R: Siegel-Tukey Test For Equality In Variability

SiegelTukeyTest {DescTools} | R Documentation

## Siegel-Tukey Test For Equality In Variability

### Description

Non-parametric Siegel-Tukey test for equality in variability. The null hypothesis is that the variability of x is equal between two groups. A rejection of the null hypothesis indicates that variability differs between the two groups. `SiegelTukeyRank` returns the ranks, calculated after Siegel Tukey logic.

### Usage

    SiegelTukeyTest(x, ...)

    ## Default S3 method:
    SiegelTukeyTest(x, y, adjust.median = FALSE,
                    alternative = c("two.sided", "less", "greater"),
                    mu = 0, exact = NULL, correct = TRUE, conf.int = FALSE,
                    conf.level = 0.95, ...)

    ## S3 method for class 'formula'
    SiegelTukeyTest(formula, data, subset, na.action, ...)

    SiegelTukeyRank(x, g, drop.median = TRUE)

### Arguments

`x, y` | numeric vector of data values. Non-finite (e.g. infinite or missing) values will be omitted.
`g` | a vector or factor object giving the group for the corresponding elements of x.
`adjust.median` | Should between-group differences in medians be leveled before performing the test? In certain cases, the Siegel-Tukey test is susceptible to median differences and may indicate significant differences in variability that, in reality, stem from differences in medians. Default is `FALSE`.
`alternative` | a character string specifying the alternative hypothesis, must be one of `"two.sided"` (default), `"greater"` or `"less"`. You can specify just the initial letter.
`mu` | a number specifying an optional parameter used to form the null hypothesis. See Details.
`exact` | a logical indicating whether an exact p-value should be computed. This is passed directly to `wilcox.test`.
`correct` | a logical indicating whether to apply continuity correction in the normal approximation for the p-value.
`conf.int` | a logical indicating whether a confidence interval should be computed.
`conf.level` | confidence level of the interval.
`formula` | a formula of the form `lhs ~ rhs` where `lhs` gives the data values and rhs the corresponding groups.
`data` | an optional matrix or data frame (or similar: see `model.frame`) containing the variables in the formula `formula`. By default the variables are taken from `environment(formula)`.
`subset` | an optional vector specifying a subset of observations to be used.
`na.action` | a function which indicates what should happen when the data contain NAs. Defaults to `getOption("na.action")`.
`drop.median` | logical, defining whether the median of the combined samples should be left out, ensuring that there's an even number of elements (which is a requirement of the Siegel-Tukey test). Defaults to `TRUE`.
`...` | further arguments to be passed to or from methods.

### Details

The Siegel-Tukey test has relatively low power and may, under certain conditions, indicate significance due to differences in medians rather than differences in variabilities (consider using the argument `adjust.median`). Consider also using `mood.test` or `ansari.test`.

### Value

A list of class `htest`, containing the following components:

`statistic` | Siegel-Tukey test (Wilcoxon test on tie-adjusted Siegel-Tukey ranks, after the median adjustment if specified).
`p.value` | the p-value for the test
`null.value` | is the value of the median specified by the null hypothesis. This equals the input argument `mu`.
`alternative` | a character string describing the alternative hypothesis.
`method` | the type of test applied
`data.name` | a character string giving the names of the data.

### Author(s)

Daniel Malter, Tal Galili <tal.galili@gmail.com>, Andri Signorell <andri@signorell.net>
published on: https://www.r-statistics.com/2010/02/siegel-tukey-a-non-parametric-test-for-equality-in-variability-r-code/

### References

Siegel, S., Tukey, J. W. (1960): A nonparametric sum of ranks procedure for relative spread in unpaired samples. Journal of the American Statistical Association.

Sheskin, D. J. (2004): Handbook of parametric and nonparametric statistical procedures 3rd edition. Chapman and Hall/CRC. Boca Raton, FL.

### See Also

`mood.test`, `ansari.test`, `wilcox.test`, `LeveneTest`

### Examples

    # Duller, S. 183
    x <- c(12, 13, 29, 30)
    y <- c(15, 17, 18, 24, 25, 26)
    SiegelTukeyTest(x, y)
    SiegelTukeyTest(x, y, alternative="greater")

    # Duller, S. 323
    old <- c(870,930,935,1045,1050,1052,1055)
    new <- c(932,970,980,1001,1009,1030,1032,1040,1046)
    SiegelTukeyTest(old, new, alternative = "greater")
    # compare to the recommended alternatives
    mood.test(old, new, alternative="greater")
    ansari.test(old, new, alternative="greater")

    # Bortz, S. 250
    x <- c(26.3,26.5,26.8,27.0,27.0,27.2,27.3,27.3,27.4,27.5,27.6,27.8,27.9)
    id <- c(2,2,2,1,2,2,1,2,2,1,1,1,2)-1
    SiegelTukeyTest(x ~ id)

    # Sachs, Angewandte Statistik, 12. Auflage, 2007, S. 314
    A <- c(10.1,7.3,12.6,2.4,6.1,8.5,8.8,9.4,10.1,9.8)
    B <- c(15.3,3.6,16.5,2.9,3.3,4.2,4.9,7.3,11.7,13.1)
    SiegelTukeyTest(A, B)

    ### 1
    x <- c(4,4,5,5,6,6)
    y <- c(0,0,1,9,10,10)
    SiegelTukeyTest(x, y)

    ### 2
    # example for a non equal number of cases:
    x <- c(4,4,5,5,6,6)
    y <- c(0,0,1,9,10)
    SiegelTukeyTest(x, y)

    ### 3
    x <- c(33, 62, 84, 85, 88, 93, 97, 4, 16, 48, 51, 66, 98)
    id <- c(0,0,0,0,0,0,0,1,1,1,1,1,1)
    SiegelTukeyTest(x ~ id)

    ### 4
    x <- c(177,200,227,230,232,268,272,297,47,105,126,142,158,172,197,220,225,230,262,270)
    id <- c(rep(0,8),rep(1,12))
    SiegelTukeyTest(x ~ id, adjust.median=TRUE)

    ### 5
    x <- c(33,62,84,85,88,93,97)
    y <- c(4,16,48,51,66,98)
    SiegelTukeyTest(x, y)

    ### 6
    x <- c(0,0,1,4,4,5,5,6,6,9,10,10)
    id <- c(0,0,0,1,1,1,1,1,1,0,0,0)
    SiegelTukeyTest(x ~ id)

    ### 7
    x <- c(85,106,96, 105, 104, 108, 86)
    id <- c(0,0,1,1,1,1,1)
    SiegelTukeyTest(x ~ id)

[Package DescTools version 0.99.38 Index]