Description Usage Arguments Details Value References Examples

Parametric Bootstrap of 2x2 Contingence independence test. The goodness of fit statistic is the root-mean-square statistic (RMST) or Hellinger divergence, as proposed by Perkins et al. [1, 2]. Hellinger divergence (HD) is computed as proposed in [3].

1 | ```
bootstrap2x2(x, stat = "rmst", num.permut = 100)
``` |

`x` |
A numerical matrix corresponding to cross tabulation (2x2) table (contingency table). |

`stat` |
Statistic to be used in the testing: 'rmst','hdiv', or "all". |

`num.permut` |
Number of permutations. |

For goodness-of-fit the following null hypothesis is tested
*H_θ: p = p(θ)*
To conduct a single simulation, we perform the following three-step
procedure [1,2]:

To generate m i.i.d. draws according to the model distribution

*p(θ)*, where*θ'*is the estimate calculated from the experimental data,To estimate the parameter

*θ*from the data generated in Step 1, obtaining a new estimate*θ*est.To calculate the statistic under consideration (HD, RMST), using the data generated in Step 1 and taking the model distribution to be

*θ*est, where*θ*est is the estimate calculated in Step 2 from the data generated in Step 1.

After conducting many such simulations, the confidence level for
rejecting the null hypothesis is the fraction of the statistics
calculated in step 3 that are less than the statistic calculated from
the empirical data. The significance level *α* is the same as a
confidence level of *1-α*.

A p-value probability

Perkins W, Tygert M, Ward R. Chi^2 and Classical Exact Tests Often Wildly Misreport Significance; the Remedy Lies in Computers [Internet]. Uploaded to ArXiv. 2011. Report No.: arXiv:1108.4126v2.

Perkins, W., Tygert, M. & Ward, R. Computing the confidence levels or a root-mean square test of goodness-of-fit. 217, 9072-9084 (2011).

Basu, A., Mandal, A. & Pardo, L. Hypothesis testing for two discrete populations based on the Hellinger distance. Stat. Probab. Lett. 80, 206-214 (2010).

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