g.tests {gTests}

Graph-based two-sample tests

Description

This function provides four graph-based two-sample tests.

Usage

g.tests(E, sample1ID, sample2ID, test.type="all", maxtype.kappa = 1.14, perm=0)

Arguments

E

An edge matrix representing a similarity graph with the number of edges in the similarity graph being the number of rows and 2 columns. Each row records the subject indices of the two ends of an edge in the similarity graph.

sample1ID

The subject indices of sample 1.

sample2ID

The subject indices of sample 2.

test.type

The default value is "all", which means all four tests are performed: orignial edge-count test (Friedman and Rafsky (1979)), generalized edge-count test (Chen and Friedman (2016)), weighted edge-count test (Chen, Chen and Su (2016)) and maxtype edge-count tests (Zhang and Chen (2017)). Set this value to "original" or "o" to permform only the original edge-count test; set this value to "generalized" or "g" to perform only the generalized edge-count test; set this value to "weighted" or "w" to perform only the weighted edge-count test; and set this value to "maxtype" or "m" to perform only the maxtype edge-count tests.

maxtype.kappa

The value of parameter(kappa) in the maxtype edge-count tests. The default value is 1.14.

perm

The number of permutations performed to calculate the p-value of the test. The default value is 0, which means the permutation is not performed and only approximate p-value based on asymptotic theory is provided. Doing permutation could be time consuming, so be cautious if you want to set this value to be larger than 10,000.

Value

test.statistic

The test statistic.

pval.approx

The approximated p-value based on asymptotic theory.

pval.perm

The permutation p-value when argument 'perm' is positive.

References

Friedman J. and Rafsky L. Multivariate generalizations of the WaldWolfowitz and Smirnov two-sample tests. The Annals of Statistics, 7(4):697-717, 1979.

Chen, H. and Friedman, J. H. A new graph-based two-sample test for multivariate and object data. Journal of the American Statistical Association, 2016.

Chen, H., Chen, X. and Su, Y. A weighted edge-count two sample test for multivariate and object data. Journal of the American Statistical Association, 2017.

Zhang, J. and Chen, H. Graph-based two-sample tests for discrete data.

Examples

# the "example" data contains three similarity graphs represted in the matrix form: E1, E2, E3.
data(example) 
 
# E1 is an edge matrix representing a similarity graph.
# It is constructed on two samples with mean difference.
# Sample 1 indices: 1:100; sample 2 indices: 101:250.
g.tests(E1, 1:100, 101:250) 

# E2 is an edge matrix representing a similarity graph.
# It is constructed on two samples with variance difference.
# Sample 1 indices: 1:100; sample 2 indices: 101:250.
g.tests(E2, 1:100, 101:250)

# E3 is an edge matrix representing a similarity graph.
# It is constructed on two samples with mean and variance difference.
# Sample 1 indices: 1:100; sample 2 indices: 101:250.
g.tests(E3, 1:100, 101:250)

## Uncomment the following line to get permutation p-value with 200 permutations.
# g.tests(E1, 1:100, 101:250, perm=200)