discrimPwr {sensR}

Sensory discrimination power analysis

Description

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.

Usage

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"))

Arguments

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?

Details

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)

Value

The power; a numerical scalar.

Author(s)

Rune Haubo B Christensen and Per Bruun Brockhoff

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.

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

See Also

findcr, discrim, discrimSim, AnotA, discrimSS

Examples

## 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")