Interpret Standard Error Bars
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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 overlapping error bars at two contrasting examples. What can you conclude when standard error bars do
Large Error Bars
not overlap? When standard error (SE) bars do not overlap, you cannot be sure that the difference between two sem error bars means is statistically significant. Even 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
Standard Error Bars Excel
compare proportions with a chi-square test. 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 how to calculate error bars higher P values than t tests comparing just two groups. 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. Theref
Graphpad.com FAQs Find ANY word Find ALL words Find EXACT phrase What you can conclude when two error bars overlap (or don't)? FAQ# 1362 Last Modified 22-April-2010 It is tempting to look at whether two error bars overlap or not, and try to reach
Error Bars Standard Deviation Or Standard Error
a conclusion about whether the difference between means is statistically significant. Resist that temptation (Lanzante,
What Do Small Error Bars Mean
2005)! SD error bars SD error bars quantify the scatter among the values. Looking at whether the error bars overlap lets you compare how to draw error bars the difference between the mean with the amount of scatter within the groups. But the t test also takes into account sample size. If the samples were larger with the same means and same standard deviations, the P https://egret.psychol.cam.ac.uk/statistics/local_copies_of_sources_Cardinal_and_Aitken_ANOVA/errorbars.htm value would be much smaller. If the samples were smaller with the same means and same standard deviations, the P value would be larger. When the difference between two means is statistically significant (P < 0.05), the two SD error bars may or may not overlap. Likewise, when the difference between two means is not statistically significant (P > 0.05), the two SD error bars may or may not overlap. Knowing whether SD error bars overlap or http://www.graphpad.com/support/faqid/1362/ not does not let you conclude whether difference between the means is statistically significant or not. SEM error bars SEM error bars quantify how precisely you know the mean, taking into account both the SD and sample size. Looking at whether the error bars overlap, therefore, lets you compare the difference between the mean with the precision of those means. This sounds promising. But in fact, you don’t learn much by looking at whether SEM error bars overlap. By taking into account sample size and considering how far apart two error bars are, Cumming (2007) came up with some rules for deciding when a difference is significant or not. But these rules are hard to remember and apply. Here is a simpler rule: If two SEM error bars do overlap, and the sample sizes are equal or nearly equal, then you know that the P value is (much) greater than 0.05, so the difference is not statistically significant. The opposite rule does not apply. If two SEM error bars do not overlap, the P value could be less than 0.05, or it could be greater than 0.05. If the sample sizes are very different, this rule of thumb does not always work. Confidence interval error bars Error bars that show the 95% confidence interval (CI) are wider than SE error bars. It doesn’t help to observe t
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