OneTwoSamples (version 1.1-0)

interval_var4: Two sided or one sided interval estimation of sigma1^2 / sigma2^2 of two normal samples

Description

Compute the two sided or one sided interval estimation of sigma1^2 / sigma2^2 of two normal samples when the population means are known or unknown.

Usage

interval_var4(x, y, mu = c(Inf, Inf), side = 0, alpha = 0.05)

Value

A data.frame with variables:

rate

The estimate of the ratio of population variances, rate = Sx2/Sy2. When the population means mu is known, Sx2 = 1/n1*sum((x-mu[1])^2) and Sy2 = 1/n2*sum((y-mu[2])^2. When mu is unknown, Sx2 = var(x) and Sy2 = var(y).

df1

The first degree of freedom.

df2

The second degree of freedom.

a

The confidence lower limit.

b

The confidence upper limit.

Arguments

x

A numeric vector.

y

A numeric vector.

mu

The population means. When it is known, input it, and the function computes the interval endpoints using an F distribution with degree of freedom (n1, n2). When it is unknown, ignore it, and the function computes the interval endpoints using an F distribution with degree of freedom (n1-1, n2-1).

side

A parameter used to control whether to compute two sided or one sided interval estimation. When computing the one sided upper limit, input side = -1; when computing the one sided lower limit, input side = 1; when computing the two sided limits, input side = 0 (default).

alpha

The significance level, a real number in [0, 1]. Default to 0.05. 1-alpha is the degree of confidence.

Author

Ying-Ying Zhang (Robert)

References

Zhang, Y. Y., Wei, Y. (2013), One and two samples using only an R funtion, tools:::Rd_expr_doi("10.2991/asshm-13.2013.29").

Examples

x=rnorm(10, mean = 1, sd = 0.2); x
y=rnorm(20, mean = 2, sd = 0.3); y
interval_var4(x, y, mu = c(1,2), side = -1)
interval_var4(x, y)