# Summarizing MDMR Results

### Description

`summary`

method for class `mdmr`

### Usage

1 2 |

### Arguments

`object` |
Output from |

`...` |
Further arguments passed to or from other methods. |

### Value

Calling
`summary(mdmr.res)`

produces a data frame comprised of:

`Statistic` |
Value of the corresponding MDMR test statistic |

`Pseudo R2` |
Size of the corresponding effect on the distance matrix |

`p-value` |
The p-value for each effect. |

In addition to the information in the three columns comprising
`summary(res)`

, the `res`

object also contains:

`p.prec` |
A data.frame reporting the precision of each p-value. If
analytic p-values were computed, these are the maximum error bound of the
p-values reported by the |

`lambda` |
A vector of the eigenvalues of |

`nperm` |
Number of permutations used. Will read |

Note that the printed output of `summary(res)`

will truncate p-values
to the smallest trustworthy values, but the object returned by
`summary(res)`

will contain the p-values as computed. The reason for
this truncation differs for analytic and permutation p-values. For an
analytic p-value, if the error bound of the Davies algorithm is larger than
the p-value, the only conclusion that can be drawn with certainty is that
the p-value is smaller than (or equal to) the error bound. For a permutation
test, the estimated p-value will be zero if no permuted test statistics are
greater than the observed statistic, but the zero p-value is only a product
of the finite number of permutations conduted. The only conclusion that can
be drawn is that the p-value is smaller than `1/nperm`

.

### Author(s)

Daniel B. McArtor (dmcartor@nd.edu) [aut, cre]

### References

Davies, R. B. (1980). The Distribution of a Linear Combination of chi-square Random Variables. Journal of the Royal Statistical Society. Series C (Applied Statistics), 29(3), 323-333.

Duchesne, P., & De Micheaux, P. L. (2010). Computing the distribution of quadratic forms: Further comparisons between the Liu-Tang-Zhang approximation and exact methods. Computational Statistics and Data Analysis, 54(4), 858-862.

McArtor, D. B., Lubke, G. H., & Bergeman, C. S. (second revision under review). Extending multivariate distance matrix regression with an effect size measure and the distribution of the test statistic.

### Examples

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