Prior work on perceptual effectiveness has decomposed visualizations into smaller common units (e.g., channels such as angle, position, and length) to establish rankings. While useful, these decompositions lack the computational structure to predict performance for new visualization x task combinations, requiring new experiments for each. We propose an alternative unit of analysis: operationalizing quantitative visualization interpretation as sequences of composable visual decoding operators. Using probability density function (PDF) and cumulative distribution function (CDF) charts, we examine how four chart-specific tasks can be decomposed into five reusable, chart-agnostic perceptual operations and characterize their error profiles through hierarchical Bayesian modeling. We then test generalizability by composing one kind of learned operators to predict performance on a structurally different task: Moritz et al.'s [37] scatterplot mean-estimation experiment, where the chart type, chart dimensions, and analytic goal all differ from the learning conditions. With a pre-registered analysis plan, we compose operators under six candidate strategies and evaluate each against empirical data with no parameters fit to the response data. One strategy captures both bias and variance of observed responses; five alternatives fail in distinguishable ways. We argue that this decoding-operator-oriented approach to empirical visualization research demonstrates the feasibility of a different way of doing empirical visualization research, one where findings compose, and predictions extend beyond the conditions in which they were measured. Free copy of this paper and supplemental materials: https://osf.io/prtfq.

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