sensR (version 1.5-2)

dod: Thurstonian Degree-of-Difference (DOD) model

Description

Fits the Thurstonian Degree-of-Difference (DOD) model and performs hypothesis/significance tests of d-prime (Thurstonian delta). One-sided difference and similarity tests as well as two-sided tests of d-prime are available. The user may choose from a number of tests statistics.

Usage

dod(same, diff, d.prime0 = 0, conf.level = 0.95,
    statistic = c("likelihood", "Pearson", "Wilcoxon", "Wald"),
    alternative = c("difference", "similarity", "two.sided",
    "less", "greater"), control=dodControl(), ...)
# S3 method for dod
print(x, digits = max(3, getOption("digits") - 3), ...)

Arguments

same

the answers to same-pairs; either 1) a numeric vector of counts of length equal to the number of response categories ordered appropriately or 2) a factor where the levels indicate the response categories.

diff

the answers to different-pairs in the same format as same.

d.prime0

the value of d.prime under the null hypothesis. In the standard no-difference test d.prime0 = 0, while it has to be positive for similarity tests and two-sided tests.

conf.level

the confidence level for the confidence intervals

statistic

the statistic to be used for hypothesis testing

alternative

the nature of the alternative hypothesis in the hypothesis/significance test for d-prime. Note that "greater" is an alias for "difference" and "less" is an alias for "similarity"

control

options to control the fitting process specfied via a call to dodControl.

x

an object of class "dod".

digits

number of digits in resulting table of results.

…

not currently used.

Value

An object of class dod.

Details

dod will report the likelihood based confidence interval for d.prime unless statistic = "Wald" in which case the standard symmetric Wald type confidence interval is reported. This interval can be highly inaccurate and so is not recommened for practical use.

The p-value for the standard one-tailed difference test of "no difference" is obtained with d.prime0 = 0 corresponding to the default setting.

The standard error of d-prime is not defined when the parameter estimate is zero (or numerically close) and it will be reported as NA in this case.

The "Wald" statistic is *NOT* recommended for practical use---it is only included here for completeness and to allow comparisons with other software etc.

References

Ennis, J.M. and R.H.B. Christensen (2014) A Thurstonian comparison of the tetrad and degree of difference tests. Food Quality and Preference, in press.

Christensen, R.H.B, J.M. Ennis, D.M. Ennis and P.B Brockhoff (2012) A Thurstonian model for the Degree of Difference test with extensions to unequal variance, sequence effects and replicated data. Talk at Sensometrics conference, Rennes, France, July 11th.

See Also

dodSim, dodPwr, dodControl, dod_fit, optimal_tau

Examples

# NOT RUN {
## DOD example data:
same.pairs <- c(25, 22, 33, 20)
diff.pairs <- c(18, 22, 30, 30)

## Fit Thurstonian dod-model and perform difference test:
dod(same=same.pairs, diff=diff.pairs)

## Can choose another test statistic (e.g. Wilcoxon):
dod(same=same.pairs, diff=diff.pairs, statistic="Wilcox")

## A similarity test (with simulated data):
set.seed(121)
(Data2 <- dodSim(d.prime=0, ncat=4, sample.size=200, method.tau="equi.prob"))
dod(same=Data2[1, ], diff=Data2[2, ], d.prime0=1.2,
    alternative="similarity")

## Extract parameters from a dod fit:
fm <- dod(same=same.pairs, diff=diff.pairs)
coef(fm)

# }