sharma.song.test: Sharma-Song Test for Second-Order Difference Across...

In DiffXTables: Pattern Analysis Across Contingency Tables

Description

The test detects differential departure from independence via second-order difference in joint distributions underlying two or more contingency tables.

Usage

sharma.song.test(
  tables, null.table.marginal = c("observed", "uniform"), 
  compensated = FALSE
)

Arguments

tables	a list of at least two non-negative matrices or data frames representing contingency tables of the same dimensions.
null.table.marginal	a character string to specify marginal distributions of null tables. The options are "observed"(default) and "uniform".
compensated	a logical value to compensate for the Cochran's condition. It is only used if null.table.marginal="observed". Default is FALSE.

Details

The Sharma-Song test determines whether the patterns underlying multiple input contingency tables are second-order differential. The test statistic measures differential departure form independence. Its null test statistic is proved to asymptotically follow the chi-squared distribution. For full detail of the test, see \insertCiteruby2021/BIOINF-2020-0795DiffXTables.

If null.table.marginal is set to "observed", the null hypothesis uses the observed marginals. The compensated parameter, if set to TRUE, adds a small constant to each entry of the tables to address the Cochran's condition that the expected count in any table entry is 5 or less.

If the null.table.marginal is set to "uniform", the null tables are set to have uniform marginals. No longer suffering from the Cochran's condition, it detects second-order differential patterns with additional robustness.

Value

A list with class "htest" containing the following components:

statistic	the Sharma-Song chi-squared test statistic.
parameter	degrees of freedom of the chi-squared test statistic.
p.value	p-value of the Sharma-Song test, computed using the chi-squared distribution.

Author(s)

Ruby Sharma and Joe Song

References

\insertAllCited

See Also

cp.chisq.test, heterogeneity.test, strength.test, marginal.change.test, and type.analysis.

Examples

  # Two second-order differential tables:
  tables <- list(
    matrix(c(4,0,0,
             0,4,0,
             0,0,4), nrow=3),
    matrix(c(0,4,4,
             4,0,4,
             4,4,0), nrow=3)
  )
  sharma.song.test(tables)
  
  # Three tables differ in the first-order but not second-order:
  tables <- list(
    matrix(c(2, 4,  6,  8, 
             3, 6,  9, 12, 
             4, 8, 12, 16), nrow=4),
    matrix(c( 2, 1,  3,  7,
              2, 1,  3,  7,
             10, 5, 15, 35), nrow=4),
    matrix(c(40, 16, 72, 16, 
             45, 18, 81, 18,
             25, 10, 45, 10), nrow=4)
  )
  sharma.song.test(tables, null.table.marginal = "uniform")

DiffXTables documentation built on May 16, 2021, 9:07 a.m.