Proportion Mismatch
Checks whether the bars in a bar chart are drawn at the height their printed labels claim. When the y-axis can be read, each bar's height is converted to a value and compared to its label as a per-bar lie factor. When the axis cannot be read, a calibration-free check tests whether the bar heights are a consistent linear encoding of their labels. It works from the detected bars, data labels, and axis geometry alone, with no model.
Technical description
G5 is a deterministic, generator-agnostic screen for the misleading-visualization category known as data-visual disproportion: a bar drawn at a height that does not match its stated value. The principle is Edward Tufte's graphical integrity rule, that the physical size of a mark must be proportional to the quantity it represents, formalised as the lie factor, the size of the effect shown in the graphic divided by the size of the effect in the data, which is 1.0 for an honest chart. G5 detects the bars and the numeric data labels, matches each label to its nearest bar, and then runs one of two checks. When the y-axis is calibrated, it converts each bar top to a value through the axis mapping and measures the relative error against the label (the per-bar lie factor). When the axis cannot be calibrated, it fits an affine line from the labels to the bar-top pixels and measures how well the heights encode the labels. The result is a 0 to 5 score (capped). It requires the image to be at least 32 by 32 pixels and at least one matched label-bar pair.
How it works
The indicator runs deterministically at Layer 1 using detect_bars, extract_data_labels, detect_axes, extract_axis_values, and compute_pixel_to_value_mapping.
Each data label is first matched to its nearest bar by the Manhattan distance D = |x_label − x_bar_center| + |y_label − y_bar_top|, accepting the match only when D <= 80 pixels, and each bar keeps its single closest label.
When the y-axis can be calibrated to a mapping value = f(pixel), the indicator runs the absolute check: each matched bar's top pixel is converted to a value v = f(y_top) and compared to its printed label L. The relative error is e = |L − v| / |L|, and the per-bar lie factor, in the sense of Tufte, is λ = v / L, which equals 1.0 for an honest bar. A bar with e > 0.15 is a warning and a bar with e > 0.30 an error. The score is min(5.0, 10 · ē), where ē = (1/k) Σ e_i is the mean relative error over the k matched bars; because a single OCR misread can dominate with little evidence, the score is capped at 2.5 when only one pair is compared and at 3.5 when only two are.
When the axis cannot be calibrated, the indicator runs the calibration-free consistency check: the heights are tested against the labels directly. Over the matched pairs (L_i, y_top,i) a least-squares line y_top = a · L + b is fit, and the coefficient of determination R² = r² is taken, where r is the Pearson correlation between label value and top pixel. An honest chart makes the top pixel an affine function of the value regardless of the baseline, so with at least three labeled bars an R² < 0.90 means the heights are not a consistent linear encoding of their labels; the bar with the largest residual |y_top,i − (a · L_i + b)| from the fitted line is reported as the outlier. The score is min(5.0, 10 · (1 − R²)), capped at 3.5 when only three bars are available, at error severity when R² < 0.70.
The score is rounded and capped at 5.0. The metadata records the bar and label counts, the matched-pair count, the maximum and mean relative error (absolute mode), the proportionality R² (whenever at least three labeled bars exist), and which mode was used.
Score thresholds
| Score | Meaning |
|---|---|
| 0 to 1 | Bar heights match their labels (lie factor near 1.0) or are a consistent linear encoding of them. |
| 2 to 3 | A measurable mismatch on one or two bars, or a moderately poor height-to-label fit. |
| 4 to 5 | Large or widespread mismatch: bars drawn well out of proportion to their stated values. |
Why this matters
Drawing a bar at the wrong height is one of the most direct ways to mislead with a chart, and it is a named category in every recent taxonomy of misleading visualizations: data-visual disproportion, where a value label does not match the size of its visual encoding, sits alongside truncated and inverted axes as a core deception type [1, 2, 3]. The underlying standard is decades old. Tufte defined graphical integrity as the requirement that the area or length of a mark be proportional to the quantity it encodes, and quantified violations with the lie factor, with famous examples reaching factors of fourteen [4]. G5 computes that lie factor directly: when the axis is readable, each bar's drawn value is recovered and compared to its label; when it is not, the heights are checked for internal proportionality to the labels, which catches a single resized bar even with no axis to calibrate against. Recovering values from a chart in order to check them against its text is exactly the task of chart fact-checking and chart data extraction, where claims are verified against the plotted marks and where pixel-to-value reconstruction is built from the detected bars and axis ticks [5, 6]. A bar whose height contradicts its own label is a self-inconsistency that needs no external data to detect.
