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Inference by Eye: Confidence Intervals and How to Read Pictures of Data.
Abstract
Wider use in psychology of confidence intervals (CIs), especially as error bars in figures, is a desirable development. However, psychologists seldom use CIs and may not understand them well. The authors discuss the interpretation of figures with error bars and analyze the relationship between CIs and statistical significance testing. They propose 7 rules of eye to guide the inferential use of figures with error bars. These include general principles: Seek bars that relate directly to effects of interest, be sensitive to experimental design, and interpret the intervals. They also include guidelines for inferential interpretation of the overlap of CIs on independent group means. Wider use of interval estimation in psychology has the potential to improve research communication substantially.
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“Error bars represent 95% confidence intervals (computed by following Cumming & Finch, 2005 ).”
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“In this paper, all the examples are based on between-subjects designs assuming independence between the means [44, 52].”
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“Cumming and Finch (2005) have attempted to educate investigators by providing rules to guide correct inference.”
BackgroundDulebohn, J. H., Conlon, D. E., Sarinopoulos, I. C., Davison, R. B., & McNamara, G. M. (2009) · Organizational Behavior and Human Decision Processes · doi:10.1016/j.obhdp.2009.09.001 · Cited by 80
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“…net carbon transfer was significantly greater than zero (i.e. where the interval did not include zero, then net carbon transfer was probably greater than zero) (see Di Stefano (2004) and Cumming & Finch (2005) for the interpretation and use of confidence intervals as inferential statistics).”
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“A 95%CrI that does not overlap 0 is comparable to a significant frequentistP value (Cumming and Finch 2005).”
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“…studies of how researchers interpret such results when presented in null hypothesis significance testing (NHST), or confidence interval (CI) formats. statistical rEForm Statistical reformers argue that CIs have strong advantages over NHST (e.g., Kline, 2004, Chapter 3; Cumming and Finch, 2005).”
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“As a consequence, CIs can be used (by stealth) to conduct NHST (Cumming & Finch, 2005).”
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MethodInfluentialConfidence intervals for dependent data: Equating non-overlap with statistical significance
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“On the other hand, Goldstein & Healy [1] derive the 1For the comparison of medians, Tukey [10] invented notches that are drawn on either side of the median within a boxplot.”
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Why Figures with Error Bars Should Replace p Values
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“…Zeitschrift für Psychologie / Journal of Psychology 2009; Vol. 217(1):27–37 Examples of detailed discussion of CI advantages include: Cumming & Fidler (this issue), Cumming & Finch (2005, 2001), Loftus & Masson (1994), Schmidt (1996). expect them to help alleviate this dichotomous thinking.”
BackgroundToward improved statistical reporting in the journal of consulting and clinical psychology.
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“However, the converse is not true: overlapping con dence intervals do not necessarily mean that the means are not di erent (see Figure 4 in [17] for explanation).”
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Collaborative for Academic, Social and Emotional Learning (CASEL)
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BackgroundResultMorgan‐Short, K., Marsden, E. J., Heil, J., Issa, B. I., Leow, R. P., Mikhaylova, A., Mikołajczak, S., Moreno, N., Slabakova, R., & Szudarski, P. (2018) · Language Learning · doi:10.1111/lang.12292 · Cited by 70
“Attention to Form While Processing L2 Input for Meaning Selecting Target Research for Replication As noted above and by Marsden, Morgan-Short, Thompson, and Abugaber (2018), an initial step in any replication endeavor is to establish that an initial study has high replication value (Association for Psychological Scien…”
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Varieties of Confidence Intervals
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“Sadly, there has been some confusion in the recent years on how to interpret them (e.g., Belia, Fidler, Williams, & Cumming, 2005; Cumming & Finch, 2005) or even if they should be interpreted at all (Hoekstra, Morey, Rouder, & Wagenmakers, 2014; Morey, Hoekstra, this is an open access article under…”
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“In absence of a standardized statistical test, we interpret nonoverlapping con fi dence intervals of the IRFs as indication of a statistical difference between the two levels (Cumming & Finch, 2005, e.g., high vs. low choice).”
Gender and the Predictive Validity of the LSI-R
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“…of switching to abstention furthermore show that strongly dissatisfied voters for mainstream parties are more than twice as likely to abstain compared to strongly dissatisfied voters for populist parties, this difference is statistically significant at the p 0.05 level (Cumming and Finch 2005).”
