Upper prediction limit for an estimated variance

Computes an upper prediction limit for the estimated variance in a future study for a planned sample size. The prediction limit uses a variance estimate from a prior study. Several confidence interval sample size functions in this package require a planning value of the estimated variance that is expected in the planned study. The upper variance prediction limit is useful as a variance planning value for the sample size required to obtain a confidence interval with desired width. This strategy for specifying a variance planning value is useful in applications where the population variance in the prior study is assumed to be very similar to the population variance in the planned study. This function will be replaced with pi.var which computes both one-sided and two-sided prediction limits.

Usage

pi.var.upper(alpha, var, n0, n)

Arguments

alpha

alpha value for upper 1-alpha confidence

var

estimated variance from prior study

n0

sample size used to estimate variance

n

planned sample size of future study

Value

Returns an upper prediction estimate (UL) of an estimated variance in a future study

References

Hahn GJ (1972). “Simultaneous prediction intervals to contain the standard deviations or ranges of future samples from a normal population.” Journal of the American Statistical Association, 67(340), 938–942. doi:10.1080/01621459.1972.10481322 .

Examples

pi.var.upper(.05, 15, 40, 100)
#>       UL
#>  23.9724

# Should return:
#      UL
# 23.9724