How continuous is continuous enough? Comparing the reliability of continuous and discrete scales

Designing a reliable rating scale with an appropriate number of options remains a central issue in social science measurement. Prior studies have reported inconsistent findings, with some suggesting that reliability is maximized at moderate response granularity and others indicating that finer granularity yields higher precision. These inconsistencies may partly reflect methodological differences, particularly the use of classical test theory or the discretization of continuous responses, both of which may underestimate the reliability of continuous scales. To address these issues, the present study reconceptualized discrete and continuous scales as points along a unified granularity continuum and examined reliability using the continuous rating scale model (CoRSM). Utilizing the CoRSA analytical framework (Chou et al., 2025), we conducted two complementary studies. Study 1 employed Monte Carlo simulations varying sample sizes (N = 200 to 1,000), test lengths (11 to 61 items), and response formats ranging from three-point to continuous. Study 2 provided empirical validation with 3,434 junior high school students completing a career interest assessment across 10 response formats, ranging from five-point scales to continuous visual analogue scales (VAS). Across both studies, reliability generally increased as response granularity increased, although the empirical pattern was not strictly monotonic across all intermediate formats. In Study 2, segmented regression indicated that the breakpoint in diminishing returns occurred at approximately seven to eight response options within the discrete range examined. Meanwhile, the highest reliability estimates were observed for the 101-point and VAS formats. These findings clarify one methodological source of inconsistency in prior research.