gapnet.psychoacoustics.dprime

module documentation

(source)

TODO write brief introduction to d-prime measure

Function	`dprime_analytical`	Computes the d-prime of two internal response distributions, e.g. from signal present and signal absent.
Function	`dprime_empirical`	Compute dprime from hit rate and false-alarm rate
Function	`dprime_empirical_jones`	Algorithm copied from Pete R Jones (supplementary material to Jones 2016
Function	`ideal_threshold`	Computes the ideal threshold between the two distributions, signal and noise.
Function	`inverse_cumulative_std_normfunc`	The inverse cumulative standard norm-function. This yields the same result as `norminv`, i.e. `norminv(x, mu=0., std=1.) == inverse_cumulative_std_normfunc(x)`.
Function	`norminv`	Replica of the Matlab function `norminv` (Normal inverse cumulative distribution function)

def dprime_analytical(mu1, mu2, std1, std2): (source) ¶

Computes the d-prime of two internal response distributions, e.g. from signal present and signal absent.

It assumes the simplest form of internal response, thus no correlation etc. (see Jones 2016 for a thorough tutorial).

Parameters
mu1	Mean of distribution 1
mu2	Mean of distribution 2
std1	Standard deviation of distribution 1
std2	Standard deviation of distribution 1
Returns

def dprime_empirical(hit_rate, false_alarm_rate): (source) ¶

Compute dprime from hit rate and false-alarm rate

Parameters
hit_rate	Number of "yes" responses given a stimulus with the signal, divided by the number of presentations with signal
false_alarm_rate	Number of "yes" responses given a stimulus with the signal, divided by the number of presentations without signal
Returns

def dprime_empirical_jones(h, f, threshold=0.5, eps=0.5): (source) ¶

Algorithm copied from Pete R Jones (supplementary material to Jones 2016

Parameters
h	internal variable responses due to stimuli with signal
f	internal variable responses due to stimuli without signal
threshold	threshold for determining whether response was a "yes" or "no"
eps	correction factor for avoiding infinite results
Returns

def ideal_threshold(signal, noise): (source) ¶

Computes the ideal threshold between the two distributions, signal and noise.

We use E(x) as the expected value of x, and estimate this by the mean of the samples provided.

When the E(noise) samples are larger than the E(signal), the ideal threshold returned is E(noise).

Otherwise, (E(signal) + E(noise)) / 2 is returned, i.e. the mean of the means.

Parameters
signal	responses due to stimuli with signal
noise	responses due to stimuli without signal, i.e. noise only
Returns
the ideal threshold between the two distributions

@check_annotations
def inverse_cumulative_std_normfunc(p): (source) ¶

The inverse cumulative standard norm-function. This yields the same result as norminv, i.e. norminv(x, mu=0., std=1.) == inverse_cumulative_std_normfunc(x).

Equation originates from Jones 2016

Parameters
p:`Annotated[float, ValueRange(0.0, 1.0, False, False)]`	probability values (must be in the range [0, 1])
Returns

def norminv(p, mu=0.0, std=1.0): (source) ¶

Replica of the Matlab function norminv (Normal inverse cumulative distribution function)

Parameters
p	Probability values at which to evaluate the inverse of the cdf (icdf), specified as a scalar value or an array of scalar values, where each element is in the range [0,1].
mu	Mean of the normal distribution, specified as a scalar value or an array of scalar values.
std	Standard deviation of the normal distribution, specified as a positive scalar value or an array of positive scalar values.
Returns
returns the inverse of the normal cdf with mean mu and standard deviation sigma, evaluated at the probability values in p.