MBESS (version 4.6.0)

var.ete: The Variance of the Estimated Treatment Effect at Selected Covariate Values in a Two-group ANCOVA.

Description

Calculate the variance or an estimated variance of the estimated treatment effect at selected covariate values assuming heterogeneity of regression and a random covariate in a two-group ANCOVA.

Usage

var.ete(sigma2, sigmaz2, n1, n2, beta1, beta2, muz = 0, c = 0, type = "sample", 
covariate.value = "sample.mean")

Arguments

sigma2

Variance of the residual errors if 'type = population' and sample variance of the residual errors if 'type = sample'

sigmaz2

Variance of the random covariate if 'type = population' and sample variance of the random covariate if 'type = sample'

n1

Sample size of group 1

n2

Sample size of group 2

beta1

Slope of the random covariate for group 1 if 'type = population' and estimated slope of the random covariate for group 1 if 'type = sample'

beta2

Slope of the random covariate for group 2 if 'type = population' and estimated slope of the random covariate for group 2 if 'type = sample'

muz

Population mean of the random covariate if 'type = population' and sample mean of the random covariate if 'type = sample'

c

Fixed value where the treatment effect is assessed

type

The type of variance formula: 'population' refers to the variance of the estimated treatment effect using population slopes and variances; 'sample'refers to an unbiased estimate of the variance using sample slopes and variances

covariate.value

The covariate value is chosen at the sample grand mean if 'covariate.value = sample.mean', at the sample grand mean plus or minus one sample standard deviation if 'covariate.value = SD', and at a fixed value if 'covariate.value = fixed'

Value

The function yields the variance of the estimated treatment effect for the specified input values.

References

Maxwell, S. E., Delaney, H. D., & Kelley, K. (2018). Designing experiments and analyzing data: A model comparison perspective. New York: Routledge.

Li, L., McLouth, C. J., and Delaney, H. D. (submitted). Analysis of Covariance with Heterogeneity of Regression and a Random Covariate: The Variance of the Estimated Treatment Effect at Selected Covariate Values.

Examples

# NOT RUN {
# Pygmalion in the Classroom: Teacher Expectation and Pupils' Intellectual Development. 
# This dataset has been used to illustrate heterogeneity of regression 
# by Maxwell, Delaney, and Kelley (2018).
nA <- 64
nB <- 246
muz <- 0
sigma2 <- 175.3251
sigmaz2 <- 348.9099
betaA <- 0.96895
betaB <- 0.77799
var.ete(sigma2=sigma2, sigmaz2=sigmaz2, n1=nA, n2=nB, beta1=betaA, beta2=betaB, 
type="sample", covariate.value = "sample.mean")
var.ete(sigma2=sigma2, sigmaz2=sigmaz2, n1=nA, n2=nB, beta1=betaA, beta2=betaB, 
type="sample", covariate.value = "SD")
var.ete(sigma2=sigma2, sigmaz2=sigmaz2, n1=nA, n2=nB, beta1=betaA, beta2=betaB, 
c = 4.2631, muz=muz, type="sample",covariate.value = "fixed")
# }