R: Combined Kruskal-Wallis Tests for the 2 x t Contingency...

contingency2xt.comb {kSamples} | R Documentation

## Combined Kruskal-Wallis Tests for the 2 x t Contingency Tables

### Description

This function uses the Kruskal-Wallis criterion to test the hypothesis of no association between the counts for two responses "A" and "B" across t categories and across M blocks.

### Usage

    contingency2xt.comb(...,
    	method = c("asymptotic", "simulated", "exact"),
    	dist = FALSE, Nsim = 10000)

### Arguments

`...` | Either several lists L_1,…,L_M, each of two equal length vectors A_i and B_i, i=1,…,M, of counts ≥ 0, where the common length t_i of A_i and B_i may vary from list to list or a list of `M` such lists
`method` | = `c("asymptotic","simulated","exact")`, where `"asymptotic"` uses only an asymptotic chi-square approximation with (t_1-1)+…+(t_M-1) degrees of freedom to approximate the P-value, This calculation is always done. `"simulated"` uses `Nsim` simulated counts for the two vectors A_i and B_i in list L_i, with the observed marginal totals, m_i=∑ A_i, n_i = ∑ B_i, d_i = A_i+B_i. It does this independently from list to list using the same `Nsim` each time, adding the resulting Kruskal-Wallis criteria across lists to get `Nsim` such summed values to estimate the P-value. `"exact"` enumerates all counts for A_i and B_i with the respective observed marginal totals to get an exact distribution for each list. These distributions are then convolved to obtain the P-value. It is used only when `Nsim` is at least as large as the product across blocks of the number `choose(m+t-1,t-1)` of full enumerations per block, where t = t_1,…, t_M. Otherwise, `method` reverts to `"simulated"` using the given `Nsim`.
`dist` | `FALSE` (default) or `TRUE`. If `TRUE`, the simulated or fully enumerated null distribution `null.dist` is returned for the Kruskal-Wallis test statistic. Otherwise `null.dist = NULL` is returned.
`Nsim` | `=10000` (default), number of simulated A_i splits to use per block. It is only used when `method = "simulated"`, or when `method = "exact"` reverts to `method = "simulated"`, as previously explained.

### Details

For details on the calculation of the Kruskal-Wallis criterion and its exact or simulated distribution for each block see `contingency2xt`.

### Value

A list of class `kSamples` with components

`test.name` | `"Combined 2 x t Contingency Tables"`
`t` | vector giving the number of classification categories per block
`M` | number of blocked tables
`kw.list` | a list of the `KW.cont` output componenents from `contingency2xt` for each of the blocks
`null.dist` | simulated or enumerated null distribution of the combined test statistic. It is given as an `L` by 2 matrix, where the first column (named `KW`) gives the `L` unique ordered values of the combined Kruskal-Wallis statistic and the second column (named `prob`) gives the corresponding (simulated or exact) probabilities. `null.dist = NULL` is returned when `dist = FALSE` or when `method =` `"asymptotic"`.
`method` | the `method` used.
`Nsim` | the number of simulations.

### warning

`method = "exact"` should only be used with caution. Computation time is proportional to the number of enumerations. In most cases `dist = TRUE` should not be used, i.e., when the returned distribution objects become too large for R's work space.

### Note

The required level for `Nsim` in order for `method = "exact"` to be carried out, is conservative, but there is no transparent way to get a better estimate. The actual dimension `L` of the realized `null.dist` will typically be much smaller, since the distribution is compacted to its unique support values.

### Examples

    out <- contingency2xt.comb(list(c(25,15,20),c(16,6,18)),
    list(c(12,4,5),c(13,8,9)),method = "simulated", dist=FALSE, Nsim=1e3)

[Package kSamples version 1.2-9 Index]