Permutation test for the Slope — permTestSlope • CarletonStats

Hypothesis test for a slope of a simple linear regression model. The null hypothesis is that the population slope is 0.

Usage

permTestSlope(x, ...)

# Default S3 method
permTestSlope(
  x,
  y,
  B = 999,
  alternative = "two.sided",
  plot.hist = TRUE,
  plot.qq = FALSE,
  x.name = deparse(substitute(x)),
  y.name = deparse(substitute(y)),
  xlab = NULL,
  ylab = NULL,
  title = NULL,
  seed = NULL,
  ...
)

# S3 method for class 'formula'
permTestSlope(formula, data, subset, ...)

Arguments

x: a numeric vector.
...: further arguments to be passed to or from methods.
y: a numeric vector.
B: the number of resamples to draw (positive integer greater than 2).
alternative: alternative hypothesis. Options are "two.sided", "less" or "greater".
plot.hist: a logical value. If TRUE, plot the distribution of the slopes obtained from each resample.
plot.qq: a logical value. If TRUE, plot the normal quantile-quantile plot of the slopes obtained from each resample.
x.name: Label for variable x
y.name: Label for variable y
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 y ~ x where x, y are numeric vectors.
data: a data frame that contains the variables given in the formula.
subset: an optional expression indicating what observations to use.

Value

Returns invisibly a vector of the slopes obtained by the randomization.

Details

Perform a permutation test to test \(latex\), where \(latex\)is the population slope. The rows of the second variable are permuted and the slope is re-computed.

The mean and standard error of the permutation distribution is printed as well as a P-value.

Observations with missing values are removed.

Methods (by class)

permTestSlope(default): Permutation test for the slope
permTestSlope(formula): Permutation test for the slope

References

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

Author

Adam Loy, Laura Chihara

Examples


plot(states03$HSGrad, states03$TeenBirths)

lm(HSGrad ~ TeenBirths, data = states03)
#> 
#> Call:
#> lm(formula = HSGrad ~ TeenBirths, data = states03)
#> 
#> Coefficients:
#> (Intercept)   TeenBirths  
#>     94.9878      -0.2152  
#> 

permTestSlope(states03$HSGrad, states03$TeenBirths)
#> 
#> 	** Permutation test **
#> 
#>  Permutation test with alternative: two.sided 
#>  Observed slope between states03$HSGrad ,  states03$TeenBirths :  -2.1243 
#>  Mean of permutation distribution: 0.02045 
#>  Standard error of permutation distribution: 0.44499 
#>  P-value:   0.001 
#> 
#> 	*-------------*
#> 

permTestSlope(TeenBirths ~ HSGrad, data = states03)
#> 
#> 	** Permutation test **
#> 
#>  Permutation test with alternative: two.sided 
#>  Observed slope between HSGrad ,  TeenBirths :  -2.1243 
#>  Mean of permutation distribution: -0.01319 
#>  Standard error of permutation distribution: 0.44299 
#>  P-value:   0.001 
#> 
#> 	*-------------*
#>