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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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“The mean size of the overlap across instruments was approximately 50%, or the criterion suggested for inferring statistical similarity (Cumming & Finch, 2005).”
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“We inferred a difference between levels of a covariate where model-averaged prediction intervals overlapped by less than 25% (Cumming and Finch 2005).”
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“When possible, we use a 95% confidence interval (CI) [2] to report on the estimated difference between two means.”
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“In fact, for two independently sampled populations, Cumming and Finch (2005) gave an approximate rule for using the amount of observed overlap between two confidence intervals to judge statistical significance.”
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Editorial: How to Write an Effective Results and Discussion for the Journal of Pediatric Psychology
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“In addition, JPP editorial policy requires that authors include effect sizes and confidence intervals for major findings ( Cumming & Finch, 2005, 2008; Durlak, 2009; Wilkinson & the Task Force on Statistical Inference, 1999; Vacha-Haase & Thompson, 2004).”
BackgroundLi, Y., & Singh, C. (2022) · Physical Review Physics Education Research · doi:10.1103/physrevphyseducres.18.010142 · Cited by 21
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“However, it is crucial to note that all the standard errors between 100 and 400 iterations are clearly overlapping (Figure 10), indicating the absence of significant differences (Cumming & Finch, 2005).”
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“We calculated Cohen’s 𝑑 values [19] to measure the differences between these two conditions to support the statistical analysis.”
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“The absence of overlap between the error bar and zero represents a slope value that differs from zero (Cumming and Finch, 2005).”
BackgroundMercury Exposure as a Function of Fish Consumption in Two Asian Communities in Coastal Virginia, USA
Xu, X., & Newman, M. C. (2014) · Archives of Environmental Contamination and Toxicology · doi:10.1007/s00244-014-0102-y · Cited by 18
“…discussion of significant differences for data from the communities applied Cumming’s general rules-of-thumb: Nonoverlap of 95 % confidence interval (CI) indicated a P value \ 0.01, and a proportion of overlap of 95 % CIs\0.5 indicated a P value of \0.05 (Cumming 2012; Cumming and Finch 2005).”
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“12 According to Cumming and Finch (2005), when the 95% normaltheory confidence intervals do not overlap, the means of the two groups differ at a level of significance that is at least α = 0.01. comparison of different pairs of models (e.g., models assuming configural versus loading invariance or…”
BackgroundInfluentialBeyond inference by eye: Statistical and graphing practices in JEAB, 1992‐2017
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“However, some minor overlap of the BCI with zero was tolerated in inferring relationships (see Cumming and Finch 2005).”
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“…using 95% confidence intervals, where nonoverlapping intervals indicate statistically significant differences at p .01 (Schenker & Gentleman, 2001) and intervals that overlap less than half of the margin of error indicate statistically significant differences at p .05 (Cumming & Finch, 2005).”
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“When the 95% CIs overlapped, the sensitivity/specificity between groups was deemed not statistically significantly different [18,19].”
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“Vice versa, whenever confidence intervals overlap, there is no significant difference [44].”
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“The inference by eye approach is a straightforward way to convey an overall pattern of results (Cumming, 2009; Cumming & Finch, 2005).”
MethodAssociations Between Gender Segregation and Gender Identity in College Students
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“According to Cumming and Finch (2005), any proportion of overlap smaller or equal to .5 does not invalidate the assertion that the means between groups are significantly different when p .05.”
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“…of overlapping/non-overlapping confidence intervals is a relatively common and conservative approach for examining the differences in the magnitude of effects across categorical variables in large epidemiological data files (Cumming & Finch, 2005; Hofman, Richey, Kashdan, & McKnight, 2009).”
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“…CIs for the injury percentages representing the range; they should not be used for a test of the significance of differences between ranges (see Cummings, 2005; Cumming & Finch, 2005; Newcombe & Altman, 2000); the test for significant differences in the two risk score ranges and the three risk…”
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“Overlap in confidence intervals was used to infer statistical significance for each relevant comparison (Cumming and Finch 2005).”
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“However, some minor overlap of the BCI with zero was tolerated in inferring relationships (see Cumming & Finch, 2005).”
