# How to show mean value instead of median value in box plot? Hi all,

Is there any way to show only mean value (as line) in box plot and not to show median value?

In fact, while implementing box plots, I looked around the internet for examples. I didn't find any that used the mean instead of the median. A box plot was originally conceived of as a statistical representation of multiple values, and the choice of the median was part of that representation. That's not to say that a representation using the mean isn't correct, but it is different from what Tukey published originally. I hope you note that use of the mean in the caption :)

I would love an explanation of your use of the box plot with mean as the central value.

johnweeks wrote:

In fact, while implementing box plots, I looked around the internet for examples. I didn't find any that used the mean instead of the median. A box plot was originally conceived of as a statistical representation of multiple values, and the choice of the median was part of that representation. That's not to say that a representation using the mean isn't correct, but it is different from what Tukey published originally. I hope you note that use of the mean in the caption :)

I would love an explanation of your use of the box plot with mean as the central value.

In many papers, authors write mean values (not median) with standard errors. I'd like to use box plot for graphical representation of intergroup difference for specific physical quantities.

So the box represents standard error, with the line showing the mean? In order to get all the way there, you need me to implement the standard error part. And what do the whiskers show?

johnweeks wrote:

So the box represents standard error, with the line showing the mean? In order to get all the way there, you need me to implement the standard error part. And what do the whiskers show?

Whisker show standard deviation. I found the site with documentation for Statistica software, where the information about box plots is given: http://documentation.statsoft.com/STATISTICAHelp.aspx?path=Graphs/Graph/ModifyingGraphs/Dialogs/PlotBoxWhiskerTab

From that documentation:

"Middle point. Use the Middle point drop-down box to select the statistic Mean or Median to be used to determine the center (middle) points in the plot"

"Whisker value. Use the Whisker value drop-down box to choose how the ranges of Whiskers are computed; the options available in this box depend on the Middle point you selected. For the Median middle point, the available choices include Percentiles, Non-outlier range (see Outliers), Min-Max (minimum and maximum values), and Constant (draw the whiskers to enclose a fixed-value interval around the middle point). For the Mean middle point, available options are Std. Dev. (standard deviation), Std. Err. (standard error of the mean), Conf. Interval (confidence interval for the mean), Non-outlier range (see Outliers), Min-Max(minimum and maximum value), and Constant."

OOOooohhh...

They make a box plot that shows either mean and various related statistics, or the median and percentile statistics. Mine is the old-fashioned Tukey-style median type, with some additions such as the ability to show the mean as a marker if you really want it. I'll have to think hard about that. There's a lot there to implement to make the full Statistica-style box-plot-as-normal-stats representation. They even have options to use pooled variance and other ANOVA-type stats in the mean-based version of the box plot.

Any notion how common it is to see such plots? I visited the Neuroscience meeting shortly before Igor 8 saw the light of day. That's what made be decide to push box plots and violin plots. I saw lots of both on posters there. But as far as I know, the box plots were of the Tukey sort.

My two cents here is that although a box plot can be modified to show other things, it doesn't mean that it should. The Tukey-style box plot implementation in Igor is fine. At least in my field, the only variability is what is shown in the whiskers. Median and IQR for the line and box is the standard and shouldn't be messed with.