twoAC | R Documentation |

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.

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

`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. |

`confint`

,
`profile`

,
`logLik`

, `vcov`

, and
`print`

methods are implemented for `twoAC`

objects.

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

.

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 |

`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 |

Rune Haubo B Christensen

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.

`clm2twoAC`

, `twoACpwr`

```
## 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)
```

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