PMCMRplus (version 1.9.6)

mrrTest: 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 $A:F(x,y)\ne F(y,x)$.

Usage

mrrTest(x, ...)
# S3 method for default
mrrTest(x, y = NULL, m = NULL, ...)
# S3 method for formula
mrrTest(formula, data, subset, na.action, ...)

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.

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 $n=km$ 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 NAs. Defaults to getOption("na.action").

Details

Let $X_i$ and $Y_i,i\le n$ denote continuous variables that were observed on the same $i$th test item (e.g. patient) with $i=1,\dots n$. Let $$U_i=X_i+Y_i{V}_i=X_i-Y_i$$

Let $U_{(i)}$ be the $i$th order statistic, $U_{(1)}\le U_{(2)}\le \dots U_{(n)}$ and $k$ the number of clusters, with the condition:

$$n=km.$$

Further, let the divider denote $d_0=-\mathrm{\infty }$, $d_k=\mathrm{\infty }$, and else $$d_j=\frac{U_{(jm)}+U_{(jm+1)}}{2},1\le j\le k-1$$

The two counts are $$n_j^{+}=\{\begin{array}{lr}1& \mathrm{if}{d}_{j-1}<u_i<d_j,v_i>0\\ 0& \end{array}$$

and $$n_j^{-}=\{\begin{array}{lr}1& \mathrm{if}{d}_{j-1}<u_i<d_j,v_i\le 0\\ 0& \end{array}$$

The test statistic is $$M=\sum _{j=1}^k\frac{{(n_j^{+}-n_j^{-})}^2}{m}$$

The exact p-values for $5\le n\le 30$ 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.

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. tools:::Rd_expr_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)