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“Ground electrodes were located over the processus styloideus radii.”
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“Otherwise, the difference was not considered statistically significant (22,23).”
[Design and power analysis: n and confidence intervals of means].
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Lindig, S., Moser, D., Curran, A. J., Rath, K., Khalilnejad, A., French, R. H., Herz, M., Müller, B., Makrides, G., Georghiou, G. E., et al. (2021) · Progress in Photovoltaics Research and Applications · doi:10.1002/pip.3397 · Cited by 62
“4% CIs, so as to attain a 5% capture rate.(64,65) This suggests that researchers who wish to compare on a common basis, different PLR determination methods should use 95% CIs, while a PV system fleet owner, who is wanting to determine which PV systems in the fleet are exhibiting similar or distinctly different perform…”
BackgroundCurrent concerns in visual masking.
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“To evaluate individual differences and their effects, confidence intervals as well as correlations with variables of interest (e.g., Whalen et al., 2004) can be calculated (Cumming & Finch, 2005).”
MethodInference by Eye: Pictures of Confidence Intervals and Thinking About Levels of Confidence
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“Cumming and Finch (2005) offered suggestions for inference by eye when two CIs are displayed.”
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“While variables with overlapping CIs may be significantly different, we used a conservative approach identifying non-overlapping CIs to determine significantly different associations among variables in each model [25].”
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“1a) despite slight CI overlap between them (Cumming & Finch 2005; Knol, Pestman & Grobbee 2011).”
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“Two groups are significantly different at a ∼1% significance level if their confidence intervals do not overlap [10] (pink bars in Figure 9).”
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“Larger confidence intervals denote poorer precision (for an introduction to interpreting confidence intervals, see Cumming & Finch, 2005).”
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“, those of approximate and progressive systems) can lead to poor user performance [40] and false conclusions [12, 19].”
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“Such visualizations convey uncertainty in estimating the means of each group, and facilitate null hypothesis significance testing (NHST) and "inference by eye" using various heuristics [14].”
BackgroundMethodCognitive effects of music and dance training in children.
LaPlume, A. A., & Wiseheart, M. (2018) · Archives of Scientific Psychology · doi:10.1037/arc0000048 · Cited by 68
“Because visually presenting pre and post scores biases interpretation as a result of a correlation between the measurements, confidence interval graphs were calculated using difference scores for each group (Cumming & Finch, 2005).”
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Dieckmann, N., Peters, E., & Gregory, R. (2015) · Risk Analysis · doi:10.1111/risa.12358 · Cited by 52
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“We analyze corresponding crowdsourcing scores using confdence intervals and efect sizes, instead of null hypothesis signifcance testing [14].”
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Predictive Validity and the Impact of Change in Total LSI-R Score on Recidivism
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“Table 2 also includes the confidence intervals (CIs) associated with the Pearson correlation values to assess the magnitude and precision of the point estimates (see Cummings & Finch, 2005, for a more complete discussion on how to interpret CIs).”
BackgroundMethodThe benefit of evolving multidisciplinary care in ALS: a diagnostic cohort survival comparison
Opie-Martin, S., Trevor‐Jones, E., Khan, S., Shaw, K., Marchment, D., Kulka, A. M., Ellis, C. E., Burman, R., Turner, M. R., Carroll, L. S., et al. (2017) · Amyotrophic Lateral Sclerosis and Frontotemporal Degeneration · doi:10.1080/21678421.2017.1349151 · Cited by 59
“not demonstrate lack of statistical significance (24).”
Quek, G. L., & Rossion, B. (2017) · Neuropsychologia · doi:10.1016/j.neuropsychologia.2017.08.010 · Cited by 61
“Error bars are within-subjects 95% CIs, overlap should not be interpreted by eye (Cumming & Finch, 2005).”
Clapp, J. D., Beck, G. J., Palyo, S. A., & Grant, D. M. (2008) · Pain · doi:10.1016/j.pain.2008.01.001 · Cited by 55
“56) suggest a marginal contribution of increased pain to decreases in life satisfaction [15].”
