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I am preparing a graph for publication: it has 3 panels, and two groups (line graphs) in each panel, with error bars at each time point.

For one of the panels, the last time point (with fewer observations) has quite wide error bars.

Is there a hard and fast rule about the range of the y-axis?

Anything to cite to say one way or the other?

I can extend the range of the y axis to make sure the upper limit is included, but then it squashes the bulk of the data points together and doesn't really display the main trend of the bulk of the graph well.

It's not about manipulating peoples views; it's about accurately portraying the (vast majority of the) section of interest as opposed to ensuring all points are included.

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  • $\begingroup$ would a log-scale improve things? $\endgroup$
    – Glen_b
    Apr 21, 2013 at 6:11
  • $\begingroup$ Unfortunately not. Basically every other 'line' (time point) looks fine so it's desirable to present the data in it's original scale. $\endgroup$
    – nzcoops
    May 1, 2013 at 6:59

3 Answers 3

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The only place I can think of where "error bars" (better to use confidence limits and specify the confidence level) are out of control is where they should have been shown on the log scale but weren't. For example, if one is estimating hazard ratios, odds ratios, risk ratios, or fold-change, it is more appropriate to use a log scale when presenting the point estimates and confidence limits. This will also prevent wild limits from re-scaling the graph in way that obscures the region of interest.

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  • $\begingroup$ These are confidence limits around the estimate of the mean (1.96 * SE). Shouldn't have used the vague term error bars. Log scale would bring the 'bars' in for this one time point but would mean the others which are all nice and clear would be blown off their raw scale and I think doing that would sacrifice too much to not gain much. Cheers. $\endgroup$
    – nzcoops
    May 1, 2013 at 7:06
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Options I'd consider

  1. Show the error bars fully
  2. Don't show error bars at all; show error some other way or not at all
  3. As suggested above, use log scale, if appropriate
  4. Delete the last time point (and explain why in the text)

I would not truncate the error bar. To me, that does distort the data (unintentionally, but still). The fact that that last time point is estimated very badly is part of the data.

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  • $\begingroup$ I don't get the distinction between deleting the last point and truncating the error bar, and why you consider the former ok but the latter misleading. Either without proper explanation (or a careless reader) could be misconstrued. $\endgroup$
    – Andy W
    Apr 21, 2013 at 14:31
  • $\begingroup$ Truncation of the error bar puts misleading data on the page; deleting the last time point does not. Of course any graph can be misconstrued, but I think the chance of this is higher with truncated bars. $\endgroup$
    – Peter Flom
    Apr 21, 2013 at 17:18
  • $\begingroup$ Have you ever heard of lying by omission? I still don't see the distinction, and if properly noted in the graph I suspect could be presented in a manner that isn't disingenuous (e.g. annotating the bar in a way that it is clear the bar extends beyond the range of the current plot). I just don't see the logic to think that omitting is less likely to cause error in judgement. $\endgroup$
    – Andy W
    Apr 21, 2013 at 18:04
  • $\begingroup$ I guess we just disagree, then, on what is likely to cause error. $\endgroup$
    – Peter Flom
    Apr 21, 2013 at 19:06
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    $\begingroup$ I'd have to agree with Peter here. I do know what 'lying by omission' is, however there is nothing to hide, the large confidence interval of the last point would not change the interpretation of what is being shown, but it's inclusion (forcing a large rescale of the y axis) would wipe out anything you might see at the other 12 time points (as they'd be so squashed). $\endgroup$
    – nzcoops
    May 1, 2013 at 7:01
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We may be able to find some guidance in particular situations, but hard and fast rules are unlikely. Even if someone suggested them, we would be sure to find an exception. The only guidance I have seen about the subject is in LeLand Wilkinson's The Grammar of Graphics. Wilkinson suggests that plots of distributions, even if summarized by error bars, should always contain the full range of the data in the axis. I suspect the motivation for this should be fairly intuitive.

You give on its face a reasonable exception though (Wilkinson's suggestion was more so in the context of default behavior of graphics as opposed to any rule). Alternatives (I can think of) besides truncating the error bar is to consider separate panels in which the axis length varies between panels, or simply two plots (one zoomed out and one zoomed in). Regardless of how you handle the situation, the graphic and the text should be clearly annotated so no confusion arises.

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