Interpretation Of Standard Error Bars
Contents |
in a publication or presentation, you may be tempted to draw conclusions about the statistical significance of differences between group means by looking at whether the error bars overlap. Let's look at two contrasting examples. how to interpret error bars What can you conclude when standard error bars do not overlap? When standard
Overlapping Error Bars
error (SE) bars do not overlap, you cannot be sure that the difference between two means is statistically significant. Even large error bars though the error bars do not overlap in experiment 1, the difference is not statistically significant (P=0.09 by unpaired t test). This is also true when you compare proportions with a chi-square test. sem error bars What can you conclude when standard error bars do overlap? No surprises here. When SE bars overlap, (as in experiment 2) you can be sure the difference between the two means is not statistically significant (P>0.05). What if you are comparing more than two groups? Post tests following one-way ANOVA account for multiple comparisons, so they yield higher P values than t tests comparing just two groups.
Standard Error Bars Excel
So the same rules apply. If two SE error bars overlap, you can be sure that a post test comparing those two groups will find no statistical significance. However if two SE error bars do not overlap, you can't tell whether a post test will, or will not, find a statistically significant difference. What if the error bars do not represent the SEM? Error bars that represent the 95% confidence interval (CI) of a mean are wider than SE error bars -- about twice as wide with large sample sizes and even wider with small sample sizes. If 95% CI error bars do not overlap, you can be sure the difference is statistically significant (P < 0.05). However, the converse is not true--you may or may not have statistical significance when the 95% confidence intervals overlap. Some graphs and tables show the mean with the standard deviation (SD) rather than the SEM. The SD quantifies variability, but does not account for sample size. To assess statistical significance, you must take into account sample size as well as variability. Therefore, observing whether SD error bars overlap or not tells you nothing about whether the difference is, or is not, statistical
MenuMenu Home Current issue Comment Research Archive Archive by issue Archive by category Specials, focuses & supplements Authors & referees Guide to authors error bars standard deviation or standard error For referees Submit manuscript Reporting checklist About the journal About Nature Methods how to calculate error bars About the editors Press releases Contact the journal Subscribe For advertisers For librarians Methagora blog Home archive issue
How To Draw Error Bars
This Month full text Nature Methods | This Month Print Share/bookmark Cite U Like Facebook Twitter Delicious Digg Google+ LinkedIn Reddit StumbleUpon Previous article Nature Methods | This Month The https://egret.psychol.cam.ac.uk/statistics/local_copies_of_sources_Cardinal_and_Aitken_ANOVA/errorbars.htm Author File: Jeff Dangl Next article Nature Methods | Correspondence ExpressionBlast: mining large, unstructured expression databases Points of Significance: Error bars Martin Krzywinski1, Naomi Altman2, Affiliations Journal name: Nature Methods Volume: 10, Pages: 921–922 Year published: (2013) DOI: doi:10.1038/nmeth.2659 Published online 27 September 2013 Article tools PDF PDF Download as PDF (269 KB) View interactive PDF in ReadCube Citation Reprints http://www.nature.com/nmeth/journal/v10/n10/full/nmeth.2659.html Rights & permissions Article metrics The meaning of error bars is often misinterpreted, as is the statistical significance of their overlap. Subject terms: Publishing• Research data• Statistical methods At a glance Figures View all figures Figure 1: Error bar width and interpretation of spacing depends on the error bar type. (a,b) Example graphs are based on sample means of 0 and 1 (n = 10). (a) When bars are scaled to the same size and abut, P values span a wide range. When s.e.m. bars touch, P is large (P = 0.17). (b) Bar size and relative position vary greatly at the conventional P value significance cutoff of 0.05, at which bars may overlap or have a gap. Full size image View in article Figure 2: The size and position of confidence intervals depend on the sample. On average, CI% of intervals are expected to span the mean—about 19 in 20 times for 95% CI. (a) Means and 95% CIs of 20 samples (n = 10) drawn from a normal population with mean m and s.d. σ. By cha
CatservEvolutionBlogGreg Laden's BlogLife LinesPage 3.14PharyngulaRespectful InsolenceSignificant Figures by Peter GleickStarts With A BangStoatThe Pump HandleThe Weizmann WaveUncertain http://scienceblogs.com/cognitivedaily/2008/07/31/most-researchers-dont-understa-1/ PrinciplesUSA Science and Engineering Festival: The BlogWorld's Fair2010 World Science Festival BlogA Blog Around The ClockAdventures in Ethics and ScienceA Good PoopAll of My Faults Are Stress RelatedAngry ToxicologistApplied StatisticsArt of Science LearningA Vote For ScienceBasic Concepts in SciencebioephemeraBlogging the OriginBrookhaven Bits error bars & BytesBuilt on FactsChaotic UtopiaChristina's LIS RantClass MCognitive DailyCommon KnowledgeCulture DishDean's CornerDeep Sea NewsDeveloping IntelligenceDispatches from the Creation WarsDot PhysicsDr. Joan Bushwell's Chimpanzee RefugeEffect MeasureEruptionsevolgenEvolution for EveryoneEvolving ThoughtsFraming ScienceGalactic InteractionsGene ExpressionGenetic FutureGood Math, Bad MathGreen GabbroGuilty PlanetIntegrity of ScienceIntel ISEFLaelapsLife at the standard error bars SETI InstituteLive from ESOF 2014Living the Scientific Life (Scientist, Interrupted)Mike the Mad BiologistMixing MemoryMolecule of the DayMyrmecosNeuron CultureNeuronticNeurophilosophyNeurotopiaNot Exactly Rocket ScienceObesity PanaceaObservations of a NerdOf Two MindsOmni BrainOn Becoming a Domestic and Laboratory GoddessOscillatorPhoto SynthesisPure PedantryRetrospectacle: A Neuroscience BlogRevolutionary Minds Think TankScience + SocietyScience After SunclipseScience is CultureScienceOnline 2010: The BlogSciencePunkScience To LifeSciencewomenSeed/MoMA SalonSee Jane ComputeShifting BaselinesSignoutSpeakeasy ScienceSpeaking Science 2.0Stranger FruitSuperbugTerra SigillataTetrapod ZoologyThe Blogger SAT ChallengeThe Book of TrogoolThe Cheerful OncologistThe Corpus CallosumThe Examining Room of Dr. CharlesThe Frontal CortexThe IntersectionThe Island of DoubtThe LoomThe Primate DiariesThe Quantum PontiffThe Questionable AuthorityThe Rightful Place ProjectThe ScienceBlogs Book ClubThe Scientific ActivistThe Scientific IndianThe Thoughtful AnimalThe Voltage GateThoughts from KansasThus Spake ZuskaTomorrow's TableTranscription and TranslationUniverseWalt at RandomWe BeastiesWhite Coat UndergroundZooillogix Search National Geographic Search nationalgeographic.com Submit L