diffvariance.test: Two Sample Variance Test of Normal Populations
In LearningStats: Elemental Descriptive and Inferential Statistics

Description Usage Arguments Details Value Examples

diffvariance.test allows to compute hypothesis tests about two population variances in both scenarios: known and unknown population mean.

diffvariance.test(x1 = NULL, x2 = NULL, s1 = NULL, s2 = NULL,
  sc1 = NULL, sc2 = NULL, smu1 = NULL, smu2 = NULL, mu1 = NULL,
  mu2 = NULL, n1 = NULL, n2 = NULL, alternative = "two.sided",
  alpha = 0.05, plot = TRUE, lwd = 1)

`x1`	a numeric vector containing the sample of one population.
`x2`	a numeric vector containing the sample of the other population.
`s1`	a single numeric value corresponding with the sample standard deviation of the first sample.
`s2`	a single numeric value corresponding with the sample standard deviation of the second sample.
`sc1`	a single numeric value corresponding with the cuasi-standard deviation of the first sample.
`sc2`	a single numeric value corresponding with the cuasi-standard deviation of the second sample.
`smu1`	if known, a single numeric value corresponding with the estimation of the standard deviation of the first sample.
`smu2`	if known, a single numeric value corresponding with the estimation of the standard deviation of the second sample.
`mu1`	if known, a single numeric corresponding with the mean of one population.
`mu2`	if known, a single numeric value corresponding with the mean of the other population.
`n1`	a single number indicating the sample size of `x1`. By default length of argument `x1`.
`n2`	a single number indicating the sample size of `x2`. By default length of argument `x2`.
`alternative`	a character string specifying the alternative hypothesis, must be one of "`two.sided`" (default), "`greater`" or "`less`".
`alpha`	single number between 0 and 1, significance level.
`plot`	a logical value indicating whether to display a graph including the test statistic value for the sample, its distribution, the rejection region and p-value.
`lwd`	single number indicating the line width of the plot.

The formula interface is applicable when the user provides the sample(s) or values of the sample characteristics (cuasi-standard deviation or sample standard deviation). When mu1 and mu2 or smu1 and smu2 are provided, the function performs the procedure with known population means.

A list with class "lstest" and "htest" containing the following components:

`statistic`	the value of the test statistic.
`parameter`	the degrees of the freedom of the F distribution of the test statistic.
`p.value`	the p-value of the test.
`estimate`	the ratio of the cuasi-variances of `x1` and `x2`.
`null.value`	the value specified by the null.
`alternative`	a character string describing the alternative.
`method`	a character string indicating the method used.
`data.name`	a character string giving the names of the data.
`alpha`	the significance level.
`dist.name`	a character string indicating the distribution of the test statistic.
`statformula`	a character string with the statistic's formula.
`reject.region`	a character string with the reject region.

x1 <- rnorm(40, mean = 1, sd = 2)
x2 <- rnorm(60, mean = 2, sd = 1.5)
# unknown population mean
diffvariance.test(x1, x2)
diffvariance.test(x1, sc2 = sd(x2), n2 = length(x2))
diffvariance.test(sc1 = sd(x1), sc2 = sd(x2), n1 = length(x1), n2 = length(x2))
# known population mean
diffvariance.test(x1, x2, mu1 = 1, mu2 = 2)
smu1 <- Smu(x1, mu = 1); smu2 <- Smu(x2, mu = 2)
diffvariance.test(smu1 = smu1, smu2 = smu2, n1 = length(x1), n2 = length(x2))