Confidence intervals for parameters of one-way random effects ANOVA

Source: R/statpsych1.R

Computes estimates and confidence intervals for four parameters of the one-way random effects ANOVA: 1) the superpopulation grand mean, 2) the square-root within-group variance component, 3) the square-root between-group variance component, and 4) the omega-squared coefficient. This function assumes equal sample sizes.

ci.random.anova(alpha, m, sd, n)

Arguments

alpha

1 - alpha confidence

m

vector of estimated group means

sd

vector of estimated group standard deviations

n

common sample size in each group

Value

Returns a 4-row matrix. The rows are:

  • Grand mean - the mean of the superpopulation of means

  • Within SD - the square-root within-group variance component

  • Between SD - the square-root between-group variance component

  • Omega-squared - the omega-squared coefficient

The columns are:

  • Estimate - estimate of parameter

  • LL - lower limit of the confidence interval

  • UL - upper limit of the confidence interval

Examples

m <- c(56.1, 51.2, 60.3, 68.2, 48.9, 70.5)
sd <- c(9.45, 8.79, 9.71, 8.90, 8.31, 9.75)
ci.random.anova(.05, m, sd, 20)
#>                 Estimate         LL         UL
#> Grand mean     59.200000 49.9363896 68.4636104
#> Within SD:      9.166782  8.0509046 10.4373219
#> Between SD:     8.585948  8.3239359  8.8562078
#> Omega-squared:  0.467317  0.2284142  0.8480383

# Should return:
#                 Estimate         LL         UL
# Grand mean     59.200000 49.9363896 68.4636104
# Within SD:      9.166782  8.0509046 10.4373219
# Between SD:     8.585948  8.3239359  8.8562078
# Omega-squared:  0.467317  0.2284142  0.8480383