fmri_effdf

Description

FMRI_EFFDF Estimates effective degrees of freedom for correlated time series. Estimates the effective degrees of freedom (df) for the correlation between two time series, accounting for temporal autocorrelation in both signals. Temporal autocorrelation inflates Type I error when using the nominal df (N-2); this function provides a corrected value suitable for significance testing via fmri_rtop. The effective df is computed using the formula: 1/df_eff = 1/N + (2/N) * sum_{k=1}^{N/4} ((N-k)/N) * AC1(k) * AC2(k) where AC1 and AC2 are the normalised autocorrelation functions of ts1 and ts2 respectively, evaluated up to lag N/4.

Usage

df = fmri_effdf(ts1, ts2)

Inputs

TS1, TS2 - Time series vectors (N x 1) or (1 x N). Must be the same length.

Outputs

DF: Effective degrees of freedom (scalar). Will be <= N-2.

Examples

% Compute effective df before testing a correlation
r   = corr(ts1, ts2);
df  = fmri_effdf(ts1, ts2);
p   = fmri_rtop(r, df);

References

Pyper, B.J. & Peterman, R.M. (1998). Comparison of methods to account for autocorrelation in correlation analyses of fish data. Canadian
Journal of Fisheries and Aquatic Sciences, 55(9), 2127-2140.