MethylCapSig (version 1.0.1)

patest: Park-Ayyala test statistic

Description

Calculates the two sample Park-Ayyala test statistic and p-value.

Usage

patest(X, Y)

Arguments

X

A matrix of dimension $n \times k$ whose rows represent the samples collected from $n$ ($\geq 4$) individuals from the first group on $k$ variates.

Y

A matrix of dimension $m \times k$ whose rows correspond to samples collected from $m$ ($\geq 4$) individuals from the second group on $k$ variates.

Default value is null. If not specified, the function performs a one-sample test using X.

Value

A $2 \times 1$ vector consisting of the test statistic and the p-value.

Details

The Park-Ayyala test statistic is used to test equality of mean vectors for two groups of multivariate observations, where the dimension is greater than the sample size. patest takes matrices X and Y as arguments whose rows represent samples from two groups respectively. Depending on the values in X and Y, the function initially determines whether to perform a one sample test ($\sum_{i,j} X_{i,j}^2 = 0$ or $\sum_{i,j} Y_{i,j}^2 = 0$) or a two-sample test. The appropriate test statistic is then calculated and is returned along with the p-value which is calculated using right-tailed normal distribution.

Note: The Park-Ayyala test statistic involves repeated computation of the covariance matrix, requiring at least four samples in both the groups. See Park and Ayyala (2013) for more details.

References

Park, J. and Ayyala, D. N. (2013) A test for the mean vector in large dimension and small samples, Journal of Statistical Planning and Inference, 143, 929 -- 943.

Examples

data(diffMethylData)
patest(diffMethylData$region1.x, diffMethylData$region1.y)
# patest(diffMethylData$region2.x, diffMethylData$region2.y)