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Cited by 194Data Visualization and AnalyticsVisual and Cognitive Learning ProcessesStatistics Education and Methodologies

The DOI matches its Crossref record; 42 of the 43 references it cites were found in a registry or an index.

Hypothetical Outcome Plots Outperform Error Bars and Violin Plots for Inferences about Reliability of Variable Ordering

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Hullman, Jessica, Resnick, Paul, Adar, Eytan·2015·PLOS ONE
DOI 10.1371/journal.pone.0142444PMC PMC4646698
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Abstract

Many visual depictions of probability distributions, such as error bars, are difficult for users to accurately interpret. We present and study an alternative representation, Hypothetical Outcome Plots (HOPs), that animates a finite set of individual draws. In contrast to the statistical background required to interpret many static representations of distributions, HOPs require relatively little background knowledge to interpret. Instead, HOPs enables viewers to infer properties of the distribution using mental processes like counting and integration. We conducted an experiment comparing HOPs to error bars and violin plots. With HOPs, people made much more accurate judgments about plots of two and three quantities. Accuracy was similar with all three representations for most questions about distributions of a single quantity.

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Crossref · 10.1371/journal.pone.0142444

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Figures

Fig 1 Fictitious scenario. Scientists have measured the concentration of two chemical solutes (A and B, each measured in parts per million) in many vials of sea water. Horizontal blue lines are the means, dashed vertical bars capture 95% of the measurements for each solute, and you may assume independence. Question: in what percentage of vials is there more of solute B than A (Probability(B > A)? Answer below.
Fig 1 Fictitious scenario. Scientists have measured the concentration of two chemical solutes (A and B, each measured in parts per million) in many vials of sea water. Horizontal blue lines are the means, dashed vertical bars capture 95% of the measurements for each solute, and you may assume independence. Question: in what percentage of vials is there more of solute B than A (Probability(B > A)? Answer below.CC BY · PubMed Central
Fig 2 An illustration of our different study conditions. Error bars convey the mean of a distribution of measurements (outcomes) along with a vertical “error bar” capturing a 95% confidence interval. Violin plots extend this idea by showing the distribution in a mirrored histogram. Hypothetical Outcome Plots (HOPs) present the same distribution as animated frames (that can be played in sequence or manually flipped through). Each frame contains a horizontal bar representing one outcome. An animated version of this figure is available in the animated manuscript (S1 File).
Fig 2 An illustration of our different study conditions. Error bars convey the mean of a distribution of measurements (outcomes) along with a vertical “error bar” capturing a 95% confidence interval. Violin plots extend this idea by showing the distribution in a mirrored histogram. Hypothetical Outcome Plots (HOPs) present the same distribution as animated frames (that can be played in sequence or manually flipped through). Each frame contains a horizontal bar representing one outcome. An animated version of this figure is available in the animated manuscript (S1 File).CC BY · PubMed Central
Fig 3 Violin plots showing the four one-quantity tasks, four two-quantity tasks, and single three-quantity task summarized in Tables 1–3. An animated version of this figure is available in the animated manuscript (S1 File).
Fig 3 Violin plots showing the four one-quantity tasks, four two-quantity tasks, and single three-quantity task summarized in Tables 1–3. An animated version of this figure is available in the animated manuscript (S1 File).CC BY · PubMed Central
Fig 4 Stimuli (left) and absolute error (right) of estimates of μ. Error bars indicate a 95% confidence interval. Error bars in the results plot show a 95% confidence interval. An animated version of this figure is available in the animated manuscript (S1 File).
Fig 4 Stimuli (left) and absolute error (right) of estimates of μ. Error bars indicate a 95% confidence interval. Error bars in the results plot show a 95% confidence interval. An animated version of this figure is available in the animated manuscript (S1 File).CC BY · PubMed Central
Fig 5 Stimuli (left) and absolute error (right) of estimates of Pr(A ≥ k). Both locations of the red dot (above and below mu) are shown, though subjects saw only one of the dots in each trial. Error bars in the results plot indicate a 95% confidence interval. An animated version of this figure is available in the animated manuscript (S1 File).
Fig 5 Stimuli (left) and absolute error (right) of estimates of Pr(A ≥ k). Both locations of the red dot (above and below mu) are shown, though subjects saw only one of the dots in each trial. Error bars in the results plot indicate a 95% confidence interval. An animated version of this figure is available in the animated manuscript (S1 File).CC BY · PubMed Central
Fig 6 Stimuli (top) and absolute error (bottom) of estimates of Pr(k 2 < = A< = k 3). Error bars indicate a 95% confidence interval. An animated version of this figure is available in the animated manuscript (S1 File).
Fig 6 Stimuli (top) and absolute error (bottom) of estimates of Pr(k 2 < = A< = k 3). Error bars indicate a 95% confidence interval. An animated version of this figure is available in the animated manuscript (S1 File).CC BY · PubMed Central
Fig 7 Stimuli (left) and absolute error (right) of estimates of Pr(B > A). Error bars indicate a 95% confidence interval. An animated version of this figure is available in the animated manuscript (S1 File).
Fig 7 Stimuli (left) and absolute error (right) of estimates of Pr(B > A). Error bars indicate a 95% confidence interval. An animated version of this figure is available in the animated manuscript (S1 File).CC BY · PubMed Central
Fig 8 Stimuli (top) and absolute error (bottom) of estimates of Pr(B > A, B > C). Error bars in the results plot indicate a 95% confidence interval. An animated version of this figure is available in the animated manuscript (S1 File).
Fig 8 Stimuli (top) and absolute error (bottom) of estimates of Pr(B > A, B > C). Error bars in the results plot indicate a 95% confidence interval. An animated version of this figure is available in the animated manuscript (S1 File).CC BY · PubMed Central
Fig 9 A gradient plot, where probability density of each possible outcome is encoded using mark opacity.
Fig 9 A gradient plot, where probability density of each possible outcome is encoded using mark opacity.CC BY · PubMed Central

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Metadata

Authors
Hullman, J., Resnick, P., & Adar, E.
Affiliations
  • University of Washington (US)
  • University of Michigan (US)
Corresponding author
Hullman, Jessica
ORCID
Venue
PLOS ONE
Publisher
Public Library of Science (PLoS)
Published
2015-11-16
Volume
10
Issue
11
Pages
e0142444
ISSN
1932-6203 (ISSN-L)
DOI
10.1371/journal.pone.0142444
PMC
PMC4646698
OpenAlex
W2292312835
Cited by
194
References
43
Citations by year
2026: 11 · 2025: 24 · 2024: 18 · 2023: 32 · 2022: 26 · 2021: 27 · 2020: 21 · 2019: 18 · 2018: 9 · 2017: 6 · 2016: 2
FWCI
4.92
Type
journal article
Language
en
Open access
Licence
Locations
  • PLoS ONE (publishedVersion, cc-by)
  • Europe PMC (PubMed Central) (publishedVersion, cc-by)
  • PubMed Central (publishedVersion, cc-by)
  • PubMed (publishedVersion)
  • RePEc: Research Papers in Economics (submittedVersion)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
  • Figshare (submittedVersion, cc-by)
Topics
  • Physical Sciences › Computer Science › Computer Graphics and Computer-Aided Design › Data Visualization and Analytics
  • Social Sciences › Psychology › Experimental and Cognitive Psychology › Visual and Cognitive Learning Processes
  • Physical Sciences › Mathematics › Statistics and Probability › Statistics Education and Methodologies
Keywords
error bars, violin plots
MeSH terms
Data Interpretation, Statistical, Discrimination, Psychological, Humans, Probability, Reproducibility of Results, Models, Statistical, Normal Distribution

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