Limitations
G5 analyses bar charts and needs both detected bars and readable numeric data labels, so charts without printed values on the bars, or whose labels OCR cannot read, are not scored. The absolute check additionally needs a calibrated y-axis; when axis labels cannot be read, the calibration-free consistency check still runs from the labels and heights alone, but it measures relative proportionality rather than absolute correctness, so a chart whose every bar is scaled by the same wrong factor passes it. Label-to-bar matching is by nearest position and can mislink in dense or overlapping layouts. The thresholds are directional, and rounding of printed labels produces small honest errors, which is why low single-bar errors are not flagged and sparse evidence is capped. Axis-scale manipulation, error-bar fabrication, and raster-level editing live in sibling chart indicators, so G5 stays on the bar-height-versus-label comparison to avoid duplicating them.
Theoretical background
G5 operationalises Tufte's lie factor for bar charts in two regimes. With a calibrated axis the lie factor is measured per bar as the ratio of the recovered value to the printed value, and the relative error is its distance from one. Without a calibrated axis the same proportionality is tested across bars: if the heights honestly encode the labels then top pixel is an affine function of label value, an affine form rather than a strictly proportional one so that a non-zero baseline does not by itself trigger the check, and the regression R-squared measures how well that holds while the largest residual localises the offending bar. Both regimes test a self-consistency property of the figure, the mark size against the number it carries, which is a structural integrity check independent of any external ground truth or of which tool drew the chart.
References
- Tonglet J, Zimny J, Tuytelaars T, Gurevych I. Is this chart lying to me? Automating the detection of misleading visualizations. In: Proceedings of the Association for Computational Linguistics (ACL). 2026. arXiv:2508.21675. https://arxiv.org/abs/2508.21675
- Lalai HN, Shah RS, Pfister H, Varma S, Guo G. When Visuals Aren't the Problem: Evaluating Vision-Language Models on Misleading Data Visualizations. arXiv preprint arXiv:2603.22368. 2026. https://arxiv.org/abs/2603.22368
- Chen Z, Song S, Shum K, Lin Y, Sheng R, Wang W, Qu H. Unmasking Deceptive Visuals: Benchmarking Multimodal Large Language Models on Misleading Chart Question Answering. In: Proceedings of EMNLP. 2025. arXiv:2503.18172. https://arxiv.org/abs/2503.18172
- Tufte ER. The Visual Display of Quantitative Information. 2nd ed. Cheshire (CT): Graphics Press; 2001 (first published 1983).
- Akhtar M, Subedi N, Gupta V, Tahmasebi S, Cocarascu O, Simperl E. ChartCheck: Explainable Fact-Checking over Real-World Chart Images. In: Findings of the Association for Computational Linguistics (ACL). 2024. arXiv:2311.07453. https://arxiv.org/abs/2311.07453
- Luo J, Li Z, Wang J, Lin CY. ChartOCR: Data Extraction from Charts Images via a Deep Hybrid Framework. In: IEEE/CVF Winter Conference on Applications of Computer Vision (WACV). 2021. https://openaccess.thecvf.com/content/WACV2021/html/Luo_ChartOCR_Data_Extraction_From_Charts_Images_via_a_Deep_Hybrid_WACV_2021_paper.html