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Two sided or one sided test of hypothesis of sigma1^2 and sigma2^2 of two normal samples

var_test2.Rd

Compute the two sided or one sided test of hypothesis of sigma1^2 and sigma2^2 of two normal samples when the population means are known or unknown.

Usage

var_test2(x, y, mu = c(Inf, Inf), side = 0)

Arguments

x

A numeric vector.

y

A numeric vector.

mu

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

side

A parameter used to control two sided or one sided test of hypothesis. When inputting side = 0 (default), the function computes two sided test of hypothesis, and H1: sigma1^2 != sigma2^2; when inputting side = -1 (or a number < 0), the function computes one sided test of hypothesis, and H1: sigma1^2 < sigma2^2; when inputting side = 1 (or a number > 0), the function computes one sided test of hypothesis, and H1: sigma1^2 > sigma2^2.

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.

F

The F statistic.

p_value

The P value.

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] 1.0056004 0.8513454 1.0377585 0.6390083 1.2931110 1.0306507 1.4345223
#>  [8] 1.0951019 0.8580107 1.1221453
y=rnorm(20, mean = 2, sd = 0.3); y
#>  [1] 1.719771 1.623910 2.087434 1.867012 2.000332 2.022302 1.823144 1.829399
#>  [9] 1.959446 2.353426 1.542930 2.178184 2.099885 2.318930 1.908745 2.111006
#> [17] 2.080130 1.837244 2.362360 2.348121
var_test2(x, y, mu = c(1, 2), side = 1)
#>        rate df1 df2         F  P_value
#> 1 0.8681847  10  20 0.8681847 0.575379
var_test2(x, y, side = 1)
#>        rate df1 df2         F   P_value
#> 1 0.8905436   9  19 0.8905436 0.5511375