The utility of arc length for continuous response measurement of audience responses to humour

Abstract

Continuous response measures of viewers’ reactions to media stimuli have advantages over retrospective self-report measures (Poels & Dewitte, 2006). However, it is difficult to capture continuous measures using single numbers, such as the mean, velocity (the slope), peak, and area under the curve (Kahneman, 2000). Dynamic models are required to illuminate dynamic interactions between audio-visual presentations and audience responses so as not to lose the rich data that is otherwise lost in static measures aggregated over time (Wang, Lang, and Busemeyer, 2011). This is especially the case for humour, which results from a trajectory over time. First there is the set-up, then there is the pay-off. A mean that averages over both these phases is meaningless. In this article, we propose a new measure for characterizing continuous responses: arc length, which is a measure of the length of the curve, or the length of the journey that a measure undergoes during a certain time period