# twoAC: 2-AC Discrimination and Preference Protocol In sensR: Thurstonian Models for Sensory Discrimination

## 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

 ```1 2 3``` ```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. (2011). Estimation of the Thurstonian model for the 2-AC protocol. Submitted to Food Quality and Preference.

`clm2twoAC`, `twoACpwr`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32``` ```## 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) ```