sft (version 0.0-4)

ucipTest: A Statistical Test for Super or Limited Capacity

Description

A nonparametric test for capacity values significantly different than those predicted by the estimated unlimited capacity, independent parallel model.

Usage

ucipTest(RT, CR, OR = TRUE)

Arguments

RT

A list of response time arrays. The first array in the list is assumed to be the exhaustive condition.

CR

A list of correct/incorrect indicator arrays. If NULL, assumes all are correct.

OR

Logical indicating whether to test against OR (first terminating) or AND (exhaustive) performance.

Value

• statistic
  Z-score of a null-hypothesis test for UCIP performance.
• p.val
  p-value of a null-hypothesis test for UCIP performance.

Details

The test is based on the Nelson-Aalen formulation of the log-rank test. The function takes a weighted difference between estimated unlimited capacity, independent parallel performance, based on a participants single source response times, and the participants true performance when all sources are present.

References

Houpt, J.W. & Townsend, J.T. (2010). The statistical properties of the capacity coefficient. Journal of Mathematical Psychology, XX, XXX-XXX.

See Also

capacity.or capacity.and estimateUCIPor estimateUCIPand estimateNAH estimateNAK

Examples

rate1 <- .35
rate2 <- .3
RT.pa <- rexp(100, rate1)
RT.ap <- rexp(100, rate2)

CR.pa <- runif(100) < .98
CR.ap <- runif(100) < .98
CR.pp <- runif(100) < .96
CRlist <- list(CR.pp, CR.pa, CR.ap)

#  OR Processing
RT.pp.limited <- pmin( rexp(100, .5*rate1), rexp(100, .5*rate2))
RT.pp.unlimited <- pmin( rexp(100, rate1), rexp(100, rate2))
RT.pp.super <- pmin( rexp(100, 2*rate1), rexp(100, 2*rate2))
z.limited   <- ucipTest(RT=list(RT.pp.limited, RT.pa, RT.ap), CR=CRlist, OR=TRUE)
z.unlimited <- ucipTest(RT=list(RT.pp.unlimited, RT.pa, RT.ap), CR=CRlist, OR=TRUE)
z.super     <- ucipTest(RT=list(RT.pp.super, RT.pa, RT.ap), CR=CRlist, OR=TRUE)

#  AND Processing
RT.pp.limited <- pmax( rexp(100, .5*rate1), rexp(100, .5*rate2))
RT.pp.unlimited <- pmax( rexp(100, rate1), rexp(100, rate2))
RT.pp.super <- pmax( rexp(100, 2*rate1), rexp(100, 2*rate2))
z.limited   <- ucipTest(RT=list(RT.pp.limited, RT.pa, RT.ap), CR=CRlist, OR=FALSE)
z.unlimited <- ucipTest(RT=list(RT.pp.unlimited, RT.pa, RT.ap), CR=CRlist, OR=FALSE)
z.super     <- ucipTest(RT=list(RT.pp.super, RT.pa, RT.ap), CR=CRlist, OR=FALSE)