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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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“Independent variables were considered to display ‘some evidence’ of a difference if the proportion of CI overlap was no more than half the average length of the two overlapping arms (P < 0.05; Cumming & Finch, 2005), and the two overlapping arms did not differ in length by more than a factor of two.”
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“%) does not include 0.50 (i.e., zero association with recidivism) and statistically different from another ROC area if its confidence interval does not include the other value (see Cumming & Finch, 2005, on drawing inferences from confidence intervals).”
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“The two we prefer are: (1) the CI is a range of plausible values for µ; and (2) substantive interpretation of the values anywhere in the interval, with reference to its upper and lower limits and the mean, should be undertaken (Cumming & Finch, 2005, pp. 174-175).”
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“If the confidence interval of the non-zero mean did not encompass zero, the two treatments were considered statistically different from one another (p< 0.05; Cumming & Finch 2005).”
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“Temporal change across the summits in CTWM was measured as the per cent difference between mean values between 2004 and 2011, and by examining the overlap of 95 % confidence intervals from a normal distribution of the data across the three spatial scales (Cumming and Finch 2005).”
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“Cumming and Finch offer guidance on how to interpret statistical tests using confidence intervals (CI) [13].”
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“(Cumming and Finch 2005), but we chose the more conservative threshold.”
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“Indeed, as Cumming and Finch (2005) noted, it is unclear how well CIs can be effectively used by researchers to understand effects within complex experimental designs.”
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“…BZD use and DSM-IV diagnoses for heroin dependence (Wald χ2=0.23, p>0.05; adjusted odds ratio=0.73; 95% confidence intervals: 0.21–2.60), or cocaine 1The overlap in confidence intervals is not inconsistent with the significant difference (Cumming and Finch, 2005; Wolfe and Hanley, 2002).”
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“…of 15 MEPs from a different condition falling outside of the range of values graphically presented by the 95% CI of the mean CTRL MEP points can be considered statistically significantly different at the P = 0.05 level (Loftus and Masson 1994; Masson and Loftus 2003; Cumming and Finch 2005).”
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“By contrast, inference about the difference requires s diff , the SD of the paired differences — whether for a paired t test or to calculate a CI on the difference (Cumming & Finch, 2005).”
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“Because we aimed to investigate the differential effects of the two factors (depressed affect and somatic complaints), we calculated 95% confidence intervals around the point estimates (Cumming & Finch, 2005; Greenland et al., 2016).”
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“If confidence intervals do not include the mean of the norm T-distribution (M = 50), it can be assumed that they significantly differ from the birth-assigned sex and age equivalent reference group (Cumming & Finch, 2005).”
BackgroundPutting Research in Context: Understanding Confidence Intervals from One or More Studies
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“Cumming and Finch (2005) discuss some principles for interpreting overlapping CIs in some simple situations.”
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“Also, an inferential assessment using simple t-statistics was used to assess if the prevalence of overweight or obesity across the key variables (except for smoking status) was statistically different between periods [55].”
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“In keeping with previous research, we examined the overlapping/no overlapping confidence intervals in order to test the differences in the magnitude effects across gender and race/ethnicity [56] With categorical data, this approach is preferable to more traditional (i.”
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“Similarity of placebo effect sizes on pain and touch (both self and other) was tested via inspection of Cohen’s d confidence intervals (Cumming and Finch 2005).”
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“Intercept and slope coefficients are estimated as continuous functions of time, and figures are used to represent the coefficient functions, along with pointwise 95% confidence intervals, across time (Cumming & Finch, 2005; Greenland et al., 2016).”
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“Means with different letters were significantly different based on proportion overlap between the 95% confidence intervals of the estimated means and the average margin of error at p .05 (Cumming & Finch, 2005).”
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“05 results.(14,15) Given the exploratory nature”
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“S100A12 (ng/mL) 56 [41–72] 78 [37–119] 44 [33–55]”
The case for interactive data exploration accelerators (IDEAs)
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“Furthermore, the human eye has limitations and humans are particularly bad at understanding the impact of error bars [9].”
BackgroundKok, E. M. A., Burant, J. B., Dekinga, A., Manche, P., Saintonge, D., Piersma, T., & Mathot, K. J. (2019) · The American Naturalist · doi:10.1086/704593 · Cited by 40
“With this CI, we indicate that we are 95% confident that our CI includes the actual effect size (Cumming and Finch 2005).”
BackgroundMethodDong, N., Stuart, E. A., Lenis, D., & Nguyen, T. Q. (2020) · Evaluation Review · doi:10.1177/0193841x20938497 · Cited by 46
“Conventional confidence intervals represent the uncertainty associated with each effect estimate individually and can 96 Evaluation Review 44(1) overlap even when there is a statistically significant difference between the estimates (Cumming & Finch, 2005).”
BackgroundDeferring to Clarity, Parsimony, and Evidence in Reply to Ward, Yates, and Willis
Wormith, J. S., Gendreau, P., & Bonta, J. L. (2011) · Criminal Justice and Behavior · doi:10.1177/0093854811426087 · Cited by 40
“The CIs documented above are a crucial piece of evidence that demonstrates the strength of the RNR findings.”
