AnotA: Analysis of A-not-A tests

In perbrock/sensR: Thurstonian Models for Sensory Discrimination

Analysis of A-not-A tests

Description

Computation of dprime and it's uncertainty for the monadic A-not-A test together with the one-tailed P-value of the difference test (Fisher's Exact test).

Usage

AnotA(x1, n1, x2, n2, ...)

## S3 method for class 'anota'
confint(object, parm, level = 0.95, ...)

## S3 method for class 'anota'
plot(x, main = TRUE, length = 1000, ...)

Arguments

x1	the number of (correct) A-answers on A-samples
n1	the total number of A-samples
x2	the number of A-answers on not-A-samples
n2	the number of not-A-samples
object	an anota object
parm	currently not used
level	the desired confidence level
x	an anota object
main	should the plot have a main title?
length	the discretization of the curves
...	additional arguments passed to glm for AnotA; not used for confint and plot

Details

The AnotA function uses the glm and fisher.test functions of the stats package. Note that all arguments have to be positive integers.

Value

For AnotA an object of class anota (which has a print method). This is a list with elements

coefficients	named vector of coefficients (d-prime)
res.glm	the glm-object from the fitting process
vcov	variance-covariance matrix of the coefficients
se	named vector with standard error of the coefficients (standard error of d-prime
data	a named vector with the data supplied to the function
p.value	one-sided p-value from Fisher's exact test (fisher.test)
test	a string with the name of the test (A-Not A) for the print method
call	the matched call

For plot a figure of the distributions of sensory intensity is produced, and for confint a 2-by-2 matrix of confidence intervals is returned.

Author(s)

Rune Haubo B Christensen and Per Bruun Brockhoff

References

Brockhoff, P.B. and Christensen, R.H.B. (2010). Thurstonian models for sensory discrimination tests as generalized linear models. Food Quality and Preference, 21, pp. 330-338.

See Also

print.discrim, discrim, discrimPwr, discrimSim, discrimSS, findcr

Examples

# data: 10 of the A-samples were judged to be A
#       20 A-samples in total
#       3 of the not-A samples were judged to be A
#       20 not-A-samples in total

AnotA(10, 20, 3, 20)
(m1 <- AnotA(10, 20, 3, 20))

## plot distributions of sensory intensity:
plot(m1)

## likelihood based confidence intervals:
confint(m1)


## Extended example plotting the profile likelihood
xt <- cbind(c(3, 10), c(20 - 3, 20 - 10))
lev <- gl(2, 1)
summary(res <- glm(xt ~ lev,
                   family = binomial(link = probit)))
N <- 100
dev <- double(N)
level <- c(0.95, 0.99)
delta <- seq(1e-4, 5, length = N)
for(i in 1:N)
  dev[i] <- glm(xt ~ 1 + offset(c(0, delta[i])),
                family = binomial(probit))$deviance
plot(delta, exp(-dev/2), type = "l",
     xlab = expression(delta),
     ylab = "Normalized Profile Likelihood")
## Add Normal approximation:
lines(delta, exp(-(delta - coef(res)[2])^2 /
                 (2 * vcov(res)[2,2])), lty = 2)
## Add confidence limits:
lim <- sapply(level, function(x)
              exp(-qchisq(x, df=1)/2) )
abline(h = lim, col = "grey")

perbrock/sensR documentation built on Nov. 5, 2023, 10:41 a.m.