Madhava Rao-Raghunath Test for Testing Treatment vs. Control
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).
mrrTest(x, ...) ## Default S3 method: mrrTest(x, y = NULL, m = NULL, ...) ## S3 method for class 'formula' mrrTest(formula, data, subset, na.action, ...)
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 |
data |
an optional matrix or data frame (or similar: see
|
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 |
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.
A list with class "htest" containing the following components:
a character string indicating what type of test was performed.
a character string giving the name(s) of the data.
the estimated quantile of the test statistic.
the p-value for the test.
the parameters of the test statistic, if any.
a character string describing the alternative hypothesis.
the estimates, if any.
the estimate under the null hypothesis, if any.
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.
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
## 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)
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