# Two sample variance tests

`test-varianceTest.Rd`

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`

## 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.

## Examples

```
set.seed(1234)
## rnorm -
# Generate Series:
x = rnorm(50)
y = rnorm(50)
## varianceTest -
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
#>
```