ss.power.pcm {MBESS}

Sample size planning for power for polynomial change models

Description

Returns power given the sample size, or sample size given the desired power, for polynomial change models (currently only linear, that is, straight-line, change models)

Usage

ss.power.pcm(beta, tau, level.1.variance, frequency, duration, desired.power = NULL, 
N = NULL, alpha.level = 0.05, standardized = TRUE, directional = FALSE)

Arguments

beta

the level two regression coefficient for the group by time (linear) interaction; where "X" is coded -.5 and .5 for the two groups.

tau

the true variance of the individuals' slopes

level.1.variance

level one variance

frequency

frequency of measurements per unit of time duration of the study in the particular units (e.g., age, hours, grade level, years, etc.)

duration

time in some number of units (e.g., years)

desired.power

desired power

N

total sample size (one-half in each of the two groups)

alpha.level

Type I error rate

standardized

the standardized slope is the unstandardized slope divided by the square root of tau, the variance of the unique effects for beta.

directional

should a one (TRUE) or two (FALSE) tailed test be performed.

Author(s)

Ken Kelley (University of Notre Dame; [e-mail])

References

Raudenbush, S. W., & X-F., Liu. (2001). Effects of study duration, frequency of observation, and sample size on power in studies of group differences in polynomial change. Psychological Methods, 6, 387–401.

Examples

# Example from Raudenbush and Liu (2001)
ss.power.pcm(beta=-.4, tau=.003, level.1.variance=.0262, frequency=2, duration=2, 
desired.power=.80, alpha.level=.05, standardized=TRUE, directional=FALSE)
ss.power.pcm(beta=-.4, tau=.003, level.1.variance=.0262, frequency=2, duration=2,
N=238, alpha.level=.05, standardized=TRUE, directional=FALSE)


# The standardized effect size is obtained as beta/sqrt(tau): -.4/sqrt(.003) = -.0219.
# ss.power.pcm(beta=-.0219, tau=.003, level.1.variance=.0262, frequency=2, duration=2, 
# desired.power=.80, alpha.level=.05, standardized=FALSE, directional=FALSE)
ss.power.pcm(beta=-.0219, tau=.003, level.1.variance=.0262, frequency=2, duration=2, 
N=238, alpha.level=.05, standardized=FALSE, directional=FALSE)