variance.CI {LearningStats}

Confidence Interval for the Variance and the Standard Deviation of a Normal Population

Description

variance.CI provides a pointwise estimation and a confidence interval for the variance and the standard deviation of a normal population in both scenarios: known and unknown population mean.

Usage

variance.CI(x = NULL, s = NULL, sc = NULL, smu = NULL, mu = NULL,
  n = NULL, conf.level)

Arguments

x

a numeric vector containing the sample.

s

a single numeric value corresponding with the sample standard deviation.

sc

a single numeric value corresponding with the cuasi-standard deviation.

smu

if known, a single numeric value corresponding with the estimation of the standard deviation for known population mean.

mu

if known, a single numeric value corresponding with the population mean. Even when the user provides smu, mu is still needed.

n

a single positive integer corresponding with the sample size; not needed if the sample is provided.

conf.level

a single numeric value corresponding with the confidence level of the interval; must be a value in (0,1).

Details

The formula interface is applicable when the user provides the sample and also when the user provides the value of sample characteristics (cuasi-standard deviation or sample standard deviation and the sample size).

Value

A list containing the following components:

var.estimate

the cuasi-variance for unknown population mean, and the estimation of the variance for known population mean.

sd.estimate

the cuasi-standard deviation for unknown population mean and the estimation of the standard deviation for known population mean.

CI.var

a numeric vector of length two containing the lower and upper bounds of the confidence interval for the population variance.

CI.sd

a numeric vector of length two containing the lower and upper bounds of the confidence interval for the population standard deviation.

Independently on the user saving those values, the function provides a summary of the result on the console.

Examples

#Given the estimation of the standard deviation with known population mean
dat=rnorm(20,mean=2,sd=1)
smu=Smu(dat,mu=2)
variance.CI(smu=smu,mu=2,n=20,conf.level=0.95)

#Given the sample with known population mean
dat=rnorm(20,mean=2,sd=1)
variance.CI(dat,mu=2,conf.level=0.95)

#Given the sample with unknown population mean
dat=rnorm(20,mean=2,sd=1)
variance.CI(dat,conf.level=0.95)

#Given the cuasi-standard deviation with unknown population mean
dat=rnorm(20,mean=2,sd=1)
variance.CI(sc=sd(dat),n=20,conf.level=0.95)