There is no standard recommendation for length of errorbars to be used while showing spread of data or means in graphics. Standard deviation (SD), standard error of mean (SEM) and 95% confidence intervals (CI) are all used.
It is also common to have 2 means with errorbars shown in a single graph. An obvious question arises: whether non-overlap of errorbars indicate that the difference between 2 means is statistically significant (P<0.05)?
For 2 Means to be significantly different (P<0.05), the errorbars of length SEM*√2 should not be overlapping.
In contrast to above, errorbars of length 2*SEM (95% confidence interval) may be overlapping even if difference between 2 series is significant (P<0.05).
On the other hand, errorbars of length SEM may be non-overlapping even if difference between 2 series is not significant (P>0.05). Hence, SEM errorbars often give misleading impression of a significant difference between two similar series.
In view of above, why shouldn't errorbars of length
SEM*√2 be used as a standard for graphical purposes?
Also, is there any specific name for this value: