Permutation test

Permutation test to test a hypothesis involving two samples.

Usage

permTest(x, ...)

# Default S3 method
permTest(
  x,
  group,
  statistic = mean,
  success = NULL,
  B = 9999,
  alternative = "two.sided",
  plot.hist = TRUE,
  plot.qq = FALSE,
  xlab = NULL,
  ylab = NULL,
  title = NULL,
  seed = NULL,
  ...
)

# S3 method for class 'formula'
permTest(formula, data = parent.frame(), subset, ...)

Arguments

x

a numeric, logical, factor, or character vector. Logical, factor, and character vectors with exactly two unique values are converted to 0/1, and mean is used to compute the proportion.

...

further arguments to be passed to or from methods.

group

a factor variable with two levels. If group is a binary numeric vector, it will be coerced into a factor variable.

statistic

the statistic of interest.

success

a character string naming the level of x to code as 1 when x is a logical, factor, or character variable. Defaults to NULL, which uses the second factor level (alphabetically) or TRUE for logical vectors.

B

the number of resamples (positive integer greater than 2).

alternative

the alternative hypothesis. Options are "two.sided", "less" or "greater".

plot.hist

a logical value. If TRUE, the permutation distribution of the statistic is plotted.

plot.qq

a logical value. If TRUE, then a normal quantile-quantile plot of the resampled test statistic is created.

xlab

an optional character string for the x-axis label

ylab

an optional character string for the y-axis label

title

an optional character string giving the plot title

seed

optional argument to set.seed

formula

a formula of the form y ~ group where y is numeric and group is a factor variable.

data

a data frame with the variables in the formula.

subset

an optional expression specifying which observations to keep.

Value

Returns invisibly a vector of the replicates of the test statistic.

Details

Permutation test to see if a population parameter is the same for two populations. For instance, test \(latex\) where \(latex\) denotes the population mean. The values of the numeric variable are randomly assigned to the two groups and the difference of the statistic for each group is calculated. The command will print the mean and standard error of the distribution of the test statistic as well as a P-value.

Observations with missing values are removed.

Methods (by class)

• permTest(default): Permutation test

• permTest(formula): Permutation test

References

Tim Hesteberg's website: https://www.timhesterberg.net/bootstrap-and-resampling

Author

Laura Chihara

Examples

# Testing the difference in means
permTest(states03$ViolentCrime, states03$DeathPenalty)
#> 
#> 	** Permutation test **
#> 
#>  Permutation test with alternative: two.sided 
#>  Observed mean 
#>   No :  286.6917 	 Yes :  453.7974 
#>  Observed difference: -167.1057 
#> 
#>  Mean of permutation distribution: -1.11434 
#>  Standard error of permutation distribution: 61.82947 
#>  P-value:   0.005 
#> 
#> 	*-------------*
#> 


#using formula syntax
permTest(ViolentCrime ~ DeathPenalty, data = states03, alt = "less")
#> 
#> 	** Permutation test **
#> 
#>  Permutation test with alternative: less 
#>  Observed mean 
#>   No :  286.6917 	 Yes :  453.7974 
#>  Observed difference: -167.1057 
#> 
#>  Mean of permutation distribution: -0.9316 
#>  Standard error of permutation distribution: 61.95138 
#>  P-value:  0.0023 
#> 
#> 	*-------------*
#> 


# Testing the difference in proportions
permTest(penguin_survival$Status, penguin_survival$TagType, B = 999)
#> Note: "Survived" coded as the success (1).
#> 
#> 	** Permutation test **
#> 
#>  Permutation test with alternative: two.sided 
#>  Observed proportion 
#>   Electronic :  0.3597884 	 Metal :  0.1976048 
#>  Observed difference: 0.16218 
#> 
#>  Mean of permutation distribution: 0.00141 
#>  Standard error of permutation distribution: 0.04742 
#>  P-value:   0.001 
#> 
#> 	*-------------*
#> 


#using formula syntax
permTest(Status ~ TagType, data = penguin_survival, B = 999)
#> Note: "Survived" coded as the success (1).
#> 
#> 	** Permutation test **
#> 
#>  Permutation test with alternative: two.sided 
#>  Observed proportion 
#>   Electronic :  0.3597884 	 Metal :  0.1976048 
#>  Observed difference: 0.16218 
#> 
#>  Mean of permutation distribution: 0.00112 
#>  Standard error of permutation distribution: 0.04798 
#>  P-value:   0.003 
#> 
#> 	*-------------*
#>