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The Impact of Phloem Nutrients on Overwintering Mountain Pine Beetles and Their Fungal Symbionts
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“CIs can be used by readers to visually approximate two sample comparison tests at whatever alpha level they choose (Payton et al. 2000, Cumming and Finch 2005).”
MethodMiccoli, L., Delgado, R., Guerra, P. M., Versace, F., Rodríguez‐Ruiz, S., & Fernández‐Santaella, M. C. (2016) · PLoS ONE · doi:10.1371/journal.pone.0158991 · Cited by 56
“To facilitate the interpretation of the data [30], we report the differences between the means with their corresponding Bonferroni-adjusted 95% confidence intervals (CI).”
MethodPlotsOfDifferences – a web app for the quantitative comparison of unpaired dataPreprint
Goedhart, J. (2019) · bioRxiv · doi:10.1101/578575 · Cited by 59
“A direct, but qualitative comparison of the different categories/conditions can be done by ‘visual inference’ if 95% confidence intervals are supplied (Cumming and Finch, 2005; Cumming et al., 2007; Gardner and Altman, 1986).”
BackgroundAgarwal, R., & Selen, W. J. (2013) · Journal of Management & Organization · doi:10.1017/jmo.2014.5 · Cited by 55
“Using the procedure by Cumming and Finch (2005), it concludes that Hypothesis 1c or the ORC to CIC path was not supported.”
A field study of adult witness interviewing practices in a Canadian police organization
Snook, B., & Keating, K. (2010) · Legal and Criminological Psychology · doi:10.1348/135532510x497258 · Cited by 55
“…all the information provided by null hypothesis significance testing and, instead of making a dichotomous yes/no decision about differences between groups, they give a range of values within which the true difference is likely to lie (see Cumming & Finch, 2005; Gendreau & Smith, 2007; Kirk, 1996).”
BackgroundSustaining Actor Engagement During the Opportunity Development Process
Snihur, Y., Reiche, B. S., & Quintane, E. (2016) · Strategic Entrepreneurship Journal · doi:10.1002/sej.1233 · Cited by 55
Jevšenak, J. (2019) · Quaternary Science Reviews · doi:10.1016/j.quascirev.2019.105868 · Cited by 55
Morton, K. R., Lee, J. W., Haviland, M. G., & Fraser, G. E. (2012) · Psychology of Religion and Spirituality · doi:10.1037/a0027553 · Cited by 56
“…of indirect effects for two reasons: (a) bootstrap confidence intervals do not require the normality assumptions of maximum likelihood methods; and, (b) non-overlap of confidence intervals is a conservative test of statistical significance and readily interpretable (Cumming & Finch, 2005).”
BackgroundWilliams, I. D., White, D. J., Sparks, R., Lino, K. C., Zamzow, J. P., Kelly, E. L. A., & Ramey, H. L. (2016) · PLoS ONE · doi:10.1371/journal.pone.0159100 · Cited by 54
“as mean and quantile range of difference) provides substantial additional information compared to simply reporting a significance test result [43].”
BackgroundThe effects of prey depletion on dietary niches of sympatric apex predators in Southeast Asia
Steinmetz, R., Seuaturien, N., INTANAJITJUY, P., INRUEANG, P., & PREMPREE, K. (2020) · Integrative Zoology · doi:10.1111/1749-4877.12461 · Cited by 55
Lane, D. M., & Sándor, A. (2009) · Psychological Methods · doi:10.1037/a0016620 · Cited by 54
“…three types of information in graphs: shapes of distributions (Wilkinson & the Task Force on Statistical Inference, 1999), trends (Gelman, Pasarica, & Dodhia, 2002), and inferential statistics (Cumming & Finch, 2005; Masson & Loftus, 2003; Wilkinson & the Task Force on Statistical Inference, 1999).”
BackgroundInfluentialLi, J. H., Chang, X. R., Li, L., & Ma, L. Y. (2014) · Journal of Knowledge Management · doi:10.1108/jkm-08-2013-0316 · Cited by 56
“Thus, even if 95 per cent CIs overlap, values can still be significantly different from one another (Cumming and Finch, 2005).”
