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

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)

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.

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.

References

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

Author

Ying-Ying Zhang (Robert) robertzhangyying@qq.com

Examples

x=rnorm(10, mean = 1, sd = 0.2); x
#>  [1] 1.3168995 1.0011351 0.8703591 1.3717326 1.1656606 1.2398071 1.1200102
#>  [8] 1.0117520 0.7420473 0.9747332
y=rnorm(20, mean = 2, sd = 0.3); y
#>  [1] 2.115196 1.837262 2.066782 1.806542 1.875650 1.311562 1.810536 1.840571
#>  [9] 2.213104 1.925540 2.202581 1.821395 2.033027 2.111601 1.817043 2.313182
#> [17] 1.909188 2.425184 1.739870 1.334558
interval_var4(x, y, mu = c(1,2), side = -1)
#>        rate df1 df2 a        b
#> 1 0.5273226  10  20 0 1.462802
interval_var4(x, y)
#>        rate df1 df2         a        b
#> 1 0.5041512   9  19 0.1750493 1.856959