# Monte Carlo Permutation Test for Paired Individual Scores

`permutationTest.Rd`

The difference between mean `scores`

from model 1 and
mean `scores`

from model 2 is used as the test statistic.
Under the null hypothesis of no difference, the actually observed
difference between mean scores should not be notably different from
the distribution of the test statistic under permutation.
As the computation of all possible permutations is only feasible for
small datasets, a random sample of permutations is used to obtain the
null distribution. The resulting p-value thus depends on the
`.Random.seed`

.

## Arguments

- score1, score2
numeric vectors of scores from models 1 and 2, respectively.

- nPermutation
number of Monte Carlo replicates.

- plot
logical indicating if a

`truehist`

of the`nPermutation`

permutation test statistics should be plotted with a vertical line marking the observed difference of the means. To customize the histogram,`plot`

can also be a list of arguments for`truehist`

replacing internal defaults.- verbose
logical indicating if the results should be printed in one line.

## Details

For each permutation, we first randomly assign the membership of the n
individual scores to either model 1 or 2 with probability 0.5. We then
compute the respective difference in mean for model 1 and 2 in this
permuted set of scores. The Monte Carlo p-value is then given by
(1 + #{permuted differences larger than observed difference (in
absolute value)}) / (1 + `nPermutation`

).

## Value

a list of the following elements:

- diffObs
observed difference in mean scores, i.e.,

`mean(score1) - mean(score2)`

- pVal.permut
p-value of the permutation test

- pVal.t
p-value of the corresponding

`t.test(score1, score2, paired=TRUE)`

## References

Paul, M. and Held, L. (2011):
Predictive assessment of a non-linear random effects model for
multivariate time series of infectious disease counts.
*Statistics in Medicine*, **30** (10), 1118-1136.
doi:10.1002/sim.4177

## See also

Package coin for a comprehensive permutation test framework.