sensR (version 1.2.2)

AnotA: 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, ...)

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

...

Additional arguments passed to glm

Value

• An object of class "discrim" (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

Details

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

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)

## 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")