twoAC {sensR}

2-AC Discrimination and Preference Protocol

Description

Computes estimates and standard errors of d-prime and tau for the two alternative (2-AC) protocol. A confidence interval and significance test for d-prime is also provided. The 2-AC protocol is equivalent to a 2-AFC protocol with a "no-difference" option, and equivalent to a paired preference test with an "no-preference" option.

Usage

twoAC(data, d.prime0 = 0, conf.level = 0.95,
      statistic = c("likelihood", "Wald"),
      alternative = c("two.sided", "less", "greater"), ...)

Arguments

data

a non-negative numeric vector of length 3 with the number of observations in the three response categories in the form ("prefer A", "no-preference", "prefer B"). If the third element is larger than the first element, the estimate of d-prime is positive.

d.prime0

the value of d-prime under the null hypothesis for the significance test.

conf.level

the confidence level.

statistic

the statistic to use for confidence level and significance test.

alternative

the type of alternative hypothesis.

...

not currently used.

Details

confint, profile, logLik, vcov, and print methods are implemented for twoAC objects.

Power computations for the 2-AC protocol is implemented in twoACpwr.

Value

An object of class twoAC with elements

coefficients

2 by 2 coefficient matrix with estimates and standard errors of d-prime and tau. If the variance-covariance matrix of the parameters is not defined, the standard errors are NA.

vcov

variance-covariance matrix of the parameter estimates. Only present if defined for the supplied data.

data

the data supplied to the function.

call

the matched call.

logLik

the value of the log-likelihood at the maximum likelihood estimates.

alternative

the name of the alternative hypothesis for the significance test.

statistic

the name of the test statistic used for the significance test.

conf.level

the confidence level for the confidence interval for d-prime.

d.prime0

the value of d-prime under the null hypothesis in the significance test.

p.value

p-value of the significance test.

confint

two-sided condfidence interval for d-prime. This is only available if the standard errors are defined, which may happen in boundary cases. Use profile and confint methods to get confidence intervals instead; see the examples.

Author(s)

Rune Haubo B Christensen

References

Christensen R.H.B., Lee H-S and Brockhoff P.B. (2012). Estimation of the Thurstonian model for the 2-AC protocol. Food Quality and Preference, 24(1), pp.119-128.

See Also

clm2twoAC, twoACpwr

Examples

## Simple:
fit <- twoAC(c(2,2,6))
fit

## Typical discrimination-difference test: 
(fit <- twoAC(data = c(2, 5, 8), d.prime0 = 0, alternative = "greater"))

## Typical discrimination-similarity test: 
(fit <- twoAC(data = c(15, 15, 20), d.prime0 = .5, alternative = "less"))

## Typical preference-difference test:
(fit <- twoAC(data = c(3, 5, 12), d.prime0 = 0,
              alternative = "two.sided"))

## Typical preference (non-)inferiority test:
(fit <- twoAC(data = c(3, 5, 12), d.prime0 = 0,
              alternative = "greater"))

## For preference equivalence tests (two-sided) use CI with alpha/2:
## declare equivalence at the 5% level if 90% CI does not contain,
## e.g, -1 or 1: 
(fit <- twoAC(data = c(15, 10, 10), d.prime0 = 0, conf.level = .90))

## The var-cov matrix and standard errors of the parameters are not
## defined in all situations. If standard errors are not
## defined, then confidence intervals are not provided directly:
(fit <- twoAC(c(5, 0, 15)))
## We may use profile and confint methods to get confidence intervals
## never the less: 
pr <- profile(fit, range = c(-1, 3))
confint(pr)
plot(pr)