Confidence interval for an average variance

Computes the estimate and confidence interval for an average variance from two or more studies. The estimated average variance or the upper confidence limit could be used as a variance planning value in sample size planning. The confidence intervals assume normality, and this function is not recommended if the variances have been estimated from leptokurtic data.

For more details, see Chapter 2 of Bonett (2021, Volume 5).

Usage

meta.ave.var(alpha, var, n, bystudy = TRUE)

Arguments

alpha

alpha level for 1-alpha confidence

var

vector of sample variances

n

vector of sample sizes

bystudy

logical to also return each study estimate (TRUE) or not

Value

Returns a matrix. The first row is the average estimate across all studies. If bystudy is TRUE, there is 1 additional row for each study. The matrix has the following columns:

• Estimate - estimated variance

• LL - lower limit of the confidence interval

• UL - upper limit of the confidence interval

References

Bonett DG (2021). Statistical Methods for Psychologists, Vol 1-5, https://dgbonett.sites.ucsc.edu/.

Examples

var <- c(26.63, 22.45, 34.12)
n <- c(40, 30, 50)
meta.ave.var(.05, var, n, bystudy = TRUE)
#>         Estimate       LL       UL
#> Average 27.73333 21.45679 35.84589
#> Study 1 26.63000 17.86939 43.90614
#> Study 2 22.45000 14.23923 40.57127
#> Study 3 34.12000 23.80835 52.98319

# Should return:
#         Estimate       LL       UL
# Average 27.73333 21.45679 35.84589
# Study 1 26.63000 17.86939 43.90614
# Study 2 22.45000 14.23923 40.57127
# Study 3 34.12000 23.80835 52.98319