discrimPwr | R Documentation |

Computes the power of a difference or similarity test for a sensory
discrimination experiment using the binomial distribution.
`d.primePwr`

is a convenience function that calls
`discrimPwr`

but has arguments in terms of d-prime rather than
pd, the probability of discrimination.

```
discrimPwr(pdA, pd0 = 0, sample.size, alpha = 0.05, pGuess = 1/2,
test = c("difference", "similarity"),
statistic = c("exact", "normal", "cont.normal"))
d.primePwr(d.primeA, d.prime0 = 0, sample.size, alpha = 0.05,
method = c("duotrio", "tetrad", "threeAFC", "twoAFC",
"triangle", "hexad", "twofive", "twofiveF"),
double = FALSE,
test = c("difference", "similarity"),
statistic = c("exact", "normal", "cont.normal"))
```

`pdA` |
the probability of discrimination for the model under the alternative hypothesis; scalar between zero and one |

`d.primeA` |
d-prime for the model under the alternative hypothesis; non-negative numerical scalar |

`pd0` |
the probability of discrimination under the null hypothesis; scalar between zero and one |

`d.prime0` |
d-prime under the null hypothesis; non-negative numerical scalar |

`sample.size` |
the sample size; a scalar positive integer |

`alpha` |
the type I level of the test; scalar between zero and one |

`method` |
the discrimination protocol for which the power should be computed |

`double` |
should the 'double' variant of the discrimination protocol be used? Logical scalar. Currently not implemented for "twofive", "twofiveF", and "hexad". |

`pGuess` |
the guessing probability for the discrimination protocol, e.g. 1/2 for duo-trio and 2-AFC, 1/3 for triangle, tetrad and 3-AFC, 1/10 for two-out-of-five and hexad and 2/5 for two-out-of-five with forgiveness; scalar between zero and one |

`test` |
the type of one-sided binomial test (direction of the alternative hypothesis): "difference" corresponds "greater" and "similarity" corresponds to "less" |

`statistic` |
should power determination be based on the 'exact' binomial test, the normal approximation to this, or the normal approximation with continuity correction? |

The power of the standard one-tailed difference test where the null
hypothesis is "no difference" is obtained with `pd0 = 0`

.

The probability under the null hypothesis is
given by `pd0 + pg * (1 - pd0)`

where `pg`

is the guessing
probability `pGuess`

. Similarly, the probability of the
alternative hypothesis is given by `pdA + pg * (1 - pdA)`

The power; a numerical scalar.

Rune Haubo B Christensen and Per Bruun Brockhoff

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.

Bi, J. (2001) The double discrimination methods. Food Quality and Preference, 12, pp. 507-513.

`findcr`

,
`discrim`

, `discrimSim`

,
`AnotA`

, `discrimSS`

```
## Finding the power of a discrimination test with d-prime = 1,
## a sample of size 30 and a type I level of .05:
pd <- coef(rescale(d.prime = 1, method = "twoAFC"))$pd
discrimPwr(pd, sample.size = 30)
d.primePwr(1, sample.size = 30, method = "twoAFC")
## Obtaining the equivalent normal approximation with and without
## continuity correction:
discrimPwr(pd, sample.size = 30, statistic = "cont.normal")
discrimPwr(pd, sample.size = 30, statistic = "normal")
# Example from Bi (2001) with n=100 and 35 correct answers in a
# double duotrio test:
p1 <- 0.35
# Estimate of d-prime quoted by Bi(2001) was 1.06:
dp <- psyinv(p1, method="duotrio", double=TRUE)
# Power using normal approximation w/o continuity adjustment quoted by Bi(2001):
d.primePwr(dp, sample.size = 100, method="duotrio",
double=TRUE, stat="normal") # 0.73
# d.primePwr(dp, sample.size = 100, method="duotrio", double=TRUE,
# stat="cont.normal")
# Power of exact test:
d.primePwr(dp, sample.size = 100, method="duotrio",
double=TRUE, stat="exact") # 0.697
## A similarity example:
discrimPwr(pdA = 0.1, pd0 = 0.2, sample.size = 100, pGuess = 1/3,
test = "similarity")
```

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