Two sample variance tests

Tests if two series differ in their distributional variance parameter.

Usage

varianceTest(x, y, method = c("varf", "bartlett", "fligner"), 
    title = NULL, description = NULL)

Arguments

x, y

numeric vectors of data values.

method

a character string naming which test should be applied.

title

an optional title string, if not specified the inputs data name is deparsed.

description

optional description string, or a vector of character strings.

Details

The method="varf" can be used to compare variances of two normal samples performing an F test. The null hypothesis is that the ratio of the variances of the populations from which they were drawn is equal to one.

The method="bartlett" performs the Bartlett test of the null hypothesis that the variances in each of the samples are the same. This fact of equal variances across samples is also called homogeneity of variances. Note, that Bartlett's test is sensitive to departures from normality. That is, if the samples come from non-normal distributions, then Bartlett's test may simply be testing for non-normality. The Levene test (not yet implemented) is an alternative to the Bartlett test that is less sensitive to departures from normality.

The method="fligner" performs the Fligner-Killeen test of the null that the variances in each of the two samples are the same.

Value

an object from class fHTEST

Note

Some of the test implementations are selected from R's ctest package.

References

Conover, W. J. (1971); Practical nonparametric statistics, New York: John Wiley & Sons.

Lehmann E.L. (1986); Testing Statistical Hypotheses, John Wiley and Sons, New York.

Author

R-core team for hypothesis tests implemented from R's package ctest.

Examples

x <- rnorm(50)
y <- rnorm(50)
   
varianceTest(x, y, "varf")
#> 
#> Title:
#>  F Test of Variances
#> 
#> Test Results:
#>   PARAMETER:
#>     Hypothesized Ratio: 1
#>     Numerator   df: 49
#>     Denumerator df: 49
#>   SAMPLE ESTIMATES:
#>     Ratio of Variances: 1.2973
#>   STATISTIC:
#>     F: 1.2973
#>   P VALUE:
#>     Alternative Two-Sided: 0.3655 
#>     Alternative      Less: 0.8173 
#>     Alternative   Greater: 0.1827 
#>   CONFIDENCE INTERVAL:
#>     Two-Sided: 0.7362, 2.286
#>          Less: 0, 2.0851
#>       Greater: 0.8071, Inf
#> 
varianceTest(x, y, "bartlett")
#> 
#> Title:
#>  Bartlett Test for Homogeneity of Variances
#> 
#> Test Results:
#>   STATISTIC:
#>     Bartlett's Chi-squared: 0.8191
#>   P VALUE:
#>     0.3655 
#> 
varianceTest(x, y, "fligner")
#> 
#> Title:
#>  Fligner-Killeen Test for Homogeneity of Variances
#> 
#> Test Results:
#>   STATISTIC:
#>     FK:med chi-squared: 0.6764
#>   P VALUE:
#>     0.4108 
#>