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“Based on the visual inference rule (Cumming and Finch 2005) for error bar overlaps, the interaction e ff ect of Pride with Russia Aggressor was statistically signi fi cant except for those respondents who were not at all proud of their Ukrainian citizenship.”
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“05 [37].”
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“…more strictly: G.H.’s values were considered outside the control participant’s range only if the distance between G.H.’s and any control participant’s values exceeded this control participant’s CI plus G.H.’s half CI (which is the p = .05 limit, Cumming & Finch, 2005; Sedlmeier & Renkewitz, 2007).”
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“extremely important, but this topic is beyond the scope of this paper; refer to Cumming et al. (2004) and Cumming and Finch (2005) for a discussion on the use”
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“The 95% CI ‘‘is an interval estimate that indicates the precision, or likely accuracy, of our point estimate’’ (Cumming and Finch 2005, p. 170).”
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“[Drug Name], a drug with early promising study results showing that the drug may demonstrate substantial improvement over available therapiesh 1378 (37, 32-42) 81 170 (41, 38-44) 82 548 (41, 38-43) 6 (5-9)”
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“…with 10,000 bootstrap samples as recommended in current research to reduce potential sampling errors (Fox, 2008) and provide confidence intervals that are believed to be more informative than traditional significance testing alone (American Psychological Association, 2009; Cumming & Finch, 2005).”
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“Confidence intervals and power curves include all of the information captured in point estimates, yet also give estimates of precision, which are less amenable to tweaking (Cumming & Finch, 2005; Wilkinson & the Task Force on Statistical Inference, 1999).”
BackgroundLessons learned from statistical reform efforts in other disciplines
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“The case for reform is compelling, and we believe reform is both necessary and urgent ( Cumming & Finch, 2005; Thompson, 2006b).”
BackgroundSelf-citationEstimating and graphing interactions.
Aiken, L. S., West, S. G., Luhmann, M., Baraldi, A. N., & Coxe, S. J. (2012) · American Psychological Association eBooks · doi:10.1037/13621-005 · Cited by 15
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“If the point estimate of the ICC from one group was contained within the 95% CI of the ICC from the other group, the reliability of the groups was considered similar [44, 45].”
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The interchangeability of liking and friend nominations to measure peer acceptance and friendship
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“Confidence interval comparisons (Cumming & Finch, 2005) indicated that within each grade, adjusted Kappa coefficients were highest for best friends; the top two ranked friends were less likely to be nominated as liked than were first ranked friends, but were more likely to be nominated as liked…”
BackgroundReporting Confidence Intervals and Effect Sizes: Collecting the Evidence.
Zientek, L. R., Özel, Z., Özel, S., & Allen, J. M. (2012) · Career and Technical Education Research · doi:10.5328/cter37.3.277 · Cited by 13
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“According to Cumming and Finch (2005), any proportion of overlap smaller or equal to .5 does not invalidate the assertion that the means between groups are significantly different when p .05.”
BackgroundMarsh, P. J., Polito, V., Singh, S., Coltheart, M., Langdon, R. A., & Harris, A. W. F. (2016) · BMC Psychiatry · doi:10.1186/s12888-016-1064-6 · Cited by 15
“Specifically, we focused on whether the CI of the mean difference captured zero as a test of no effect of treatment [43].”
BackgroundMorrison, M. A., Bishop, C., & Morrison, T. G. (2018) · Psychology and Sexuality · doi:10.1080/19419899.2018.1484798 · Cited by 17
“The upper and lower values for these intervals delimit the plausible range of alpha coefficients that should be obtained if the measure were distributed to another demographically similar sample (Cumming & Finch, 2005).”