BackgroundKaiser, F. G., & Byrka, K. (2014) · The Journal of Social Psychology · doi:10.1080/00224545.2014.959884 · Cited by 54
“…significantly less—even in a statistical sense—than what could be seen as their fair share, which is noticeable in Figure 1 (for more details, see Cumming & Finch, 2005): The 95% confidence interval of the average amount of energy demanded by people with high environmental attitudes (M = 1.68…”
BackgroundInfluentialNipping Temptation in the Bud: Examining Strategic Self-Control in Daily Life
Williamson, L. Z., & Wilkowski, B. M. (2019) · Personality and Social Psychology Bulletin · doi:10.1177/0146167219883606 · Cited by 57
“Any interval that does not overlap with zero provides evidence for statistical significance at a 95% confidence level (Cumming & Finch, 2005).”
BackgroundResultMotivational Profiling of League of Legends Players
Brühlmann, F., Baumgartner, P., Wallner, G., Kriglstein, S., & Mekler, E. D. (2020) · Frontiers in Psychology · doi:10.3389/fpsyg.2020.01307 · Cited by 59
“5 or less, they indicate statistical significance at an alpha-level of 5% (Cumming and Finch, 2005).”
BackgroundChristensen, H. S., & Rapeli, L. (2020) · Policy Sciences · doi:10.1007/s11077-020-09408-w · Cited by 58
The Use of Control Charts to Interpret Environmental Monitoring Data
Morrison, L. W. (2008) · Natural Areas Journal · doi:10.3375/0885-8608(2008)28[66:tuocct]2.0.co;2 · Cited by 53
Gebauer, J. E., Leary, M. R., & Neberich, W. (2011) · Social Psychological and Personality Science · doi:10.1177/1948550611431644 · Cited by 59
“Indeed, following comparison recommendations by Cumming and Finch (2005), the alternative mediation models were significantly outperformed by the hypothesized model in each and every case.”
BackgroundMethodThe Warm Glow of Restaurant Checkout Charity
Giebelhausen, M. D., Lawrence, B., Chun, H. H., & Hsu, L. (2017) · Cornell Hospitality Quarterly · doi:10.1177/1938965517704533 · Cited by 53
Statistical Significance Testing at CHI PLAY: Challenges and Opportunities for More Transparency
Vornhagen, J. B., Tyack, A., & Mekler, E. D. (2020) · Annual Symposium on Computer-Human Interaction in Play · doi:10.1145/3410404.3414229 · Cited by 60
“• Interpreting results [36, 48]: Exploratory analysis is less constrained than a confrmatory approach.”
BackgroundBabchishin, K. M., Blais, J., & Helmus, L. M. (2012) · Canadian Journal of Criminology and Criminal Justice/La Revue canadienne de criminologie et de justice pénale · doi:10.3138/cjccj.2010.e.40 · Cited by 53
Temporal and spatial limitations in global surveillance for bat filoviruses and henipaviruses
Becker, D. J., Crowley, D. E., Washburne, A. D., & Plowright, R. K. (2019) · Biology Letters · doi:10.1098/rsbl.2019.0423 · Cited by 52
“Some overlap in 95% confidence intervals does not imply lack of statistical difference in mean estimates [52].”
Background
Metadata
- Authors
- Cumming, G., & Finch, S.
- Affiliations
- La Trobe University (AU)
- Venue
- American Psychologist
- Published
- 2005
- Volume
- 60
- Issue
- 2
- Pages
- 170-180
- ISSN
- 0003-066X (ISSN-L)
- 1935-990X
- OpenAlex
- W2005534705
- Cited by
- 1,449
- References
- 59
- Citations by year
- 2026: 62 · 2025: 66 · 2024: 74 · 2023: 92 · 2022: 102 · 2021: 110 · 2020: 92 · 2019: 86 · 2018: 80 · 2017: 82 · 2016: 76 · 2015: 89 · 2014: 63 · 2013: 59 · 2012: 48
- FWCI
- 39.36
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- American Psychologist (publishedVersion)
- PubMed (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Physical Sciences › Mathematics › Statistics and Probability › Statistics Education and Methodologies
- Social Sciences › Decision Sciences › Statistics, Probability and Uncertainty › Meta-analysis and systematic reviews
- Keywords
- confidence intervals, error bars, statistical significance testing, interval estimation, scholarly communication
- MeSH terms
- Humans, Confidence Intervals
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Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
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