Description Usage Arguments Details Value Note Author(s) References See Also Examples
Performs twosample nonparametric multivariate test of variance based on the minimum spanning tree (MST) and KolmogorovSmirnov statistic. It tests the null hypothesis that a set of features has the same scale in two conditions versus different scales.
1 
object 
a numeric matrix with columns and rows respectively corresponding to samples and features. 
group 
a numeric vector indicating group associations for samples. Possible values are 1 and 2. 
mst.order 
numeric value to indicate the consideration of the union
of the first 
nperm 
number of permutations used to estimate the null distribution of the test statistic. If not given, a default value 1000 is used. 
pvalue.only 
logical. If 
This function tests the null hypothesis that a set of features has the
same scale in two conditions. It performs a twosample nonparametric
multivariate test based on the minimum spanning tree (MST) and
KolmogorovSmirnov statistic as proposed by Friedman and Rafsky (1979). The
MST of the weighted undirectional graph created from the samples is found.
The nodes of the MST are ranked based on their position in the MST. The MST is
rooted at the node with smallest geodisic distance (rank 1) and nodes with
higher depths from the root are assigned higher ranks. The quantity
d_i = (r_i / n_1)  (s_i / n_2) is calculated where r_i(s_i)
is the number of nodes (samples) from condition 1(2) which ranked lower than
i, 1 ≤ i ≤ N and N is the total number of samples. The
KolmogorovSmirnov statistic is given by the maximum absolute difference
D = √{\frac{n_{1}n_{2}}{n_{1}+n_{2}}} maxd_i. The performance of
this test under different alternative hypotheses was thoroughly examind in
Rahmatallah et. al. (2012). The null distribution of the test statistic is
estimated by permuting sample labels nperm
times and calculating the
test statistic for each. Pvalue is calculated as
p.value = \frac{∑_{k=1}^{nperm} I ≤ft[ D_{k} ≥q D_{obs} \right] + 1}{nperm + 1}
where D_{k} is the test statistic for permutation k
, D_{obs} is the
observed test statistic, and I
is the indicator function.
When pvalue.only=TRUE
(default), function RKStest
returns
the pvalue indicating the attained significance level. When
pvalue.only=FALSE
, function RKStest
produces a list of
length 3 with the following components:
statistic 
the value of the observed test statistic. 
perm.stat 
numeric vector of the resulting test statistic for

p.value 
pvalue indicating the attained significance level. 
The variance of both the Poisson and negative Bionomial distributions, used
to model count data, is a function of their mean. Therefore, using the radial
KolmogorovSmirnov test (RKStest
) to detect pathways with differential
variance for RNASeq counts is not recommended without proper data
normalization.
Yasir Rahmatallah and Galina Glazko
Rahmatallah Y., EmmertStreib F. and Glazko G. (2012) Gene set analysis for selfcontained tests: complex null and specific alternative hypotheses. Bioinformatics 28, 3073–3080.
Friedman J. and Rafsky L. (1979) Multivariate generalization of the WaldWolfowitz and Smirnov twosample tests. Ann. Stat. 7, 697–717.
RMDtest
, WWtest
, MDtest
,
KStest
.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20  ## generate a feature set of length 20 in two conditions
## each condition has 20 samples
## use multivariate normal distribution
library(MASS)
ngenes < 20
nsamples < 40
## let the mean vector have zeros of length 20 for both conditions
zero_vector < array(0,c(1,ngenes))
## set the covariance matrix to be an identity matrix for condition 1
cov_mtrx < diag(ngenes)
gp1 < mvrnorm((nsamples/2), zero_vector, cov_mtrx)
## set some scale difference in the covariance matrix for condition 2
cov_mtrx < cov_mtrx*3
gp2 < mvrnorm((nsamples/2), zero_vector, cov_mtrx)
## combine the data of two conditions into one dataset
gp < rbind(gp1,gp2)
dataset < aperm(gp, c(2,1))
## first 20 samples belong to group 1
## second 20 samples belong to group 2
pvalue < RKStest(object=dataset, group=c(rep(1,20),rep(2,20)))

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