Error Bars Variability
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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 at two contrasting examples. What can you conclude when standard error bars do not overlap? what are error bars in excel When standard error (SE) bars do not overlap, you cannot be sure that the difference between
How To Use Error Bars
two means is statistically significant. Even though the error bars do not overlap in experiment 1, the difference is not statistically significant (P=0.09
Calculating Error Bars
by unpaired t test). This is also true when you 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
Error Bars Standard Deviation Or Standard Error
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. 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 how to draw error bars 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, statistically significant. What if the groups were matched and analyzed with a paired t test? All the comments above assume you are performing an unpaired t test. When you analyze matched data with a paired t test, it doesn't matter how much scatter each group has -- what matters is the consistency of the changes or differences. Whether or not the error bars for each group overlap tells you nothin
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for error bars is to show variability in the measures which are plotted in the chart. There are other ways to use error bars to embellish Excel charts, as listed at the end of this article. This article was written based on the error bar system in Excel 97 through 2003. If you are using Excel 2007, you will have noticed a lot of differences from earlier versions, particularly in charting. Error bars have been changed substantially, to the extent that Excel 2007 users have had a lot of problems finding and applying error bars. I have written a new article about Error Bars in Excel 2007. Adding Error Bars Error bars are easy to add to a chart series. Double click on the series, or select the series and press CTRL+1, to open the Format Series dialog. Most chart types allow Y error bars, and XY Scatter types allow X error bars as well. The Error Bar dialogs, shown below, are not at all complicated. These dialogs allow you to display no error bars, positive error bars, negative error bars, and error bars in both directions. There are several ways to enter values: fixed values, a percentage of the point's value, a number of standard deviations, the standard error of the plotted points, and custom values. As a means of explaining these options, each will be shown using the following simple data set, which results in a basic series of points. You should make up your own data set to practice making error bars. C D E F 2 X Y Xerr Yerr 3 1.6 1.97 0.897 0.897 4 2.51 3.1 0.732 0.732 5 3.55 2.79 0.633 0.633 6 3.83 3.96 0.6 0.6 7 5.47 4.4 0.633 0.633 8 5.77 5.72 0.732 0.732 9 6.89 7.2 0.897 0.897 10 7.76 7.65 1.128 1.128 11 8.78 8.34 1.425 1.425 This is a simple XY Scatter chart of the sample data set, without error bars. This shows our sample chart with positive and negative X and Y error bars, with a fixed value of 0.75. This shows our chart with positive and negative X and Y error bars, using a percentage of 12%. As the data values increase from the bottom left to the top right, the length of the error bars, 12% of the value, also increases. Here is our