Dear users,
I am not commonly use boxplot to draw data, neither to inference differences between groups so I am kind of confused.
Recently I read that "If the median line of a box plot lies outside of the box of another, there is likely to be a difference between the two groups", is this true? Can someone recommend me a citation confirming it?
Thanks
A box plot is a univariate display of a data distribution in a sample or population. The box highlights the middle 50% of the data distribution for that variable. It seems to me that drawing inferences about the likelihood of difference in the comparison of two groups (assuming the measurement occurred on the same variable) in the manner described would be tenuous, and probably only reliably indicative under certain specific conditions. Perhaps I've misunderstood your characterization but I cannot imagine that the procedure you've described would be a best practice approach other than perhaps as a means to draw a preliminary impression. I hope that helps. I do, however, look forward to seeing the responses of folks who are better versed in this area to find out if my impression has any veracity.
You may like to look at section 5.6 in Crawley (2013, The R Book, 2nd ed.) that provides a clear overview of boxplots, including how to make statistical inferences (5.6.1, p. 213) and the assumptions your data should meet.
If this happens, only the box plot tells you that the median of one group is not in the middle 50% of observations in another group by its definition because the box is drawn by the first/lower quartile (25th percentile) and the third/upper quartile (75th percentile) of another group. So if this happens we should take a close look.... There are tons of good books out there to describe it.....
I think the likely to be a difference should be followed up with a statistical test to see for sure.
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