y error bars

[Timothy Spier]

I often add y error bars to my XY graphs. I have seen authors use 1 standard
deviation for the positive and negative error bars, and I have also seen the
standard error used. Which is better? Is there any convention? Is there
anything better, like a 95% confidence interval?

[Sumsq]

When you use standard deviation error bars, they are all centered on the mean
of the associated axis. So y error bars that use the standard deviation are
centered on the mean of the y axis. Regardless of whether you look at 1, 2 or 3
standard deviation bars, you are referencing each data point to the dispersion
of all the data points. This sort of analysis is conventional in situations
such as statistical process control.

When you use the standard error as the basis for the error bars, they are each
centered on individual data points. The standard error is the inferred bracket
within which some percentage of sample means would fall if the population mean
were identical to the actual sample mean. It's also the standard deviation
divided by the square root of the sample size.

The convention used by Excel's standard error error bars, to center each error
bar on the individual data point, is bizarre. I have a PhD in statistics and
have never understood the rationale. The only explanation I can come up with is
that the approach is useful when using the standard error of estimate (which
isn't employed in Excel error bars) and that someone got confused. It wouldn't
be the first time. Take a look at Excel's SKEW and KURT functions, for example,
and the ATP's "F-test 2 sample for variances" is and always has been straight
out of Lewis Carroll.

As to a confidence interval, that's just the standard error of the mean
multiplied by some factor that enables the capture of some percent of imaginary
sample means. So, +/- 1.96*s.e.m is a 95% confidence interval. You would have
to calculate that and then supply it as a Custom Amount. Again, the choice
depends on the inference you want to make or the context that you want to
supply.

Of course, that's just my opinion. But I'm not wrong.

C^2
Conrad Carlberg
Microsoft MVP - Excel