SPM one-way MANOVA (Hotelling's T^2 / chi-square vector field)

Computes a multivariate SPM field for a one-way MANOVA at every node, for vector-valued waveforms (e.g. 3D joint angles). With two groups the field is Hotelling's \(T^2\) (reducing to the squared two-sample t-field for a single component); with more than two groups it is the chi-square field of the Bartlett-transformed Wilks' \(\Lambda\). Field-level significance uses random-field theory (an F-field threshold for \(T^2\), a chi-square-field threshold for the \(X^2\) field).

Usage

spmMANOVA(x, groups, vector_components = NULL, alpha = 0.05)

Arguments

x: A 3D array time x obs x component, or a list of component matrices (each time x obs), or a single time x obs matrix (one component).
groups: A grouping factor, one value per observation.
vector_components: Optional integer; only used to disambiguate a 2D matrix input (defaults to a single component).
alpha: Significance level (default 0.05).

Value

A list of class "spm_result" (test_type = "manova") with the statistic field (T2 or X2), RFT threshold, significant clusters, p_values, degrees of freedom, fwhm, and resel_count.

References

Pataky 2016 (vector-field 1D SPM); Worsley 1994 (chi-square RFT). spm1d.stats.manova1 / hotellings2.

Examples

set.seed(1)
# two groups, 3 components (e.g. hip flexion/abduction/rotation)
arr <- array(rnorm(50 * 16 * 3), c(50, 16, 3))
arr[20:30, 1:8, ] <- arr[20:30, 1:8, ] + 1.2
spmMANOVA(arr, groups = rep(c("A", "B"), each = 8))
#> SPM Analysis Result
#> ==================
#> Test type: manova
#> Time points: 50
#> Alpha: 0.050
#> Threshold: 42.471
#> FWHM (smoothness): 2.21
#> Resel count: 22.15
#> 
#> Significant clusters: 2
#>   Cluster 1: [22-22] extent=1, p=0.0056
#>   Cluster 2: [30-30] extent=1, p=0.0056