GET (version 0.1-6)

GET.necdf: Graphical n sample test of correspondence of distribution functions

Description

Compare the distributions of two (or more) groups.

Usage

GET.necdf(
  x,
  r = seq(min(unlist((lapply(x, min)))), max(unlist((lapply(x, max)))), length = 100),
  contrasts = FALSE,
  nsim,
  ...
)

Arguments

x

A list (of length n) of values in the n groups.

r

The sequence of argument values at which the distribution functions are compared. The default is 100 equally spaced values between the minimum and maximum over all groups.

contrasts

Logical. FALSE and TRUE specify the two test functions as described in description part of this help file.

nsim

The number of random permutations.

...

Additional parameters to be passed to global_envelope_test.

Details

A global envelope test can be performed to investigate whether the n distribution functions differ from each other significally and how do they differ. This test is a generalization of the two-sample Kolmogorov-Smirnov test with a graphical interpretation. We assume that the curves in the different groups are an i.i.d. samples from the distribution $$F_i(r), i=1, \dots, n$$, and we want to test the hypothesis $$F_1(r)= \dots = F_n(r)$$. If contrasts = FALSE (default), then the test statistic is taken to be $$\mathbf{T} = (\hat{F}_1(r), \dots, \hat{F}_n(r))$$ where \(\hat{F}_i(r) = (\hat{F}_i(r_1), \dots, \hat{F}_i(r_k))\) is the ecdf of the $i$th sample evaluated at argument values \(r = (r_1,\dots,r_k)\). This is our recommended test function for the test. Another possibility is given by contrasts = TRUE, and then the test statistic is $$\mathbf{T} = (\hat{F}_1(r)-\hat{F}_2(r), \dots, \hat{F}_{n-1}(r)-\hat{F}_n(r))$$

The simulations under the null hypothesis that the distributions are the same can be obtained by permuting the individuals of the groups. The default number of permutation, if nsim is not specified, is n*1000 - 1 for the case contrasts = FALSE and (n*(n-1)/2)*1000 - 1 for the case contrasts = TRUE, where n is the length of x.

Examples

# NOT RUN {
if(require(fda, quietly=TRUE)) {
  # Heights of boys and girls at age 10
  f.a <- growth$hgtf["10",] # girls at age 10
  m.a <- growth$hgtm["10",] # boys at age 10
  # Empirical cumulative distribution functions
  plot(ecdf(f.a))
  plot(ecdf(m.a), col=grey(0.7), add=TRUE)
  # Create a list of the data
  fm.list <- list(Girls=f.a, Boys=m.a)
  
# }
# NOT RUN {
  res_m <- GET.necdf(fm.list)
  plot(res_m)
  res_c <- GET.necdf(fm.list, contrasts = TRUE)
  plot(res_c)
  
# }
# NOT RUN {
  
# }
# NOT RUN {
  # Heights of boys and girls at age 14
  f.a <- growth$hgtf["14",] # girls at age 14
  m.a <- growth$hgtm["14",] # boys at age 14
  # Empirical cumulative distribution functions
  plot(ecdf(f.a))
  plot(ecdf(m.a), col=grey(0.7), add=TRUE)
  # Create a list of the data
  fm.list <- list(Girls=f.a, Boys=m.a)
  
# }
# NOT RUN {
  res_m <- GET.necdf(fm.list)
  plot(res_m)
  res_c <- GET.necdf(fm.list, contrasts = TRUE)
  plot(res_c)
  
# }
# NOT RUN {
  
# }
# NOT RUN {
}
# }