power.calc: Power Calculator

In ANOVAreplication: Test ANOVA Replications by Means of the Prior Predictive p-Value

Description

Calculates the power for the prior predictive check

Usage

power.calc(n.r,posterior,g.m,p.sd,
           statistic,Amat=0L,exact=0L,difmin=0L,effectsize=FALSE,
           alpha=.05)

Arguments

n.r	vector with the sample size per group (i.e., n_jr) for new study (i.e., y_r).
posterior	matrix (e.g., the output of Gibbs.ANOVA) with samples from the posterior based on the original data (i.e., y_o).
g.m	vector; the population values the alternative distribution. To calculate the power to reject replication if the means are equal specify the grand mean of the study variables in the original dataset.
p.sd	integer; the population value for the pooled standard deviation in the alternative distribution. We advice to specify the pooled standard deviation for the study variables in the original dataset.
statistic	the type of hypothesis to be evaluated: "ineq" for inequality constrained means, "dif" for inequality constraints plus minimum differences between means, "exact" for specific values for the means.
Amat	p by q matrix, where p is the number of means in the ANOVA model, and q is the number of constraints to be imposed on the model. Each row represents one constraint where the parameter with the lower value according to the constraint receives the value -1, and the parameter with the higher value according to the constraint receives the value 1. Other parameters within the same row obtain the value 0. The create_matrices function can be used to obtain Amat.
exact	vector of length p, where p is the number of means in the ANOVA model, with the exact values of the constrained hypothesis.
difmin	vector of length q with the minimum difference per constraint as specified in Amat. The create_matrices function can be used to obtain difmin. Default = 0L, indicating that only the ordering of means is evaluated.
effectsize	logical; If TRUE the values in difmin are interpreted as Cohen's d.
alpha	integer; the level of alpha that should be taken into account while calculating the required sample size.

Value

power	The acquired power given the input
rejection.value	The 1-alpha'th percentile of the null distribution. The proportion of H1 larger than this value constitues power.

Author(s)

M. A. J. Zondervan-Zwijnenburg, H. Hoijtink

References

Zondervan-Zwijnenburg, M.A.J., Van de Schoot, R., & Hoijtink, H. (2017). Testing ANOVA replication by means of the prior predictive p-value.

See Also

See also runShiny, Gibbs.ANOVA, Fbar.ineq, Fbar.dif, and Fbar.exact, create_matrices, prior.predictive.check, sample.size.calc.

Examples

#analysis original data
data_o <- data.frame(y=ChickWeight$weight,g=ChickWeight$Diet)
g.m <- rep(mean(data_o$y),3)
#compute pooled sd
sd.g <- aggregate(data_o$y,by=list(data_o$g),sd)[,2]
n.g <- table(data_o$g)
p.sd<- pooled.sd(data_o)

means <- aggregate(data_o$y,by=list(data_o$g),mean)[,2]

post <- Gibbs.ANOVA(data_o)

power.calc(n.r=c(20,21,22,23),posterior=post$posterior,g.m=g.m,p.sd=p.sd,
           statistic="exact",exact=means,alpha=.05)

ANOVAreplication documentation built on Sept. 27, 2021, 9:06 a.m.