622
#> 2 0.28275954
#> 3 0.08381293
#> 4 1.00624073
#> 5 -0.51642519
#> 6 -0.24693939