Bar graphs of mean values produce inflated and variable estimates of effect size
Bibliographic record
Abstract
Bar graphs of mean values (BGoMs) are frequently criticized for abstracting beyond, and thus hiding, the individual values that are averaged to produce their plotted mean values. Yet does this abstraction produce miscommunication? BGoMs are often presumed, due to their visual simplicity, to communicate well, especially to non-expert viewers. Here, we tested that presumption. In a study of 29 non-expert viewers, we first found that viewers overestimated the effect sizes conveyed by two real BGoMs taken directly from popular Introductory Psychology textbooks. We then asked whether manipulation of the y-axis range would reduce this overestimation and found that it did, but only partly, and only in some viewers. We measured estimated effect sizes in Cohen’s d (SD) units via a drawing-based method developed by our lab that requires no prior statistical knowledge (Kerns & Wilmer, 2021). Participants simply sketch a version of a viewed BGoM, adding hypothesized data points that, when averaged, would produce the plotted mean values. For two BGoMs whose real effect sizes were 1.0 and 0.7, the median drawn effect sizes were 4.4 and 9.5. Expansion of the y-axis range reduced, but did not eliminate the overestimation (median effect sizes were 3.2 and 2.1, respectively, for a 2x expansion, and 3.7 and 2.5, respectively, for a 4x expansion). Moreover, the variation between the largest and smallest drawn effect size in every condition (2 BGoMs x 3 y-axis ranges) represented at least a fivefold difference; therefore, though overestimation was reduced on average, different viewers still came away with markedly different, often highly inaccurate, conceptions of the data. We conclude that BGoMs are capable of producing distorted, highly varied interpretations of data in non-expert viewers, and that abstraction in BGoMs is not just a theoretical concern, but an evidence-based concern.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.106 | 0.458 |
| Meta-epidemiology (narrow) | 0.003 | 0.002 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.007 | 0.005 |
| Science and technology studies | 0.001 | 0.008 |
| Scholarly communication | 0.004 | 0.007 |
| Open science | 0.003 | 0.005 |
| Research integrity | 0.002 | 0.005 |
| Insufficient payload (model declined to judge) | 0.009 | 0.002 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".