Measuring "Where": A Comparative Analysis of Methods Measuring Spatial Perception

Abstract

The literature offers various methods for measuring sound localization. In this study, we aimed to compare these methods to determine their effectiveness in addressing different research questions by examining the effect sizes obtained from each measure. Data from 150 participants who identified the location of a sound source were analyzed to explore the effects of speaker angle, stimuli, HPD type, and condition (with/without HPD) on sound localization, using six methods for analysis: mean absolute deviation (MAD), root-mean-squared error (RMSE), very large errors (VLE), percentage of errors larger than the average error observed in a group of participants (pMean), percentage of errors larger than half the distance between two consecutive loudspeakers (pHalf), and mirror image reversal errors (MIRE). Results indicated that the MIRE measure was the most sensitive to the effects of speaker angle and HPD type, while the VLE measure was most sensitive to the effect of stimuli type. The condition variable provided the largest effect sizes, with no difference observed between measures. The data suggest that when effect sizes are substantial, all methods are adequate. However, for cases where the effect size is expected to be small, methods that yield larger effect sizes should be considered, considering their alignment with the research question.

Keywords: mean absolute deviation (MAD); measuring methods; mirror image reversal errors (MIRE); root-mean-squared error (RMSE); sound localization.

Figure 1

The spectrum of the four stimuli used in the study: pink noise, a spoken word (Hebrew word “esh” meaning fire), and single and triple M16 gunshots captured at a distance of 200 feet.

Figure 2

Experimental setting. The symbol in the middle represents participant orientation. (a) The actual setting: Participants sat in the middle of a circle of eight monitors separated by 45°, starting from 22.5° through 337.5°. (b) The setting presented to participants on a computer screen: participants were asked to indicate on the circle the location of the perceived sound source.

Figure 3

Effect sizes obtained by MAD, RMSE, VLE, pMean, pHalf, and MIRE, for the independent variables speaker angle, stimuli type, HPD type, and condition. The striped bars indicate the measure with the largest effect size for each independent variable. Two-sided arrows indicate the 0.06 distance criteria from the largest effect size. * Effect size significantly smaller (i.e., difference larger than 0.06) than the largest.

Figure 4

Confidence intervals of the methods MAD, RMSE, VLE, pMean, pHalf, and MIRE for the independent variables speaker angle, stimuli type, HPD type, and condition.