# Permutation test: randomization test for small size samples

### Description

Permutation test for means and variance comparisons.

### Usage

1 |

### Arguments

`x` |
numeric vector. Sample group X. |

`y` |
numeric vector. Sample group Y. |

### Details

In the one–sample problem, the function builds all *2^n*
possible *+/- x_i* combinations. For the two–sample problem,
all possible *B(n+m,n)* samples size
*n* (=`length(x)`

) and *m* (=`length(y)`

) are
generated and the permutation distributions for the *t*-statistics
and *F*-ratios. *p*-values are computed based on these
distributions.

### Value

The function returns the number *N* of different samples
generated for the permutation distribution, the observed *t*-statistic,
its *p*-value, based on both, the parametric and permutation
distributions as well as the observed *F*-ratio and its corresponding
*p*-values. The test may take a long time to generate all the possible
combinations. It has been tested for *n + m = 22* and
*n < 12*.

### WARNING

The test may take a long time to generate all the possible combinations.

### Author(s)

Ernesto Barrios

### References

Box G. E. P, Hunter, J. S. and Hunter, W. C. (2005).
*Statistics for Experimenters II*. New York: Wiley.

### See Also

`onet.permutation`

and `towt.permutation`

of DAAG package, and `perm.test`

of the exactRankTests.

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 | ```
library(BHH2)
# Permutation test for Tomato Data
data(tomato.data)
cat("Tomato Data (not paired):\n")
attach(tomato.data)
a <- pounds[fertilizer=="A"]
b <- pounds[fertilizer=="B"]
print(round(test <- permtest(b,a),3))
detach()
# Permutation test for Boy's Shoes Example
data(shoes.data)
cat("Shoes Data (paired):\n")
attach(shoes.data)
x <- matB-matA
print(round(test <- permtest(x),3))
detach()
``` |

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