Zrms: Large-sample Z-tests for the total absolute variation in a...

In baolinwu/RAMgt: Statistical tests in a Random-effects ANOVA Model

Description

Given a random-effects ANOVA model, Y_{ij}=μ+u_i+ε_{ij} with u_i\sim N(0,σ_b^2), ε_{ij}\sim N(0,σ_w^2), we want to make inference on the total absolute variation parameter, ρ^2=μ^2+σ_b^2+σ_w^2. Large-sample Z-tests can be conducted based on approximating ∑_{i,j}Y_{ij}^2 with a normal distribution.

Usage

Zrms(ng, mus, sse, alpha = 0.1, rho0 = 3, REML = TRUE)

Arguments

ng	sample sizes for each factor level
mus	sample mean values at each factor level
sse	total error sum of squares (sum of within-group sample variances)
alpha	desired CI coefficient
rho0	the null threshold value to test H_0: ρ≥ ρ_0
REML	whether we use REML or MLE, default to TRUE

Value

p.value

Z-score and Z-Wald test p-values

par0

estimated parameters, test statistic and its variance, and CI for ρ^2, under the null hypothesis

pars

estimated parameters, test statistic and its variance, and CI for ρ^2

References

Ndikintum, N. K. and Rao, M. (2016). A Special Inference Problem in Repeated Measures Design Test of Statistical Hypothesis on Accuracy Root Mean Square Application to Pulse Oximetry Studies. Statistics in Biopharmaceutical Research 8, 60–76.

Pennello, G. A. (2002). Sample size for paired repeated measures designs of method compari- son studies: Application to pulse oximetry. ASA Proceedings of the Joint Statistical Meetings pages 2671–2675.

Pennello, G. A. (2003). Comparing monitoring devices when a gold standard in unavailable: Application to pulse oximeters. ASA Proceedings of the Joint Statistical Meetings pages 3256–3263.

Bai,Y., Wang,Z., Lystig,T., and Wu,B. (2019) Efficient and powerful equivalency test on combined mean and variance with application to diagnostic device comparison studies. arXiv:1908.07979

Examples

A = rep(1:10, 5:14)
Y = 0.5+rnorm(length(A))+rnorm(length(unique(A)))[A]
ng = as.vector(table(A))
sse = sum(tapply(Y, A, var)*(ng-1), na.rm=TRUE)
mus = tapply(Y, A, mean)
Zrms(ng,mus,sse, rho0=2.5)

baolinwu/RAMgt documentation built on Nov. 3, 2019, 2:06 p.m.