fdars (version 0.3.3)

group.test: Permutation Test for Group Differences

Description

Tests whether groups of functional data are significantly different using permutation testing.

Usage

group.test(
  fdataobj,
  groups,
  n.perm = 1000,
  statistic = c("centroid", "ratio"),
  ...
)

Value

An object of class 'group.test' containing:

statistic

Observed test statistic

p.value

Permutation p-value

perm.dist

Permutation distribution of test statistic

n.perm

Number of permutations used

Arguments

fdataobj

An object of class 'fdata'.

groups

A factor or character vector specifying group membership.

n.perm

Number of permutations (default 1000).

statistic

Test statistic: "centroid" (distance between group means) or "ratio" (between/within group variance ratio).

...

Additional arguments passed to distance functions.

Details

Null Hypothesis (H0): All groups come from the same distribution. That is, the group labels are exchangeable and there is no systematic difference between the functional curves in different groups.

Alternative Hypothesis (H1): At least one group differs from the others in terms of location (mean function) or dispersion.

The test works by:

1. Computing a test statistic on the observed data

2. Repeatedly permuting the group labels and recomputing the statistic

3. Calculating the p-value as the proportion of permuted statistics >= observed

Two test statistics are available:

• "centroid": Sum of pairwise L2 distances between group mean functions. Sensitive to differences in group locations (means).

• "ratio": Ratio of between-group to within-group variance, similar to an F-statistic. Sensitive to both location and dispersion.

A small p-value (e.g., < 0.05) indicates evidence against H0, suggesting that the groups are significantly different.

Examples

# \donttest{
set.seed(42)
n <- 30
m <- 50
t_grid <- seq(0, 1, length.out = m)
X <- matrix(0, n, m)
for (i in 1:15) X[i, ] <- sin(2 * pi * t_grid) + rnorm(m, sd = 0.1)
for (i in 16:30) X[i, ] <- cos(2 * pi * t_grid) + rnorm(m, sd = 0.1)
fd <- fdata(X, argvals = t_grid)
groups <- factor(rep(c("A", "B"), each = 15))

# Test for significant difference
gt <- group.test(fd, groups, n.perm = 500)
print(gt)
# }