R: Madhava Rao-Raghunath Test for Testing Treatment vs. Control

mrrTest {PMCMRplus} | R Documentation

## Madhava Rao-Raghunath Test for Testing Treatment vs. Control

### Description

The function has implemented the nonparametric test of Madhava Rao and Raghunath (2016) for testing paired two-samples for symmetry. The null hypothesis H: F(x,y) = F(y,x) is tested against the alternative A: F(x,y) != F(y,x).

### Usage

    mrrTest(x, ...)

    ## Default S3 method:
    mrrTest(x, y = NULL, m = NULL, ...)

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

### Arguments

`x` | numeric vector of data values. Non-finite (e.g., infinite or missing) values will be omitted.
`...` | further arguments to be passed to or from methods.
`y` | an optional numeric vector of data values: as with x non-finite values will be omitted.
`m` | numeric, optional integer number, whereas n = k m needs to be full filled.
`formula` | a formula of the form `response ~ group` where `response` gives the data values and `group` a vector or factor of 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 `NA`s. Defaults to `getOption("na.action")`.

### Details

Let X_i and Y_i, ~ i ≤ n denote continuous variables that were observed on the same ith test item (e.g. patient) with i = 1, … n. Let

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Let U_{(i)} be the ith order statistic, U_{(1)} ≤ U_{(2)} ≤ … U_{(n)} and k the number of clusters, with the condition:

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Further, let the divider denote d_0 = -∞, d_k = ∞, and else

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The two counts are

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and

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The test statistic is

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The exact p-values for 5 ≤ n ≤ 30 are taken from an internal look-up table. The exact p-values were taken from Table 7, Appendix B of Madhava Rao and Raghunath (2016).

If `m = NULL` the function uses n = m for all prime numbers, otherwise it tries to find an value for m in such a way, that for k = n / m all variables are integer.

### Value

A list with class `"htest"` containing the following components:

method

  a character string indicating what type of test was performed.

data.name

  a character string giving the name(s) of the data.

statistic

  the estimated quantile of the test statistic.

p.value

  the p-value for the test.

parameter

  the parameters of the test statistic, if any.

alternative

  a character string describing the alternative hypothesis.

estimates

  the estimates, if any.

null.value

  the estimate under the null hypothesis, if any.

### Note

The function returns an error code if a value for `m` is provided that does not lead to an integer of the ratio k = n /m.

The function also returns an error code, if a tabulated value for given n, m and calculated M can not be found in the look-up table.

### References

Madhava Rao, K.S., Ragunath, M. (2016) A Simple Nonparametric Test for Testing Treatment Versus Control. J Stat Adv Theory Appl 16, 133–162. doi: 10.18642/jsata_7100121717

### Examples

    ## Madhava Rao and Raghunath (2016), p. 151
    ## Inulin clearance of living donors
    ## and recipients of their kidneys
    x <- c(61.4, 63.3, 63.7, 80.0, 77.3, 84.0, 105.0)
    y <- c(70.8, 89.2, 65.8, 67.1, 87.3, 85.1, 88.1)
    mrrTest(x, y)

    ## formula method
    ## Student's Sleep Data
    mrrTest(extra ~ group, data = sleep)

[Package PMCMRplus version 1.9.0 Index]