Table 3.

Form and interpretation of various DVARS variants, expressed as functions of original ${\text{DVARS}}_t$. Here $\left\{Y_{it}\right\}$ are the 4D data, A is the overall mean square variance, ${\mu }_0$ is the expected ${\text{DVARS}}_t^2$ under a null model, $P\left({\text{DVARS}}_t\right)$ is the p-value for ${\text{DVARS}}^2$, and ${\text{Φ}}^{-1}$ is the inverse cumulative distribution function of a normal.

Name	Expression	Interpretation
DVARS	${\text{DVARS}}_t=\sqrt{\sum _i{\left(Y_{it}-Y_{i,t+1}\right)}^2/I}$	RMS of differenced image
$\surd \text{D}-\text{var}$	${\text{DVARS}}_t/2$	Fast component of noise, as RMS
%D-var	${\text{DVARS}}_t^2/\left(4A\right)\times 100$	Fast noise, as % of average noise variance
$\text{Δ}$%D-var	$\left({\text{DVARS}}_t^2-{\mu }_0\right)/\left(4A\right)\times 100$	Excess fast noise, as % of average noise variance
Rel. DVARS	${\text{DVARS}}_t/\sqrt{{\mu }_0}$	DVARS as a multiple of null mean
Z(D-var)	${\text{Φ}}^{-1}\left(1-P\left({\text{DVARS}}_t\right)\right)$	DVARS p-value as Z-score