BackgroundPerley-Robertson, B., Helmus, L. M., & Forth, A. (2018) · Psychology, Crime and Law · doi:10.1080/1068316x.2018.1519827 · Cited by 14
“If two 95% confidence intervals do not overlap, those effects sizes are significantly different at p < .01 (Cumming & Finch, 2005). their sentence) before the end of follow-up were excluded from these analyses because they would not have an opportunity for revocation (restricting the sample to 1400…”
BackgroundMethodPartner in crime: Beneficial cooperation overcomes children’s aversion to antisocial others
Myślińska‐Szarek, K., Bocian, K., Baryła, W., & Wojciszke, B. (2020) · Developmental Science · doi:10.1111/desc.13038 · Cited by 15
Streiner, D. L. (2016) · Journal of Clinical Psychopharmacology · doi:10.1097/jcp.0000000000000490 · Cited by 15
Multidimensional perfectionism and orthorexia: a systematic review and meta-analysis
Pratt, V. B., Hill, A. P., & Madigan, D. J. (2024) · Eating and Weight Disorders - Studies on Anorexia Bulimia and Obesity · doi:10.1007/s40519-024-01695-z · Cited by 18
“Specific differences were examined by comparing the overlap between 95% CIs for effect sizes [62].”
MethodMammal responses to spatial pattern in fire history depend on landscape context
Delaney, L., Stefano, J. D., & Sitters, H. (2021) · Landscape Ecology · doi:10.1007/s10980-020-01186-3 · Cited by 14
Modeling and Measuring Tree-Reading Skills in Undergraduate and Graduate Students
Schramm, T., Jose, A., & Schmiemann, P. (2021) · CBE—Life Sciences Education · doi:10.1187/cbe.20-06-0131 · Cited by 14
“This was further corroborated by the overlap of the confidence intervals, which usually reflects nonhierarchical organization, although overlapping confidence intervals are more an indication than proof of significance (Cumming and Finch, 2005).”
BackgroundRossi, C., Roemmich, R. T., Schweighofer, N., Bastian, A. J., & Leech, K. A. (2021) · Frontiers in Aging Neuroscience · doi:10.3389/fnagi.2021.729284 · Cited by 17
“For each epoch, we interpreted step length asymmetry to be significantly different between the Single and Dual groups if the CI did not overlap zero (Efron and Tibshirani, 1994; DiCiccio and Efron, 1996; Cumming and Finch, 2005).”
MethodEffects of Ethnic Classification on Substantive Findings in Adolescent Mental Health Outcomes
Yao, E. S., Bullen, P., Meissel, K., Tiatia‐Seath, J., Fleming, T. M., & Clark, T. C. (2022) · Journal of Youth and Adolescence · doi:10.1007/s10964-022-01612-6 · Cited by 14
“Note some combination groups (e.g., Māori/Pacific) had relatively small sample sizes, resulting in wider CIs.”
BackgroundInfluentialNightingale, S. J., Wade, K. A., & Watson, D. G. (2022) · Psychology and Aging · doi:10.1037/pag0000682 · Cited by 15
“Error bars represent 99.99% CIs, if the 99.99% CIs do not overlap, this provides evidence of difference that would be approximately equivalent to p ≤ 0.0001 (Cumming & Finch, 2005).”
ResultInfluentialGalipaud, M., Bollache, L., Wattier, R. A., Dubreuil, C., Dechaume‐Moncharmont, F., & Lagrue, C. (2015) · Animal Behaviour · doi:10.1016/j.anbehav.2015.01.032 · Cited by 14
Lingelbach, K., Piechnik, D., Gado, S., Janssen, D., Eichler, M., Hentschel, L., Knopf, D., Schuler, M. K., Sernatinger, D., & Peißner, M. (2021) · Frontiers in Public Health · doi:10.3389/fpubh.2021.655083 · Cited by 14
Melman, T., Visser, P., Mouton, X., & de Winter, J. (2021) · Journal of Advanced Transportation · doi:10.1155/2021/4396401 · Cited by 14
“According to Cumming and Finch [67], nonoverlapping CIs correspond to a p-value smaller than 0.006.”
BackgroundInfluentialParasites make hosts more profitable but less available to predators
Prosnier, L., Loeuille, N., Hulot, F. D., Renault, D., Piscart, C., Bicocchi, B., Deparis, M., Lam, M., & Médoc, V. (2024) · Oikos · doi:10.1111/oik.10469 · Cited by 14
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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