MethodInfluentialIles, I. A., Nan, X., & Verrill, L. A. (2017) · Health Communication · doi:10.1080/10410236.2017.1351277 · Cited by 39
“As such, even though the CIs overlapped, it is still possible for the two means to be statistically different, as per Cumming and Finch (2005). referral might have increased participants’ likelihood to view the NFL. Claims 2 and 3 both stated that the product contained “as much Calcium and Vitamin…”
BackgroundTurning the other cheek: the viewpoint dependence of facial expression after-effects
Benton, C. P., Etchells, P. J., Porter, G., Clark, A. P., Penton‐Voak, I. S., & Nikolov, S. G. (2007) · Proceedings of the Royal Society B Biological Sciences · doi:10.1098/rspb.2007.0473 · Cited by 39
“0.01 (Cumming & Finch 2005).”
InfluentialThe influence of different graphical displays on nonexpert decision making under uncertainty.
Padilla, L., Hansen, G., Ruginski, I. T., Kramer, H., Thompson, W. B., & Creem-Regehr, S. H. (2014) · Journal of Experimental Psychology Applied · doi:10.1037/xap0000037 · Cited by 39
The statistical crisis in science: how is it relevant to clinical neuropsychology?
Gelman, A., & Geurts, H. M. (2017) · The Clinical Neuropsychologist · doi:10.1080/13854046.2016.1277557 · Cited by 40
“However, a graphical depiction of reliability intervals, for example, might help to interpret reported p -values (see e.g. Cumming & Finch, 2005), even if it will not solve the afore-mentioned problems of the overinterpretation of statistical significance.”
MethodBornmann, L., & Haunschild, R. (2018) · Journal of Informetrics · doi:10.1016/j.joi.2018.01.010 · Cited by 39
Jurich, D. P., Daniel, M. M., Paniagua, M. A., Fleming, A., Harnik, V., Pock, A. R., Sein, A. S., Barone, M., & Santen, S. A. (2018) · Academic Medicine · doi:10.1097/acm.0000000000002458 · Cited by 39
Schoonmaker, A., Hillabrand, R., Lieffers, V. J., Chow, P. S., & Landhäusser, S. M. (2021) · Tree Physiology · doi:10.1093/treephys/tpab013 · Cited by 39
Happiness and age in European adults: The moderating role of gross domestic product per capita.
Morgan, J. R., Robinson, O. C., & Thompson, T. (2015) · Psychology and Aging · doi:10.1037/pag0000034 · Cited by 41
Reform of statistical inference in psychology: The case ofMemory & Cognition
Finch, S. J., Cumming, G., Williams, J., Palmer, L., Griffith, E., Alders, C., Anderson, J. L., & Goodman, O. (2004) · Behavior Research Methods, Instruments, & Computers · doi:10.3758/bf03195577 · Cited by 39
Self-citationHigh Mercury Concentrations Reflect Trophic Ecology of Three Deep-Water Chondrichthyans
Newman, M. C., Xu, X., Cotton, C., & Tom, K. R. (2010) · Archives of Environmental Contamination and Toxicology · doi:10.1007/s00244-010-9584-4 · Cited by 39
Bornmann, L., Wagner, C., & Leydesdorff, L. (2018) · PLOS ONE · doi:10.1371/journal.pone.0194805 · Cited by 39
Subliminal emotion perception in brain imaging: findings, issues, and recommendations
Wiens, S. (2006) · Progress in brain research · doi:10.1016/s0079-6123(06)56006-6 · Cited by 39
“Although variability among participants can be evaluated in terms of confidence intervals (Cumming and Finch, 2005) and correlations with variables of interest, this is not commonly discussed in research.”
BackgroundPhonological factors of Spanish/English word internal code-switching
Stefanich, S., & Cabrelli, J. (2018) · Issues in Hispanic and Lusophone linguistics · doi:10.1075/ihll.19.08ste · Cited by 38
Variables are valuable: making a case for deductive modeling
Couto, D. T., & Lorenz, D. (2021) · Linguistics · doi:10.1515/ling-2019-0050 · Cited by 38
Do delayed judgements of learning reduce metamemory illusions? A meta-analysis
Luna, K., Мартин-Луенго, Б., & Albuquerque, P. B. (2017) · Quarterly Journal of Experimental Psychology · doi:10.1080/17470218.2017.1343362 · Cited by 43
Genetic Vulnerability to Experiencing Child Maltreatment
Pezzoli, P., Antfolk, J., Hatoum, A. S., & Santtila, P. O. (2019) · Frontiers in Genetics · doi:10.3389/fgene.2019.00852 · Cited by 40
“No overlap or CIs just touching were considered indicative of a significant difference (p 0.01, Cumming and Finch, 2005).”
BackgroundInfluentialBorger, T., Mosteiro, P. J., Kaya, H., Rijcken, E., Salah, A. A., Scheepers, F. E., & Spruit, M. R. (2022) · Expert Systems with Applications · doi:10.1016/j.eswa.2022.116720 · Cited by 38
Zientek, L., Yetkiner, Z. E., & Thompson, B. (2010) · The Journal of Educational Research · doi:10.1080/00220670903383093 · Cited by 37
“Indeed, Cumming and Finch (2005) suggested a variety of ways of thinking about CIs, none of which involved p values.”
BackgroundMcCart, M. R., Zajac, K., Danielson, C. K., Strachan, M. K., Ruggiero, K. J., Smith, D. W., Saunders, B. E., & Kilpatrick, D. G. (2011) · Journal of Clinical Child & Adolescent Psychology · doi:10.1080/15374416.2011.533411 · Cited by 38
“01 if their 95% confidence intervals do not overlap (Cumming & Finch, 2005 ).”
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
About these checks
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.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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