Obtaining quantitative survey responses that are both accurate and informative is crucial to a wide range of fields (e. g. perceptual and categorical judgement, expert risk assessment, attitudinal measurement, consumer and public opinion research). Traditional and ubiquitous response formats such as Likert and Visual Analogue Scales require condensation of responses into discrete or point values-but sometimes a range of options may better represent the correct answer. In this paper, we propose an efficient interval-valued response mode, whereby responses are made by marking an ellipse along a continuous scale. We discuss its potential in the context of survey research, describing how this approach can capture and quantify valuable information arising from multiple sources of response uncertainty-which would be lost using conventional approaches--while preserving a high degree of response-efficiency.  We then report a validation study, which utilizes our recently introduced open-source software (DECSYS) to administer an electronic interval-valued survey. This is designed to explore how interval-values reflect experimental manipulations of response (un)certainty across multiple contexts. Results consistently indicated that respondents used interval widths effectively-to communicate uncertainty (e.g. lack of available information), ambiguity (e.g. lack of clarity in question phrasing), and inherent variability in their responses. Subjective participant feedback was also positive. We present this as initial empirical evidence for the efficacy and value of interval-valued response capture. Interestingly, intervals also provided insight into respondents' reasoning about different types of uncertainties, suggesting a tendency to underestimate lack of available information relative to observable variability when making a stimulus judgement .
Obtaining quantitative survey responses that are both accurate and informative is crucial to a wide range of fields . Traditional and ubiquitous response formats such as Likert and Visual Analogue Scales require condensation of responses into discrete point values - but sometimes a range of options may better represent the correct answer. In this paper, we propose an efficient interval-valued response mode, whereby responses are made by marking an ellipse along a continuous scale. We discuss its potential to capture and quantify valuable information that would be lost using conventional approaches, while preserving a high degree of response-efficiency. The information captured by the response interval may represent a possible response range - i.e., a conjunctive set, such as the real numbers between three and six. Alternatively, it may reflect uncertainty in respect to a distinct response - i.e., a disjunctive set, such as a confidence interval. We then report a validation study, utilizing our recently introduced open-source software (DECSYS) to explore how interval-valued survey responses reflect experimental manipulations of several factors hypothesised to influence interval width, across multiple contexts. Results consistently indicate that respondents used interval widths effectively, and subjective participant feedback was also positive. We present this as initial empirical evidence for the efficacy and value of interval-valued response capture. Interestingly, our results also provide insight into respondents' reasoning about the different aforementioned types of intervals - we replicate a tendency towards overconfidence for those representing epistemic uncertainty (i.e., disjunctive sets), but find intervals representing inherent range (i.e., conjunctive sets) to be well-calibrated .
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