what do lines that double back on themselves mean box plots

HI

i'm using anova1 and it produces plots like this

it's a dumb question: but what do the lines mean that double back on themselves? red line in median i thin whiskers are outliers and the boxes should be 75 and 25 percentiles i thought

thanks

Charlie

[mura0087]

This was super helpful- thanks!

Answer 1

[Adam Danz]

It's not a dumb question.

The notches on the sides of a box plot can be interpreted as a comparison interval around the median values. The height of the notch is the median +/- 1.57 x IQR/sqrt(n) where IQR is the interquartile range defined by the 25th and 75th percentiles and n is the number of data points [1]. If the notches of two boxes do not overlap, there is strong evidence that their medians "significantly differ"[2], a phrase that is working its way out of statistics [3].

The reason why your notches extend beyond the 25th and/or 75th percentiles is due to the uncertainty of the true median value. This often happens if your sample size is small (because you're dividing by the sqrt(n) to calculate the notch height).

image above: [2]

To apply that to your box plots:

Update: a pictoral explanation of boxplot notches has been added to Matlab's documentation [4,5].

[1] https://www.mathworks.com/help/stats/boxplot.html#bu180jd-Notch

[2] https://sites.google.com/site/davidsstatistics/home/notched-box-plots

[3] https://www.nature.com/articles/d41586-019-00857-9

[4] https://www.mathworks.com/help/stats/boxplot.html#mw_dc07acfe-6b0a-4d0a-94e0-1e9e0718439f

[5] https://www.mathworks.com/help/matlab/ref/boxchart.html#mw_1cab7873-4e6e-4f10-b11d-7cc7acdcdcc2

[cgenes]

thanks for this very full an informative answer!!

[Adam Danz]

Glad I could help.

[John Kearns]

I have just started looking into box plots/charts and this is the first description I've found that's clear to me at all. Thank you for taking the time to make descriptive figures, this is very helpful.

[Daniel Hall]

This has helped me a lot too thank you for this