Table 1.

Error Measures Used

Error name	Error calculation	Error description
Raw error	eRij = dIij – dAij	Response error for object i, turn j, relative to actual target direction (dA) on a circular scale (dI = indicated target direction)
Linear error	eLij = eRij ± 360°	Raw error (eR) adjusted to be within 180° of a particular reference direction (e.g., 0°, eLij – 1)
Heading error	$e_{{\mathrm{H}}_j}=\text{arc tan}\frac{\left({\sum }_i\text{sin}{e}_{{\mathrm{R}}_j}\right)∕4}{\left({\sum }_i\text{cos}{e}_{{\mathrm{R}}_j}\right)∕4}$ a	Mean (using circular statistics) raw error (eR) for all 4 objects for a particular turn (j)
Deviation error	eDij = eRij – eHj	Raw error (eR), for object i adjusted by mean eR for all 4 objects on corresponding turn (j)
Adjusted linear error	eALij = eLij – eLij–1	Linear error (eL) for object i on turn j adjusted by eL for object i on turn j – 1
Adjusted linear deviation error	$e_{{\mathrm{ALD}}_{ij}}=e_{{\mathrm{AL}}_{ij}}-\frac{{\sum }_i{e}_{{\mathrm{AL}}_j}}{4}$	Adjusted linear error (eAL) for object i adjusted by mean eAL for all objects on corresponding turn
Angular separation error	$e_{{\mathrm{AS}}_{i_1,i_{2j}}}=\mid e_{{\mathrm{AL}}_{i_{1j}}}-e_{{\mathrm{AL}}_{i_{2j}}}\mid$	Absoluteb error in angular separation between a given pair of objects (i1, i2) on a given turn (j)
Position error	$e_{{\mathrm{P}}_{i_1,i_{2j}}}=\mid e_{{\mathrm{AL}}_{i_{1j}}}+e_{{\mathrm{AL}}_{i_{2j}}}\mid$	Absolute sum of adjusted linear error for a given pair of objects (i1, i2) on a given turn (j)

^aIf $({\sum }_i\text{cos}{e}_{{\mathrm{R}}_j}∕4)<0$, then e_Hj = e_Hj + 180.

^bAbsolute differences and sums were used so that the error scores could be aggregated within and across participants without positive and negative errors canceling each other out. Transforming the differences and sums in this way also rendered irrelevant the issue concerning which way around the circle angular separation was measured.